Lecture1-1_Basic_FinancialEngineering_DataScience_KK.ipynb

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    "# **금융시장의 발전** \n",
    "\n",
    "[![Open in Colab](http://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/thekimk/Tutorial-Probability-Statistics-Algorithm-DataScience/blob/main/Lecture1-1_Basic_FinancialEngineering_DataScience_KK.ipynb)\n",
    "\n",
    "<!-- # **금융의 발달**\n",
    "\n",
    "**1) 금융의 문화:** `시간`이 지나도 `경제적 가치를 재할당`하는 도구 `가족`\n",
    "\n",
    "> - `가족` 또는 `공동체`란 경제적 가치를 다른 시점으로 옮기는 `기본적 제도`\n",
    "> - 늙은 부모를 돌보는 사회적 약속은 `퇴직연금`으로 등장\n",
    "> - 가족, 친구, 공동체 구성원 사이에 선물을 주고 받으며 보답하는 약속은 `금융대출`과 같은 기능\n",
    "> - 이자라는 개념 대신 `사회적 의무`를 강조하는 교육으로 사회 연결망을 탄탄하게 만듬\n",
    "> - `가치의 시점문제를 해결`하는 전통적 방식을 대체하거나 개선하며 등장\n",
    "\n",
    "**2) 금융의 기초:** 고대 서남아에서 발견된 금융 기초문서 `드레헴 서판`\n",
    "\n",
    "> - `기원전 3천년기`에서부터 사업을 `계량적`으로 수치화하고 `미래가치`를 평가하는 기본도구 전부 개발\n",
    "> - `시간` 자체에도 가격을 부여했고, `가격의 근본`을 당시 경제를 떠받치던 소의 번식에 기초를 둔 경제라는 통찰 정의\n",
    "\n",
    "**3) 이자의 발명:** 만만하고 친할수록 배려하지 않는 인간의 기본 탐욕 `이자`\n",
    "\n",
    "> - `농경 또는 목축 사회`에서 빌려준 소는 시간이 지나면 번식을 할 것이고 돌려받을 때 더욱 많은 소를 기대\n",
    "> - 소가 표준화폐 역할을 했다면 다른 물건의 경우들에도 마찬가지의 `기대`로 자연스레 `이자가 탄생` (by 드레헴 서판)\n",
    "> - `협동`은 공동체에 닥친 위기를 대응하는 암묵적 `무이자` 계약의 `함께사는 방식`\n",
    "> - `선물 또는 대출`은 상대방에게 기대하는게 있거나 단순히 빌려준 것을 되돌려 받을 때에도 기대를 명시적으로 `이자`로 표현한 `함께사는 방식`\n",
    "> - `상호 협동`으로 공동체가 유지되던 시절엔 가족, 친구 또는 이웃들에게 `기대와 욕심을 전하기 어렵기`에 이자를 청구하는 행동이 바람직하지 않았음\n",
    "> - `도시가 발전`하면서 협동이 덜 필요해지면서 개개인의 `기대와 욕심이 누적되고 당연시`되어 오히려 쉽게 이자를 청구하고 기대에 미치지 못할때는 오히려 아쉬운 소리를 더욱 쉽게 꺼내는 행동들이 당연시 됨\n",
    "> - 장부기록, 노동력/배분량 문서화, 개인끼리의 금융계약(기원전 24세기부터) 등은 `이상적 세계와 도시국가를 구분`한 특징\n",
    "> - 인류의 존중과 배려가 당연시 된 에덴동산에서 `이자가 발명`되면서 오히려 `기대, 욕심이 당연시되며 타락`하기 시작했을지 모름\n",
    "\n",
    "**4) 금융제도의 출현:** 안정적인 거래와 비즈니스를 위한 `제도 개발`\n",
    "\n",
    "> - 고전 시대 `그리스와 로마 문명`에서는 금융경제가 `화폐와 시장에 기초`를 두고 정교하게 발전\n",
    "> - 그리스인은 `은행, 화폐, 상사법정`을 발명하고 로마인은 이러한 혁신을 토대로 `금융을 발달`시키며 `주식회사, 유한책임 투자`와 일종의 `중앙은행`을 추가로 발명\n",
    "> - 아테네와 로마는 매우 성장하여 주로 `해외무역`에 의지했으며 필요한 밀 대부분을 멀리는 `흑해에서까지 수입`\n",
    "> - 대담하고 광범위한 경제를 운영하려면 `새로운 금융구조`가 필요했고 아테네와 로마는 곡식이 `중앙`으로 흘러오게 만듬\n",
    "> - 두 국가는 해외의 농부들이 곡식을 재배하고 선원과 선장이 목숨을 걸고 곡식을 실어 오며 투자자가 배와 교역품에 투자하도록 동기를 부여\n",
    "> - 국제무역에 수반되는 `불확실성`에도 견딜만큼 `확고한 결제체계`를 만들어야 해서 `시장의 보이지 않는 손`으라고 하는 예측 불가한 바다에 대응할 금융기술과 어디서나 통용되는 가치를 위해 `화폐경제` 발명\n",
    "> - 토지와 같이 보이는 `가시적 재산`은 실제 세계지만 예치금, 장부, 계약은 `추상적 재산`\n",
    "> - `금융을 개념적으로 사업과 분리`하여 장거리 해상교역에 적절하고 제국의 요구에 부응할 만큼 유연하게 만든 것은 `아테네 은행`\n",
    "> - 투자자들은 수백 킬로미터 모험을 떠나기보다는 안전하고 편안하게 아테네에 머무르는 편을 선호했을 것임에도, 교역에서 20-30%의 이익을 얻으려고 다른 사람에게 투자하도록 `투자자를 유도해 낸 금융제도는 놀라운 발명품`\n",
    "> - `아테네 정부`는 재산권을 공정하고 투명하게 할당하는 수단과 분쟁해결 방법을 이용하여, 투자자들이 해양항해뿐 아니라 제조사업이나 채굴사업에까지 다양하게 `분산투자를 가능하게 함`\n",
    "> - 금융제도는 `투자를 촉진하고 위험을 분산`했으며, 위대한 도시에 필요했던 `복잡한 수입기반 경제를 뒷받침`\n",
    "\n",
    "> - `민주주의`는 정치구조일 뿐 아니라 `경제구조로 활용`\n",
    "> - 아테네는 `돈`을 사람들이 국가와 소통하는 `매개체`이자 `보상체계`이고 `측정체계`이자 공동의 부를 저장하는 수단으로 활용\n",
    "> - 원로원 의원은 이익이 많이 남는 사업에 직접 참여하지 않으면서도 엄청난 재산을 소유해야 했기에 `소유와 경영을 분리`하는 능력이 중요했고 로마 `금융체계 발달`\n",
    "> - 법은 금융에 중요한 영향을 끼치지만 `금융기술이 필요로 해야` 효과가 있었으며, 로마의 법과 금융은 모두 `정치, 경제가 공화국에서 제국으로 이동`했다는 증거\n",
    "> - `계좌통화`가 없었다면, 그리고 투자와 장거리 교역을 뒷받침하는 `금융제도`가 없었다면 로마는 대병력을 주둔시키지도, 바다를 가로질러 상품을 운송해야 할 만큼 광활하게 `확장된 제국을 유지하지 못했을 것`\n",
    "> - 로마는 화폐제도나 투자, 신용제도 같은 `금융기술` 덕분에 제국이 되었고 금융은 로마의 곁가지가 아니라 `생명선`\n",
    "> - 로마는 `조폐제도, 은행, 해상계약, 담보, 부동산담보대출, 공공금고, 중앙은행 등` 이미 존재했던 금융도구를 도입\n",
    "> - 로마처럼 거대한 제국이 상업을 장려하고 수입을 안정시켜 위기에 대응하려면 `화폐, 공공부채, 구제금융, 징세대리, 화폐가치 절하 등` 금융도구를 이용\n",
    "\n",
    "**2) 증권시장의 발달:**\n",
    "\n",
    "> - 유럽에서 서로 끊임없이 싸우던 약소 도시국가들은 투자자들에게 돈을 빌리고 나중에 갚기로 약속하는 방법을 터득\n",
    "> - 12세기에는 이탈리아에서 국채가 등장했고, 13세기에는 온전한 채권시장이 등장\n",
    "> - '관자'에는 '만물이 유통돼야 비로소 변화가 있고, 변화가 있어야 비로소 가격이 떨어진다'는 말이 나옴\n",
    "> - 시장이 있다면 거래가 일어날 것이고, 거래가 자유로워지면 가격은 내려가고, 그 이익은 모든 지역이 나누어 가지게 됨\n",
    "> - 오늘날 세계무역기구 고위층도 시장과 가격의 원리를 이보다 더 멋지게 표현하지는 못함\n",
    "> - 중국과 서양의 차이는 기술발전에서 벌어지기 전에 금융 발달에서 먼저 벌어졌다는 것이 가장 강력한 근거\n",
    ">> - 유럽 금융시장은 증기기관이 발명되고 생산공정이 기계화될 때 갑자기 출현한 것이 아님\n",
    ">> - 상업은행과 조직화한 증권시장은 산업혁명이 일어나기 최소한 2세기전부터 유럽에 존재했음\n",
    ">> - 19세기에 철도회사가 철로를 깔고 기차를 만들어 자본을 얻으려고 접촉한 폭넓은 투자자 층은 거액을 내고 미래에 돌려받기로 하는 방식에 익숙\n",
    ">> - 서양에는 투자기회를 얻으려는 수요와, 이 수료를 충족하는 상품을 개발할 구조화된 노하우가 존재\n",
    ">> - 중국에는 기술 우위를 지닌 사업체와 자본을 지닌 민간 투자자를 한데 모아 줄 체계적 수단이 거의 없었음\n",
    ">> - 중국에는 재화와 상품을 거래할 거대하고 체계적 시장이 있었지만, 자본시장의 발달수준은 그에 미치지 못했음\n",
    "\n",
    "> - 서기 1000년 이후 유럽 금융구조가 이처럼 급격하게 재편되자 여러 문제가 놀라울 정도로 신기하게 해결\n",
    "> - 2천년기 동안 유럽은 금융을 시험하는 거대한 실험장이 되었고 현대금융기술이 발달한 과정은 절대 일직선이 아니었음\n",
    "> - 새로운 발상은 제대로 효과를 내기도 했지만 대실패를 겪기도 함\n",
    "> - 은행이라는 조직은 예금을 받고 대출을 하고 다양한 금융 서비스를 제공\n",
    "> - 영업하는 지역의 법적 환경에 적합하다면 지분투자를 하기도 하고, 증권발행을 주선하기도 하며, 회사 경영에 참여하기도 함\n",
    "> - 13세기에 고리대금업 금지가 더더욱 강조된 데는 종교뿐 아니라 법과 사상의 영향도 있음\n",
    "> - 다시 학문적 주목을 받게 된 아리스토텔레스의 저작에 따르면 고리대금의 폐해 존재\n",
    ">> - 화폐의 본래 기능인 교역과정이 아니라 화폐 자체에서 이득을 취함\n",
    ">> - 화폐는 교역에 쓰라고 만든 것이지 이자를 낳으라고 만든 것이 아님\n",
    ">> - 고리대금은 어떠한 재산 획득 기술보다도 자연 법칙에 어긋남\n",
    ">> - 금융의 악덕 중에서도 가장 악한 것은 차입자에게 고통을 주는 것이 아니라 생명을 창조하여 신에게 도전한다는 것\n",
    ">> - 돈은 무생물이면서도 자손을 만드는 일종의 자동인형이자 인간이 신의 특권에 손을 뻗어 만든 괴물\n",
    ">> - 돈은 '죽은 것'이므로 번식하게 두어서는 안됨\n",
    "> - 기욤 도세르는 1220년에 \"고리대금업자는 모든 생명에 주어진 시간을 팔기 때문에 자연법칙을 위배한다\"라고 썼음\n",
    ">> - 금융계약은 주기적으로 이자를 매김으로써 시간에 가격을 매기고, 존재의 흐름을 현금의 흐름으로 전락\n",
    ">> - 베네치아 영구채의 만기는 정말로 신에게만 허용된 시간인 영원이었음\n",
    "\n",
    "> - 새로 등장한 베네치아 채권과 이를 거래하는 리알토의 2차시장은 국가와 개인 모두에게 중요한 금융기술\n",
    ">> - 새로운 자본이 등장하자 마찬가지로 새로운 관점에 따라, 즉 시간 자체가 세상을 생각하는 새로운 방법이라 재정의하고 시간을 세속화하게 되었음\n",
    ">> - 베네치아 리알토의 금융구조는 이탈리아 전체로, 그리고 유럽 각지에 있는 금융중심지로 퍼짐\n",
    ">> - 사람들은 시간에 가격이 매겨진다는 사실을, 그리고 새로 등장한 재산과 투자방식으로 돈을 굴릴 수 있게 되었다는 사실을 바로 깨달음\n",
    ">> - 리알코의 산자코모 성당에 이상하리만치 큰 시계를 건 것은, 옛날 이탈리아 금융업자는 시계를 보고 시간이 중요한 차원이라는 사실을 깨달았다는 증거\n",
    "\n",
    "> - 중국에서는 중앙정부가 방대하고 복잡한 관료체제를 통제하려다 보니 회계혁명이 일어난 반면, 유럽에서는 사업이 시간흐름에 따라 어떻게 발전해나갔는지 계산하기 위해 수량화하고 기록하는 수단으로 회계가 출현\n",
    "> - 기록수단이 불라에서 서판으로, 파피루스에서 죽간으로, 다시 양피지에서 종이로 변해가는 와중에도 사업과 금융의 근본은 언제나 숫자를 세고 기록하며 특정 시점의 경제가치를 검증하는 것\n",
    "\n",
    "**3) 주식회사의 출현:**\n",
    "\n",
    "> - 로마의 부는 대부분 민간에 속했고 지배계층은 정복활동 덕분에 부유해짐\n",
    "> - 재산은 어디에든 투자되어야 했고, 실제로도 신용체계를 통해 아래로 흘러감\n",
    "> - 경제불황이 오면 정치가들은 채무를 탕감하여 안정을 유지하려 했던 반면 주식회사 구조에서는 모든 주주가 동등하게 취급\n",
    "> - 이윤을 주식수에 따라 배분한다면 회사의 이익이 늘어나는 데 비례하여 투자자의 재산도 증가\n",
    "> - 주식이 공공연히 거래된다면, 특히 무기명으로 소유할 수 있다면 주식은 이해당사자 사이에 벌어질지도 모를 분쟁을 중재하는 도구가 됨\n",
    "> - 징세인 조합주식은 원로원 의원, 기사, 황제 사이에서 벌어지는 권력분쟁을 해결하는 수단이었고 주식회사라는 형식이 정치, 경제세력 사이에 벌어지는 분쟁을 중재하고 해결하는 수단으로서 처음 등장했다는 결론\n",
    "\n",
    "> - 오늘날 주식회사에서 드러나는 문제는 소유와 경영의 분리\n",
    ">> - 툴루즈 회사는 위임, 경영, 감독 문제를 푸는 데 성공했기 때문에 오랫동안 살아남았음\n",
    ">> - 오늘날 바자클 회사는 현대적 주식회사의 시조로 잘 언급되지 않지만 전혀 시조가 아니라고도 하기 어려움\n",
    ">> - 수력을 활용한 것은 당시 가장 중요한 기술진보였고, 제분소를 제대로 지으려면 상당한 자본을 투자해야 했음\n",
    ">> - 프랑스 남부에 있던 다른 회사도 틀림없이 주주자본주의, 유한책임, 환금성 같은 발상을 툴루즈에서 빌려왔을 것\n",
    "> - 독일 광업회사들은 쿡센이라는 주식을 발행\n",
    "> - 스웨덴의 유서 깊은 회사 스토라엔소는 기원이 13세기까지 올라가는데, 1347년에 받은 칙허장을 지금까지 보관\n",
    "> - 지분을 나눈 합작 채광회사로 설립된 스토라엔소의 형태은 아마 툴루즈 최초의 제분회사와 비슷했을 것\n",
    "> - 유럽 중세 후기는 사업체의 형태를 다양하게 만들고 자금을 조달하는 방법을 적극적으로 실험한 시기\n",
    "\n",
    "> - 자본주의란 역사에 반복하여 출현하는 경제적 해결책이라는 결론\n",
    "> - 경제적 생태계에서 자연스럽고도 흔히 나타나는 돌연변이에 가까움\n",
    ">> - 등장했다가 사라지면서도 미약하게 살아남는 과정에서 엿볼 수 있듯, 주주자본주의는 제대로 된 주변환경과 정치적 조건을 갖추어야만 번영 가능한 연약한 제도일지도 모름 \n",
    ">> - 모택동은 자본주의가 중국에서 필연적으로 발생했을 것이라 보았고, 자본주의는 등장할 수 있는 만큼 사라질 수도 있음\n",
    "> - 자본주의는 수많은 균형상태 중 하나에 불과한 것\n",
    "\n",
    "> - 엘리자베스 1세 시절은 스페인 무적함대를 격파하고 버지니아 식민지를 개척하였으며, 골칫거리였던 스코틀랜드 여왕 메리 1세가 반란에 실패한 후 왕권을 강화하는 등 영국이 강력한 힘을 떨쳤던 시기였지만, 영국의 금융은 취약\n",
    ">> - 국내 자본시장이 없었기 때문에 엘리자베스 1세는 신용장을 개설하려고 벨기에 안트베르펜 은행업자에게 사절을 보내고, 정부 세수와 왕실의 재산을 담보로 잡히며, 단기 차입금을 만기마다 연장하고, 영국이 채무를 불이행할지도 모른다는 매우 그럴듯한 가능성을 반영하여 점점 높아지는 이자를 물면서도 끊임없이 국제금융시장에서 돈을 빌려가며 연명\n",
    ">> - 유럽 대륙에 있는 도시국가와는 달리 영국 도시에는 채권을 발행하던 전통도 없었고, 증권을 사서 거래하려는 투자자층이 국내에 폭넓게 존재하지도 않았음\n",
    ">> - 영국은 금융발달이 더딘 탓에 전략적 열위에 처해 대안이 없었고 세금을 매기거나 차입하거나 혹은 권리를 파는 수밖에 없었는데, 팔 수 있는 권리라면 이미 대부분 팔린 뒤\n",
    ">> - 해외무역 대부분을 독점할 권리는 오래전부터 '상업모험가'라 불리는 무역권을 독점하려고 서로 연합한 상인조합에 가까운 회사가 독점 소유\n",
    "\n",
    "> - 주식회사라는 형태는 자본을 사업체로 끌어올 유연한 사업구조를 제공\n",
    ">> - 영국은 비록 실패를 거듭해도 계속하여 탐사와 해외무역을 전담하는 회사에 칙허를 내주었음\n",
    ">> - 버지니아 회사는 미국 대서양 해안 중부에 식민지를 건설하여 유명하고, 허드슨만 회사는 지금의 캐나다 지역에서 성공적으로 영업했으며, 그중에서도 가장 눈에 띄는 동인도 회사(VOC)는 1600년에 칙허를 받은 후 남아시아 교역에서 영국의 교두보를 마련했고 인도에 식민제국을 건설하는 데도 앞장섰음\n",
    ">> - 투자자들은 품질이 의심스러운 금광석, 신대륙에서 살아남지 못할 확률, 태평양에서 스페인인과 마주치면 일어날 싸움, 포르투갈인과 네덜란드인을 상대로 벌이는 경쟁 등 심각한 불확실성과 마주하면서 돈을 쏟아부었음\n",
    "> - VOC와 오늘날 주식회사의 모든 특징을 갖추지 못했다 하더라도 암스테르담에 자본을 거래하는 주식시장이 생겼다는 사실만으로도 중요한 금융혁신\n",
    "> - VOC는 주식을 거래하는 공개시장 덕에 여러가지가 달성\n",
    ">\n",
    "> (1) 투자자는 주식을 샀다면 팔 수도 있다는 구체적 증거를 시장에서 얻었고 베네치아 프레스티티 이래 유럽에 존재했던 채권과 마찬가지 권리를 주식도 지니게 되었기 때문에 유동성에는 엄청난 가치 생김\n",
    ">\n",
    "> (2) 시장은 도박하고 투기하려는 인간 고유의 경향을 활용했음. 어떤 매매자는 천성부터 비관적인 반면 어떤 매매자는 천성부터 낙관적이라 묘사한 드 라 베가는, 몇 년 동안 배당을 지급하지 못한 회사의 재산을 두고 자연스레 거래가 이어지는 장면을 목격. VOC 주식이 공개발행되자 암스테르담 증권거래소는 미래 향신료 무역을 예상하는 여론 측정기가 되었음. 바자클 회사 주식은 15세기에도 자유롭게 거래가능했고, 툴루즈 곡식시장은 분명 투기가 벌어지는 장소였지만, 결국 이때까지는 낙관론자와 비관론자가 광란을 벌이는 주식시장은 현실화되지 못했음. 암스테르담 투기꾼들로부터 탐욕을 이끌어 낸 요소는 엄청난 부를 가져올 잠재력과 심각한 재앙을 맞을 위협이 공존하던 사업체, 바로 VOC의 불확실성과 위험 자체였을 것\n",
    "\n",
    "> - 주식회사가 해외교역, 그리고 궁극적으로는 식민지 확장에 적합한 형태였느냐는 문제는 지금도 논쟁 대상\n",
    "> - 영국과 네덜란드 동인도 회사가 우월한 금융기술 덕분에 비교적 큰 성공을 거두었다는 주장에는 설득력이 있음\n",
    "> - 금융사에서 1688년은 대영제국이 국제적 금융강국으로 떠오르는 분수령\n",
    ">> - 네덜란드에서 왕을따라 온 은행업자와 금융업자는 개방된 자본시장으로 가는 지침, 채권을 사용하여 정부 운영자금을 대는 방법, 투기심리를 자극할 복권, 불로소득자 계층에게 제공할 종신임차료와 종신연금, 그리고 재정정책 도구로 쓸 만한 중앙은행 등을 망라하는 네덜란드 금융의 유전자정보를 가져옴\n",
    ">> - 영국인은 이런 도구에 넘쳐나는 상상력을 더하여 1688년 이전 영국 사회가 감히 상상하지 못하던 방식으로 적용\n",
    ">> - 명예혁명은 영국인의 금융 상상력을 해방시켜 대영제국이 들어선 새로운 금융시대를 가리켜 작가이자 사업가인 대니얼 디포는 '기획의 시대'(projecting age)'라 명명\n",
    "> - 1688년 이후 새로 등장한 금융시장은 창의력과 지식재산권을 자본과 혼인시킨 것으로 혁신동력이었을 주식회사가 경제에서 지닌 중요성은 다른 구성요소에 비하여 극적으로 커짐\n",
    "> - 역사가 윌리엄 로빈슨 스코트가 추정한 바에 따르면 주식회사는 1695년에 대영제국 국부 중 1.3%를 차지했지만 1720년에는 13%를 차지할 정도로 성장\n",
    "> - 주식회사는 무역독점 특권에 의존하는 소수상인이 소유하고 지배하는 회사 모임에서, 서로 무관한 투기꾼들이 부자가 될 꿈을 꾸며 새로운 발상이나 특허에 열광적으로 투자한 자본이 가벼운 규제만을 받으며 한데 모인 장소로 바뀜\n",
    "\n",
    "**4) 주식시장의 위기:**\n",
    "\n",
    "> - 일반적 시각에 따르면 산업혁명은 18세기 후반에 영국에서 시작하여 19세기 중반에 생산공정 기계화와 공업의 분업으로 경제적 전환이 완료되며 절정에 달함\n",
    "> - 17세기가 저물무렵 암스테르담에는 런던이상으로 세련된 금융기법이 있었음\n",
    "> - 17세기 초 런던 시장이 등장하는 데는 명예혁명과 함께 들어온 네덜란드 금융업자도 공헌\n",
    "> - 영국 증권과 은행제도의 기본구조 및 작동방식은 대부분 네덜란드에서 빌려온 것\n",
    "> - 채권시장, 연금 및 기타 저축 수단이 발달한 네덜란드 등 유럽 대륙 경제권에서는 자본이 공급되면 투자증서 시장이 움직인다는 사실도 이미 입증\n",
    "> - 유럽이나 일본, 그리고 미국 세 시장 모두 금융제도와 활발하게 돌아가는 기술연구 프로그램을 갖추었으나 인터넷이 변혁을 일으킬 가능성, 새로운 마케팅 모형과 통신수단, 옛 기술의 죽음, 이익보다는 클릭수와 판매량에 따라 가치를 평가하는 새 시대의 금융 등을 논하며 진정한 열기가 시작된 곳은 분명 미국\n",
    "> - 유럽, 아프리카, 아메리카를 잇는 그 유명한 삼각무역은 1711년에야 시작되었고 18세기 서양사회에서 경쟁력이 순환하는 주된 방식\n",
    "> - 노예무역 분야에서 손꼽히는 역사가 조지프 이니코리는 삼각무역이 활성화된 덕분에 대영제국이 18세기에 기계화, 공업화가 발생했고, 재화와 사람이 멕시코만류를 따라 크게 순환하며 간접적으로 현대 유럽을 만들어냈다고 주장\n",
    "\n",
    "> - 금융시장의 실수를 기록한 '어리석음을 비추는 위대한 거울'은 그대로 받아들이고 싶을 정도로 매력적인 지혜를 담음\n",
    "> - 런던, 파리, 암스테르담에서 새로 발전하던 주식시장이 대표하는 복잡한 혁신, 도구, 시장, 계약, 그리고 정보흐름을 나타낼 수 없었음\n",
    "> - 최근에 붕괴한 일 주택저당대출 유동화는 손쓸 수 없이 복잡하여 결국 실패한 금융혁신으로 일축되고, 사회는 현대에 일어난 위기를 유명 금융업자가 악당으로 출연하는 단순한 도덕극으로 바꾸어 놓음\n",
    "> - 유럽은 1720년에 대규모 주식 거품 붕괴를 겪고 움츠러들었고, 그 후 수십년 동안 금융기술은 다른 방향으로 발전\n",
    ">> - 거품방지법은 영국에서 주식회사를 설립하고 지분을 거래하는 행위를 엄격하게 제한\n",
    ">> - 네덜란드에서는 동인도회사와 서인도회사를 제외한 주식거래가 완전히 자취를 감추었고 스타트 로테르담과 같이 성공을 거둔 회사주식조차 현금화하기 어려워짐\n",
    ">> - 주식거래는 18세기 말까지 사실상 중단되었다가 1820년대가 되어서야 시장이 본격적으로 회복\n",
    ">> - 네덜란드는 주식금융이 죽은 한 세기를 보냈고 18세기 내내 인가를 받은 회사는 소수에 불과\n",
    ">> - 프랑스에서는 미시시피회사 주식이 계속 거래되었지만 딱 그뿐\n",
    ">> - 영국과 프랑스에서 주식을 혐오하는 분위기가 만연하고 법적 규제로 심했던 18세기와 19세기 초반에 산업혁명에 일어나는 사실은 굉장한 아이러니\n",
    "> - 미국 독립전쟁 지도자 중 다수는 토지투기라는 공통점으로 연결\n",
    ">> - 오하이오 회사를 설립한 버니지아 부자 중에는 조지 워싱턴의 아버지와 형제 두 명이 관여\n",
    ">> - 1749년 설립된 로열 컴퍼니 오브 버지니아에는 앞으로 대통령의 아버지가 될 피터 제퍼슨이 연관\n",
    ">> - 토지회사가 제시한 사업계획은 비옥하고 넓은 땅을 취득하고 여러 구획으로 분할하여 기본 기반시설을 개발한 다음 여기에 정착할 미국인 또는 외국인에게 파는 것\n",
    ">> - 오하이오 지역 정착민에게는 부동산을 담보로 하는 금융조건이 필요했을 것\n",
    ">> - 금융은 주식회사를 통한 담보대출이나 부동산 투기와 관계가 밀접하므로 독립을 추진할 중요 요인\n",
    ">> - 독립전쟁이 끝난 이후 미국의 금융 역시 거품방지법이나 1763년 포고령에서 자유롭게 풀려나 해방\n",
    "\n",
    "> - 마르크스나 엥겔스라면 자본시장이 만들어낸 이 엄청난 숫자를 어떻게 보았을지 잠시 생각해 보자\n",
    ">> - 1870년 런던 증권거래소에서 시세를 발표하던 금융자산 가치는 대략 36억 파운드로, 당시 지구상에 있는 사람들 모두에게 2파운드씩 나누어줄 수 있는 금액\n",
    ">> - 노동단위로 환산해보면 1860년대 런던에 보통 노동자는 한 주에 20실링, 즉 1파운드를 받았으니 1년에는 52파운드를 번 셈이지만 노동가능기간이 50년이라고치면 런던 증권거래소에서 거래되던 자본은 노동자 140만명이 평생 일한 만큼과 동일\n",
    "> - 런던 자본시장이라는 기술은 엄청나게 많이 저장된 인간의 에너지를 과거와 미래 사이에서 중개\n",
    "> - 주식과 채권을 발행한 이렇게 비축한 자본의 현재가치를 증권 소유자에게 약속한 셈\n",
    "> - 자본은 도둑맞은 노동이 아니라 불확실한 미래라는 위험에 대비하기 위해 막대하게 모아 둔 비축물자\n",
    "> - 1870년 런던 증권거래소는 현재에 심은 받침대 위에 올라 과거의 저축과 미래의 가능성 사이에서 균형을 잡는 거대한 경제 지렛대\n",
    "\n",
    "> - 17세기와 18세기에 벌어진 무역대국이 국가차원에서 국제무역을 보호하려던 결과\n",
    "> - 반면 19세기에 주권을 잃게 되는 과정은 차츰 계약 위반의 결과라는 형태가 나타나며 투자자 권리보호라는 명목은 주권침해를 정당화\n",
    "> - 금융계약은 역사의 임계점에 도달하여, 이제 정치권력을 재조정하는 중요한 역할을 담당\n",
    "> - 1차 아편전쟁 전 중국에서 유일한 개항장이던 광저우에서 처음 설립된 서양회사들은 공식허가를 받은 공행을 써야만 했음\n",
    "> - 중국은 매판제도를 도입하는 한편, 특히 금융 및 기술 근대화를 배우려고 학생을 유학시켜 단 40여년 만에 주식회사 자본주의의 교훈을 흡수\n",
    "> - 미국에서는 세금, 토지회사, 해외무역 규제가 촉매 역할을 했고 중국에서는 발전에 깊이 개입하던 중앙정부가 중요 요소\n",
    "> - 러시아도 1720년 전후에 회사를 만드는 실험을 했으며, 러시아에서 최초로 주식을 발행하여 자금을 조달한 시기는 1704년이라고 기록되어 있고, 1830년까지는 지나친 투기를 우려할 정도로 주식이 거래되었음\n",
    "> - 러시아 투기열풍은 1869년과 1893년에 불었는데, 이 중 1893년에는 주식담보대출 규제가 완화되었기 때문에 발생했으며 러시아 시장의 역사는 미국 주식시장 발전가 어느 정도 궤를 같이 함\n",
    "\n",
    "> - IMF의 중요한 특징은 국가채무를 보증받는 옛 방식을 없앴다는 점\n",
    ">> - 채무를 상환받기 위하여 루르 지역을 담보로 잡힐 필요가 없고 원리금을 직접 상환받기 위하여 채무국 관세나 운하 사용료 징수권을 차압하지도 않음\n",
    ">> - 거시경제지표를 미래 대출조건으로 설정했고, 부채수준이 심각하다면 체계적인 경제조정을 요구했으며 재정긴축, 화폐가치 절하, 수출증대, 무역자유화 정책 및 민영화 도입 등 다양했음\n",
    "> - IMF는 비록 구제금융을 제공하며 온갖 불쾌한 일을 일으켰지만 최소한 국가로서의 주권은 보전해 줌\n",
    "\n",
    "> - 만약 순현재가치를 이성적으로 판단하여 투자여부를 결정하다면 새로운 것은 절대 나타날 수 없음\n",
    "> - 기술진보가 진행되는 것은 어리석게 도박하는 사업가 덕\n",
    "> - 1720년에 대중의 마음과 자본을 사로잡은 새 기술과 새로운 회사의 꿈과 희망 때문에 거품이 일어났다는 사실을 떠올려 보자\n",
    ">> - 투기의 밀도가 높아지자 그동안 잠재해 있던 자연력이 새로 나타나 자본시장이 금융의 관심을 순식간에 극복하고 모든 가능성을 움직임\n",
    ">> - 케인스는 이를 경제의 강력한 잠재력으로 인식했을 뿐 아니라, 이 힘을 정부가 길들여 거시경제 균형을 바꾸는 데 쓸 수 있다고 믿음\n",
    ">> - 케인스가 제안한 바에 따르면 정부는 호황을 없애는 방식으로 불황을 공격하지 말고, 거품이 절정에 달할 때 개입하고 시장심리를 자극하며 관리함으로써 하방 나선을 멈추게 해야 함을 주장\n",
    "> - 29년 시장붕괴가 미국인에게 금융시장이 불확실하다고 경고했다면, 대공황은 거시경제의 엄청난 위험을 극명하게 드러냈고 이러한 위험에 대응할 금융해법이 필요했음\n",
    "> - 30년대에 실업가 빈곤이 만연하자 미국이 저축과 사회보장에서 절박한 위기에 직면했다는 사실이 명확하게 드러남\n",
    "> - 대공황이 닥치기 전 미국에는 민영보험, 다양한 개인저축상품, 연방/주/시/회사 차원의 퇴직연금제도가 모두 존재했지만, 경제위기가 닥쳐 체계적 충격에 노출되자 이들 모두 취약하다는 사실이 밝혀짐\n",
    "> - 20세기 초 미국은 주식회사에 희망을 걸었지만 불황이 오자 수많은 회사가 실패하면서 일자리와 퇴직연금도 같이 사라짐\n",
    "> - 회사를 대신하여 현재와 미래의 수요를 충족할 수 있었던 것은 바로 정부\n",
    "\n",
    "**5) 위험의 정량화 및 세계화:**\n",
    "\n",
    "> - 후손에게 엄청난 빚을 물려주는 것이 옳으냐는 논쟁은 오늘날에도 계속됨\n",
    "> - 사회보장 제도의 결손금을 떠넘긴 사람들은 할아버지 세대지만 나이가 들어가는 부모와 친척이 최소한도로나마 부양받을 거라고 생각하면 위안이 되기도 함\n",
    "> - 사회보장제도는 보기 드문 금융혁신이고 정부가 약속한 배분액보다 부채가 커질 미래가 되면 정부세입을 사용해야 파산을 막을 수 있게 설계되었기 때문에, 미래 입법자에게는 구조를 수정하여 계속 유지할 책임이 있음\n",
    "> - 35년에 설립된 사회보장제도를 살펴보면 금융사의 교훈이 절묘하게 부각\n",
    ">> - 가격을 잘못 산정한 채 종신연금을 발행하여 재정을 충당했떤 18세기 유럽 각국 정부를 떠올려보자\n",
    ">> - 보험통게는 앞으로 등장할 민족국가의 존속에 그토록 중요한데도 어떻게 철저히 무시당했을까?\n",
    ">> - 20세기 미국 사회보장제도의 설계과정을 살펴보면, 그때나 지금이나 가격책정 오류가 일어난 것은 장기비용을 무시해서가 아니라 정치구조 때문에 단기 분쟁 해결에 가중치를 두었던 때문이라고 할 만함\n",
    "> - 노동자와 은퇴자 비율이 변하면 모든 것이 영향을 받음\n",
    ">> - 예를 들어 연금이 돈줄을 완전히 쥔 상황이라면, 점점 더 많은 세계의 자본은 노년층의 소유가 되어 노년층을 위해 투자되거나 또는 그렇게 약속될 것\n",
    ">> - 가진 자와 가지지 못한 자 사이에 다시 말해 자본을 가진 노인과 자본을 가지지 못한 젊은이 사이에 분쟁이 벌어질 수도 있음\n",
    "> - 미국 사회의 보장제도는 운천징수방식을 기본으로 30년대에 설립되었고, 1770년대 프랑스 종신연금제도는 지킬 수 없는 약속이었기 때문에 파산함\n",
    "> - 역사는 미래를 거의 똑같이 찍어내는 틀이며 수학과 통계로 아무리 세세하게 예측한다 한들 제대로 된 연금저축과 사회보장제도를 만들어낼 수 없다는 맬서스의 예언은 통렬할 정도로 옳았는지도 모르고 결국은 금융이 소용없는 날이 올 수도 있음\n",
    "> - 지금 돈을 받고 미래에 돈을 주겠다는, 금융에서 가장 기본이 되는 계약은 5천년 전에 메소포타미아에서 발명된 이래 지금껏 쓰이고 있음\n",
    "> - 08년 금융위기와 제도구조 재건에 지난 10년 동안 많은 관심이 쏟아졌지만, 세계가 직면한 도전 중 가장 근본에 있는 것은 저축에 관련한 금융 그리고 정치\n",
    "> - 미국에서는 금융실패라는 미래가 이미 다가왔고 디트로이트시가 파산하자 은퇴자와 노동자 사이의 대립이 극명하게 드러남\n",
    ">> - 경찰, 소방관, 교사, 미화원 등 퇴직한 시 공무원은 돈이 가장 필요할 때 디트로이트시가 약속을 파기할 가능성에 맞닥뜨림\n",
    "> - 프랑스혁명은 기억하는 편이 현명한 것이, 가장 기본적인 저축기구를 둘러싸고 정부와 시민이 맺은 사회협약을 위반한다면, 정치제도 전체가 복구 불가능한 피해를 입을지도 모음\n",
    "> - 금융채무 재조정으로 비칠 행동이 벌어진다면 현재 수혜자인 은퇴자는, 그리고 정부와의 관계를 고민하는 젊은이는 깊이 영향을 받고, 다양한 감정을 드러낼 것 -->\n",
    "\n",
    "> **\"`주식회사 제도` 등장과 `증권 투자업`의 눈부신 발전, 그리고 `잦은 위기 부작용`\"**\n",
    "\n",
    "---\n",
    "\n",
    "**0) 금융업의 탄생**\n",
    "\n",
    "- 셰익스피어(1564∼1616)의 희곡 `베니스의 상인`에는 중세의 금융을 이해할 수 있는 이야기 한 토막이 등장\n",
    "- `기독교 중심의 세계`였던 중세에는 돈을 빌려주고 `이자를 받는 것은 나쁜 행위`로 여겨짐\n",
    "- 통상 `고리대금업`은 당시 천대받던 `유태인들의 몫`\n",
    "- `유대인`들은 오랜기간 수많은 기독교인들의 `핍박과 설움`을 받으면서 `금융업을 익힘`\n",
    "- 오늘날 `로스차일드 골드만삭스 리먼브러더스 등` 세계적인 금융회사 대부분이 `유대인에 의해 설립,운영`되고 있는 것도 이러한 역사적 배경\n",
    "\n",
    "<center><img src='Image/Basic/Jew.jpg' width='600'>(http://wealth.moneta.co.kr/column/columnDetail.jsp?seqNo=3371)</center>\n",
    "\n",
    "---\n",
    "\n",
    "**1) 주식회사 제도 등장으로 증권시장 발전**\n",
    "\n",
    "- 중세 `고리대금업을 뿌리로 하고 있는 금융업`은 18세기 이후 `자본주의의 발달에 힘입어 비약적으로 발전`\n",
    "- 주식회사 제도와 함께 등장한 `증권업은 금융업의 새로운 영역`을 탄생시킴\n",
    "- 사람들이 맡긴 돈을 기업에 대출하는 기존의 `은행 대출을 간접금융`이라고 한다면 기업이 발행한 주식이나 채권을 투자자들이 구입할 수 있도록 주선해 주는 `증권업은 직접금융`으로 각광\n",
    "- `정보통신 기술의 발달`로 주식 거래가 한층 자유로워지면서 세계 금융시장은 `직접 금융(증권) 시장 위주로 발전`\n",
    "\n",
    "<center><img src='Image/Basic/FinanceDirectIndirect.png' width='600'>(https://en.wikipedia.org/wiki/Indirect_finance)</center>\n",
    "\n",
    "- 기업들은 이제 은행대출보다는 `주식이나 채권을 발행해 직접 자금을 조달`\n",
    "- 사람들도 은행에 돈을 맡기고 고정 이자를 받기보다 위험이 있지만 가격이 올라갈 것으로 기대되는 `주식이나 채권을 구매`\n",
    "- 은행 예금보다 주식 채권으로 돈이 몰리자 `주식 채권을 활용한 다양한 금융 파생상품`이 대거 등장\n",
    "\n",
    "- 미국에서 `서브프라임 모기지(비우량 주택담보 대출) 부실` 여파로 베어스턴스 등 투자은행이 파산 위기에 몰린 것도 파생금융상품의 여파\n",
    "- `CDO(Collateralized Debt Obligation)`는 모기지 채권이나 주식 등을 혼합해 이를 담보로 `다시 발행된 파생 금융상품`\n",
    "- 주택담보 대출자들이 집값 하락으로 이자나 원금을 제때 갚지 못하게 되자 `모기지 채권이 부실화`되고 그 여파로 `파생금융상품도 연쇄적으로 부실화`\n",
    "- 파생금융상품은 기업이나 금융회사들로 하여금 자금을 보다 수월하게 조달할 수 있도록 해 주지만 자칫 `기초자산이 부실화`될 경우 그 파급 영향 또한 엄청날 수밖에 없음\n",
    "\n",
    "<center><img src='Image/Basic/CDO_CDS.jpg' width='600'>(https://www.ddanzi.com/ddanziNews/185623752)</center>\n",
    "\n",
    "---\n",
    "\n",
    "**2) 금융 안전망 갈수록 중요해져**\n",
    "\n",
    "- 금융시장은 자금의 `수요자(기업)와 공급자(투자자)를 연결시켜 주는 중요한 기능`을 하기 때문에 흔히 사람의 혈관에 비유\n",
    "- 혈관은 어느 한 곳만 막혀도 몸 전체가 움직이지 않는 결과\n",
    "- 일반 제조업과 달리 금융은 그만큼 `경제에 미치는 파급 효과가 크다`\n",
    "- 모든 국가는 금융시장이 `안정적으로 돌아갈 수 있는 안전장치` 보유\n",
    "- 우리나라에서는 `중앙은행, 금융감독원, 예금보험공사` 등을 금융안전망이라고 할 수 있다.\n",
    "- `중앙은행`은 일시적으로 자금이 모자라는 은행에 자금을 빌려 주는 `최종 대부자 기능`\n",
    "- `연방준비은행`이 `베어스턴스에 구제 금융`을 지원한 것도 미국 경제의 혼란을 막기 위한 목적\n",
    "- `금융감독원`은 은행 증권 보험 등 모든 `금융회사의 설립 요건을 정하고 이들이 규정을 지키는지 관리 감독`\n",
    "- `예금보험공사`는 은행 등이 `파산 위기`에 몰렸을 경우 `적립해 둔 보험금으로 예금을 대신 지급`함으로써 사람들이 한꺼번에 은행으로 몰려드는 혼란을 막는 역할\n",
    "\n",
    "<center><img src='Image/Basic/BankSecuritySaperation.jpg' width='500'>(https://www.mk.co.kr/news/world/view/2010/01/38961/)</center>\n",
    "\n",
    "- 금융 시장의 안전을 위한 제도로 `예금을 받는 일`과 `증권투자 업무`를 한 회사에서 할 수 있도록 할 것이냐의 문제도 자주 논란\n",
    "> - 1929년 세계 대공황이 일어나기 전까지만 하더라도 `미국은 예금은행과 투자은행(증권투자업) 업무를 같은 회사에서 할 수 있었음`\n",
    "> - 대공황 이후 많은 금융회사가 파산해 예금자들이 예금을 인출하지 못하게 되자 `1933년 예금은행업과 증권투자업무를 완전히 분리`\n",
    "> - `1980년대` 들어 `금융기법이 발달`하고 상품 수요도 다양하게 나타나자 영국은 금융의 내부 업종 간 벽을 허물었고 다른 나라도 `금융의 업종 간 벽을 낮추고 있음`\n",
    "> - 우리나라는 `금융지주회사`를 설립한 후 그 아래에 은행 보험 증권 투자은행을 둘 수 있도록 `간접적으로 겸업을 허용`\n",
    "\n",
    "---\n",
    "\n",
    "<!-- **3) 우리나라의 금융회사들**\n",
    "\n",
    "- 우리 나라의 금융회사는 크게 `예금은행, 증권 관련 회사, 할부금융회사, 보험, 부실회사 정리 회사 등` 나뉘며 모두 `금융감독원`의 인허가를 받아 설립 및 운영\n",
    "- `예금은행`에는 일반 `시중 은행을 비롯 상호저축은행, 신용협동조합`이 있고 `증권 관련 회사`로는 `증권회사 선물회사 자산운용회사 등`\n",
    "- 자금(또는 시설물)을 빌려주는 업무를 전문으로 하는 `할부금융업`에는 `리스, 카드, 캐피털회사`가, `부실 회사 정리 회사`로는 `자산관리공사와 CRC(기업구조조정전문회사, Corporate Restructuring Company)`가 영업 중\n",
    "- 자산운용회사 캐피털회사 CRC 등은 1990년대 자본시장이 개방되면서 등장한 `새로운 금융회사들`\n",
    "- 은행 증권업은 외환위기 이후 많은 회사가 시장에서 퇴출당해 숫자가 크게 감소\n",
    "- `신협`은 말 그대로 `협동조합`으로 조합원들끼리 출자를 한 돈을 바탕으로 서로 대출을 해 주는 금융회사\n",
    "- 예금보험공사는 금융회사가 부실화됐을 경우 예금을 일정 한도 내에서 대신 지급해 주는데 `신용협동조합은 예금보험의 대상이 아님`\n",
    "- 반면 증권회사의 상품 중 `근로자증권저축`은 예금 성격이 강해 `예금보험의 혜택`\n",
    "- 예금보험공사는 보험 가입 상품에 대해 해당 금융회사가 부실화됐을 경우 `5000만원까지 대신 지급` -->"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "33c2117d",
   "metadata": {},
   "source": [
    "# **파생금융혁명:** 불확실성과 리스크에 대처하기 위한 도구\n",
    "\n",
    "**1) 파생금융상품(Derivatives):** `주식, 채권, 금리, 외환 등`의 금융상품 대상 `권리나 의무`를 표시하여 거래를 대비하는 `증권`\n",
    "\n",
    "> **(1) 선물(Futures):** 차익거래, 헷지거래, 스프레드거래 등 `미래 가격을 고정`하여 위험 대비\n",
    "> - 파생금융혁명은 `선물시장에서 출발`\n",
    "> - `밀, 쌀, 옥수수 등` 농산물 생산자와 소비자들이 `미래의 가격변동`을 대비한 거래가 시작\n",
    "> - 1710년 오사카 `쌀시장`, 1877년 시카고 `옥수수시장`을 기초자산으로 시작한 것이 최초\n",
    "> - 1970년대부터 `석유, 주식, 채권, 지수상품 등` 다양한 상품을 기초자산으로 개발됨\n",
    "> - 위험제거 수단을 넘어 선물거래는 점차 `투기의 수단`으로 사용\n",
    "> - 실제 기초자산의 거래를 할 필요가 없더라도 서류상으로 `가격변화에 따른 수익이 가능`하기 때문\n",
    ">\n",
    "> <center><img src='Image/Basic/Futures.png' width='500'>(https://career.fantasy-info.net/141)</center>\n",
    ">\n",
    "> **(2) 옵션(Option):** `주식`을 사고 팔 수 있는 `권리`를 거래하여 위험 대비\n",
    "> - 파생금융혁명의 또 다른 계기가 된 것이 `옵션거래의 활성화`\n",
    "> - 미래에 주식이나 채권을 매입할 수 있는 권리를 `콜옵션(Call Option)`, 매도할 수 있는 권리를 `풋옵션(Put Option)`\n",
    "> - 싼 가격에 살 수 있길 기대하는 거래가 `콜옵션`, 비싼 가격에 팔 수 있길 기대하는 거래가 `풋옵션`\n",
    "> - 예정된 미래(만기)에만 권리를 행사할 수 있는 `유럽형 옵션`, 그 이전에도 행사할 수 있는 `미국형 옵션`\n",
    ">\n",
    "> <center><img src='Image/Basic/Options.jpg' width='700'>(https://www.donga.com/news//article/all/20020204/7785427/1)</center>\n",
    ">\n",
    "> **(3) 스왑(Swap):** 양 거래자가 `서로의 금리, 통화율 등`을 바꾸어 위험 대비\n",
    "> - 1980년대 초에 첫 스왑계약 체결\n",
    "> - 미래에 발생할 `현금흐름의 방식을 교환`하는 두 거래자 간의 `장외계약`\n",
    "> - 선물, 옵션과 같이 `파생상품 3형제`로 불리며, 한 쪽이 이득을 보면 다른쪽은 손해를 보는 Pay-off 구조인 선물 및 옵션과 달리 `거래 당사자 모두에게 이익`이기 때문에 상대적으로 피해가 적음\n",
    ">\n",
    "> <center><img src='Image/Basic/Swap.jpg' width='400'>(https://cidermics.com/contents/detail/34)</center>\n",
    ">\n",
    "> **(4) 캡(Cap):** 기초자산의 가격이 `상위 경계` 아래에선 차액을 내지 않아 위험 대비\n",
    ">\n",
    "> **(5) 플로어(Floor):** 기초자산의 가격이 `하위 경계` 위에선 차액을 내지 않아 위험 대비\n",
    "\n",
    "- 전 세계의 금융시장에서 거래되는 파생금융상품은 `수천개의 종류`에 이르며 `수십조 달러`\n",
    "- 기업들의 경제활동에서 `불확실성과 위험이 커지면서` 파생금융상품을 통해 이를 `대처하는 적절한 수단`으로 활용\n",
    "- 기업들의 위험조절을 위한 `자연적, 역사적 도구`로 적절히 이용하면 기업의 경쟁력을 높이고 효율이 증가되고 국민복지의 안정성이 증가되지만, 그렇지 않을 경우 `큰 손실과 파산`을 유발"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "47fc4db5",
   "metadata": {},
   "source": [
    "# **금융시장으로 뛰어든 수학과 공학**\n",
    "\n",
    "> **\"금융자산의 가격은 얼마가 적절한 것인가?\"**\n",
    "> \n",
    "> - `화폐시장`으로 전환 후 모든 사물과 행위 시간 등은 `가격`이 부여\n",
    "> - `주식, 채권, 외환 등`도 가격이 있는데 `얼마가 적절할까?` 라는게 시장의 문제\n",
    "> - 시장에서 거래되지 않는 각종 파생상품들은 `얼마가 적절할까?`\n",
    "\n",
    "---\n",
    "\n",
    "**1) 금융시장:**\n",
    "<center><img src='Image/Basic/FinancialMarkets.png' width='500'></center>\n",
    "\n",
    "> - **단기시장:** 상품의 만기가 `1년 이내`를 의미하며 `콜, CP, CD 등`\n",
    "> - **장기시장:** 상품의 만기가 `1년 이상`을 의미하며 주식이나 채권이 거래되는 `자본시장 또는 증권시장`\n",
    "\n",
    "> - **발행시장:** 기업에서 `신규로 주식이나 채권을 발행`하여 `최초로 투자자에게 판매`하는 시장\n",
    "> - **유통시장:** `발행된 주식, 채권 등`의 금융상품이 `투자자들간에 거래`되는 시장\n",
    "\n",
    "> - **장내시장(Exchanges):** `상장된 주식이나 채권`을 거래하며 상대를 알 수 없고 `거래정보가 투명`한 시장\n",
    "> - **장외시장(Over-the-Counter, OTC):** `상장/비상장 거래`로 양측이 `직접거래`하거나 `딜러 또는 브로커가 중개`하며 `훨씬 큼`\n",
    "\n",
    "<center><img src='Image/Basic/ExchangesOTC.jpg' width='600'>(https://www.finda.co.kr/post/financial-life/135880)</center>\n",
    "\n",
    "---\n",
    "\n",
    "**2) 가격평가(Pricing):** 금융자산의 `가격을 추정`\n",
    "\n",
    "- **평가값:** `평가된` 금융자산의 `가격`\n",
    "- **평가모델:** 가격을 평가하기 위해 사용된 `수리적 모델/모형`\n",
    "- **평가사:** 자산들의 가격을 `전문적으로 평가하는 회사`\n",
    "> - `Moody's`, `Standard & Poor's`, `Fitch`\n",
    "> - `KIS평가`, `한국자산평가`, `NICE평가`, `FN자산평가`\n",
    "- `장내시장`에서는 매수자와 매도자가 `실시간`으로 거래하는 가격 자체가 `평가값`\n",
    "- `장외시장`에서는 시장이 있는 경우 `시장가`를 그대로 사용하지만, 그렇지 않고 `기초자산의 가격변화`에 따라 가치가 변하는 `ELS, ELB, DLS, DLB`와 같은 구조화 상품은 별도의 `프라이싱 과정 필요`\n",
    "\n",
    "<span style=\"color:red\">$\\Rightarrow$ **\"실제 시장가격과 같진 않으니, 각 업계마다 공개하진 않지만 사용하고 있는 `가격결정모형들(Asset Pricing Models)`로 도출된 `이론가격(Theoretical Price)`이 있으며 `금융공학(Financial Engineering)`의 강점이 드러나는 곳\"**</span>\n",
    "\n",
    "<span style=\"color:red\">$\\Rightarrow$ **\"이론가격이 존재하는 이유는 시장은 없을 수 있으나 `거래 또는 비즈니스가 존재`하기에 필요하고 `합리적 가격추정`을 할 줄 아는 능력이 있어야 `세일즈 또는 트레이딩`이 가능할 것이기 때문\"**</span>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c5506445",
   "metadata": {},
   "source": [
    "## 자산가격 결정원리(Asset Pricing Principle)\n",
    "\n",
    "> **\"금융상품 평가를 위해 `시장가`로 알 수 없는 경우, `모델링/알고리즘`을 통해 합리적으로 `적정가격(출력값)을 추정`하는 것\"**\n",
    "\n",
    "**1) 필요성:**\n",
    "\n",
    "- 시장에서 거래되지 않는 `구조화상품이나 복잡한 파생상품`의 `합리적 가격수준`을 알고 싶은 경우\n",
    "- `시장에서 거래`되고 있으나 유동성이 낮아 `가격자체를 신뢰할 수 없는 경우`\n",
    "\n",
    "**2) 가격결정원리:** 어떤 `이론/이치에 부합`하는 가격이며 `사람들에게 납득`되는 가격\n",
    "\n",
    "<center><img src='Image/Basic/AssetPricing.png' width='600'>(https://www.goodreads.com/book/show/490648.Asset_Pricing)</center>\n",
    "\n",
    "> **\"To value as asset, we have to account for the delay and for the risk of its payments. Asset pricing theory all stems from one simple concept: `Price equals expected discounted payoff`(Asset Pricing by John H. Cochrane)\"**\n",
    ">\n",
    "> **\"어떤 자산을 평가하기 위해서, 우리는 그것의 현금흐름이 미래로 지연되는 것과 그 현금흐름의 실현 가능성을 고려해야 합니다. 따라서 모든 자산가격 이론은 `가격은 예상되는 미래 페이오프를 현재로 할인한 값이다`라는 단 하나의 간단한 생각으로부터 출발합니다.\"**\n",
    ">\n",
    ">\\begin{align*}\n",
    "P &= E(mx) \\\\\n",
    "& \\text{where P is price, E is expectation,} \\\\\n",
    "& \\text{x is future cash flow or payoff,} \\\\\n",
    "& \\text{and m is a current stochastic discount factor.}\n",
    "\\end{align*}\n",
    ">\n",
    "> **(1) Expectation:** `미래의 현금흐름`을 합리적으로 `예상`해보는 작업\n",
    "> - 주식의 경우 미래의 배당금과 차익을 `기대`\n",
    "> - 채권의 경우 미래의 이자 수익을 `기대`\n",
    "> - 부동산의 경우 미래의 임대수익과 차익을 `기대`\n",
    "> - 파생상품의 경우 기초자산의 움직임에 따른 조건부 수익 `기대`\n",
    ">\n",
    "> **(2) Discounted:** 미래의 현금흐름을 `현재로 가져오는` 작업\n",
    "> - 오늘의 1만원은 10년 뒤의 1만원과 그 가치가 다르고 일반적으로 더 클 수밖에 없음\n",
    "> - 미래의 예상되는 현금가치의 현재시점의 가격을 위해선 `적절한 할인율 필요`\n",
    "\n",
    "<span style=\"color:red\">$\\Rightarrow$ **\"해당 자산의 미리 현금흐름을 `합리적으로 뿌리고` 그 추정된 미래 현금흐름을 `합리적으로 할인`하여 현재 시점으로 거둬들이는 방법으로 `모든 투자자산`에 공통으로 사용되는 절대원칙\"**</span>\n",
    "\n",
    "<center><img src='Image/Basic/Womens.jpg' width='500'>(이이삭 줍는 여인들(1857), 장 프랑수아 밀레(1814~1875) 작, 캔버스에 유채, 오르세 미술관, 파리)</center>\n",
    "\n",
    "---\n",
    "\n",
    "**3) 금융 모델러 선언:**\n",
    "\n",
    "> **\"2008 글로벌 금융위기 이후 저명한 금융공학자인 이매뉴얼 더만(Emanuel Derman)과 폴 윌맛(Paul Wilmott)은 금융 모델러 선언을 발표\"**\n",
    ">\n",
    "> - 복잡한 `세상을 단순화한 수리적 모델`을 사용하지만 인간의 행동을 담은 `세상은 절대 단순하지 않음`\n",
    "> - `위험관리(Risk Management)`와 `계량금융(Quantitative Finance or Computational Finance)`을 사용함에 있어 좀 더 `책임의식`을 가져야 함\n",
    "> - 우리는 수학과 모델이 필요하지만 `절대 현실세계가 아님을 잊지 말아야`하며, 시장과 증권의 행동 속에서 유의미한 `인간의 행동을 모델링`하는 것으로 `정성적인 것, 정량적인 것, 상상과 관찰, 예술과 과학`을 적절히 융합시킬 필요\n",
    "\n",
    "<center><img src='Image/Basic/FinancialModelersManifesto.png' width='900'></center>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "62d5d7be",
   "metadata": {},
   "source": [
    "## 금융공학?(Financial Engineering)\n",
    "\n",
    "**0) 공학(Engineering):** \n",
    "\n",
    "> **\"`기술적 문제`를 대상으로 `문제를 발견하고 기술적 해결책을 제시(Problem Solving)`하는 학문\"**\n",
    ">\n",
    "> - 문제는 `다양한 분야`에서 나타나기 때문에 `다양한 학과 전공`들이 개설되게 되었고\n",
    "> - 기술적 해결책 보다 `문제 발견 또는 사회적 해결책`을 연구하는 학문들로 `인문, 사회 전공`이 존재하고\n",
    "> - 따라서 금융공학은 `문제 발견` + `기술적 해결` + `사회적 해결`의 융합 학문\n",
    "\n",
    "---\n",
    "\n",
    "**1) 금융공학 예시:** `문제 발견` + `기술적 해결` + `사회적 해결`의 융합 학문\n",
    "\n",
    "- **문제발견:** 달러 유동성이 낮을때 하필 시중은행이 `지금 달러가 필요`할 경우 어떻게 마련하는게 `최선`인가?\n",
    "\n",
    "<center><img src='Image/Basic/FE_Question.png' width='600'></center>\n",
    "\n",
    "- **기술적 해결:** 문제를 해결/타개하기 위해 `창의적 방법 구상 필요`\n",
    "\n",
    "> **(1)** 자금시장에서 일단 `원화를 차입`\n",
    ">\n",
    "> **(2)** 차입한 원화로 `달러 매수`\n",
    ">\n",
    "> <center><img src='Image/Basic/FE_Question_Solve1.png' width='600'></center>\n",
    "> <center><img src='Image/Basic/FE_Question_Solve2.png' width='600'></center>\n",
    ">\n",
    "> **(3)** 1년 뒤 원화 상환을 위한 원화선도 매수 + 1년 뒤 달러 상환을 위한 달러선도 매도\n",
    ">\n",
    "> <center><img src='Image/Basic/FE_Question_Solve3.png' width='600'></center>\n",
    "> <center><img src='Image/Basic/FE_Question_Solve4.png' width='600'></center>\n",
    "\n",
    "- **사회적 해결:** `합성(Synthetic) 기술`을 사용한 `달러 복제 포트폴리오(Replicating Portfolio)`를 실행하기 위한 공감대와 설득\n",
    "\n",
    "> - 완벽한 방법은 아닐 수 있지만 현재로썬 문제를 해결할 수 있는 `최적의 방법`\n",
    "> - 선도매입 비용이 추가로 들어가는 `단점`이 있으나 원화 및 달러 상환시 환차익으로 수익이 날 수 있는 `장점`들로 인해 여전히 `최소한의 불확실성 존재`\n",
    "\n",
    "---\n",
    "\n",
    "**2) 금융공학의 중요성:** 불확실성을 줄이기 위해 `정통 수학/공학이 강점`을 발휘하면서 쉽게 해결하지 못했던 `복잡한 금융문제`들을 해결하면서 영향력이 점차 확대\n",
    "\n",
    "> **\"파생금융상품으로 직접투자보다 `간접투자`가 증가하였고 `투자상품`으로 점차 인식\"**\n",
    ">\n",
    "> **\"1년간 직접노동으로 얻은 `몇만대의 수출규모`도 금융시장의 `순간손실로 하루아침에 헛고생 비즈니스`가 되는 세상 도래\"**\n",
    ">\n",
    "> **\"불확실성과 리스크를 다룰 수 있게 되었지만, `정량적`으로 `얼마가 적정`한지 계산하기 어렵다?\"**\n",
    ">\n",
    "> **\"안정적 금융시장을 위한 `위험의 정량화` 및 상품들의 `미래의 가치를 정량적으로 추정`하기 위한 도구\"**\n",
    ">\n",
    "> **\"잘 사용하면, 금융상품의 `현재가치`가 미래에 `어떻게 변할지 추정`하고 현재의 적정 가격을 계산하여 `전략적 행동(효율적인 투자)`로 인한 적정가격 달성 및 시장안정성 구축\"**\n",
    "\n",
    "<span style=\"color:red\">$\\Rightarrow$ **\"`데이터(정보)를 가공, 조립, 분석할 수 있는 능력` + `위기 또는 기회에서 빠른 의사결정을 할 수 있는 아이디어 및 전략을 찾을 수 있는 능력`\"**</span>\n",
    "\n",
    "---\n",
    "\n",
    "**3) 금융공학:**\n",
    "\n",
    "- 전 세계적인 `금융 위기와 핀테크 등장 및 디지털 혁신`으로 사람들의 금융에 대한 관심이 증가\n",
    "- 실제로 세계의 주식, 채권 시장은 `국민총생산의 10배 이상이고 점점 증가`하고 있음\n",
    "- 공학적인 마인드로 금융시장을 바라보는 `금융공학` 역시 사람들의 관심이 지속적으로 이어짐\n",
    "- `수리적 또는 공학적 도구`를 사용하여 `금융시장을 분석`하는 분야로 `경영경제, 산업심리, 응용수학, 산업공학, 컴퓨터공학 등`이 어우러진 `융합` 학문이자 분야\n",
    "- `금융수학(Financial Mathematics), 금융공학(Financial Engineering), 계산재무론(Computational Finance), 계량재무론(Quantitative Finance)` 등으로 불림\n",
    "\n",
    "<center><img src='Image/Basic/Cources.jpg' width='800'>(https://tfetimes.com/best-financial-engineering-program-rankings/)</center>\n",
    "\n",
    "- **금융수학 vs 금융공학:** \n",
    "\n",
    "> - **공학:** 정보와 컴퓨터의 발달로 수많은 `빅데이터` 속에서 `적절한 입력값`과 `적절한 출력값`을 만드는 도구\n",
    "> - **수학:** 출력값의 의미를 `정량적 및 논리적`으로 분석하여 `효과적인 투자`를 위한 의사결정을 만드는 도구\n",
    "\n",
    "| **-** \t| **금융수학** \t| **금융공학** \t|\n",
    "|:---:\t|:---:\t|:---:\t|\n",
    "| **방향** \t| 리스크 `전혀 없이` 수익을 창출 (Risk-free Return) \t| `가능한 적은` 리스크로 `가능한 많은` 수익을 창출 (Low Risk High Return) \t|\n",
    "| **목적** \t| Minimize `Risk` \t| Maximize `Return` \t|\n",
    "| **조건** \t| Under a guarantee of some `Return` \t| Under a controlable `Risk` \t|\n",
    "| **리스크** \t| 분산, VaR (Value at Risk), Shortfall, Coherent Risk Measure \t| 분산, VaR (Value at Risk), Shortfall, Coherent Risk Measure \t|\n",
    "\n",
    "> - `리스크 없는 안정적 수익`을 추구하던 금융수학의 범위에서,\n",
    "> - 리스크를 0으로 만드는 것이 너무 어렵다보니,\n",
    "> - `감당할만한 리스크` 내에서 `수익일 최대한 증가` 시키기 위한 방향도 발전"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8fd7c18b",
   "metadata": {},
   "source": [
    "# **금융공학의 역사**"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b0743038",
   "metadata": {},
   "source": [
    "## 기초자산과 파상생품의 움직임을 수학적으로 정립\n",
    "\n",
    "**1) 로버트 브라운(Robert Brown):**\n",
    "\n",
    "> - `1827년`, 로버트 브라운은 꽃가루 입자들의 `무작위적인 움직임 발견`\n",
    "> - `랜덤워크(Random Walk) 또는 브라운 운동(Brownian Motion)`으로도 불리는 아이디어는 `예측할 수 없는 연속적인 과정`을 사용한 다양한 분야와 모델들의 메커니즘에 스며들었음\n",
    "> - 주식시장에도 반영되어 `로그정규분포를 따르는 랜덤워크 모델`이 금융공학 모델링의 고전\n",
    "\n",
    "<center><img src='Image/Basic/BrownianMotion.jpg' width='500'></center>\n",
    "\n",
    "**2) 루이 바슐리에(Louis Bachelier):**\n",
    "\n",
    "> - 브라운 운동을 `처음으로 계량화(Quantify)` 및 `랜덤워크를 수학이론으로 정립`\n",
    "> - 아인슈타인에 의해 재발견되고 `1900년 당시 생소했던 옵션 상품 가격 모델링 개발`\n",
    "\n",
    "**3) 루이스 프라이 리차드슨(Lewis Fry Richardson):**\n",
    "\n",
    "> - 오늘날 대부분의 모델링들은 `열역학`에서 차용한 `확산 방정식(Diffusion Equation)` 형태\n",
    "> - 이러한 방정식의 해를 찾기 위해 `수치해석` 방법론이 사용되는데 그 중에서 `몬테카를로 시뮬레이션(Monte Carlo Simulation, MC)`과 `유한차분법(Finite Difference Method, FDM)`이 주로 사용\n",
    "> - `1911년` 방정식을 차분방정식의 형태로 이산화하는 형태를 `최초로 제안`\n",
    "> - 오늘날 당면한 금융공학 이슈를 거의 해결하게 된 계기가 `유한차분법`\n",
    "\n",
    "<center><img src='Image/Basic/FDM_Example.png' width='600'>(https://demonstrations.wolfram.com/PricingPutOptionsWithTheExplicitFiniteDifferenceMethod/)</center>\n",
    "\n",
    "**4) 노버트 위너(Norbert Wiener):**\n",
    "\n",
    "> - `1923년` 노버트 위너는 기존 브라운 운동으로 `위너 프로세스(Wiener Process)`를 개발하여 `기초자산의 움직임`을 묘사할 수 있게 된 계기 마련\n",
    "> - 모든 금융공학 책과 논문의 가장 처음에 등장하는 편이고 `금융공학의 시작`은 위너 프로세스의 이해\n",
    "\n",
    "<center><img src='Image/Basic/WeinerProcess.png' width='600'></center>\n",
    "\n",
    "**5) 폴 새뮤얼슨(Paul Samuelson):**\n",
    "\n",
    "> - 거시경제학 및 미시경제학 모두에서 `수학적 풍토`를 확립하고, 루이 바슐리에의 논문을 재발견하여 한계는 있지만 `옵션 가격 결정 이론` 기초 확립\n",
    "\n",
    "**6) 이토 키요시(Ito Kiyosi):**\n",
    "\n",
    "> - 자연계의 불규칙한 움직임을 분석해서 수식으로 나타내는 `확률미분방정식(Stochastic Differential Equation)`을 창조하고 무작위적 `독립변수와 종속변수의 연결고리` 설명\n",
    "> - 금융분야로 넘어와 `기초자산과 파생상품`의 연결고리를 통해 `금융공학의 모든것이 시작`\n",
    "> - 기존 한계를 해결하고 `옵션의 확률미분방정식` 정확하게 표현\n",
    "\n",
    "<center><img src='Image/Basic/ItoLemma.png' width='600'></center>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "aa0e0f14",
   "metadata": {},
   "source": [
    "## 시장 전체의 특징을 수학적으로 판별\n",
    "\n",
    "**1) 해리 마코위츠(Harry Markowitz):**\n",
    "\n",
    "> - 1952년 `현대적 계량금융 기법`을 최초로 창시하고 오늘날의 `포트폴리오 이론(Modern Portfolio Theory, MPT)`을 창시\n",
    "> - 계란을 한 바구니에 담지 말라는 월스트릿의 오랜 격언을 `수학적으로 증명`\n",
    "> - 동일 수준의 위험에서 `가장 높은 기대수익률 포트폴리오`를 어떻게 선택할지 최적화 방법 제시\n",
    "> - `효율적 포트폴리오` 제시를 통해 `노벨 경제학상` 수상\n",
    "\n",
    "<center><img src='Image/Basic/MPT.png' width='800'>(https://towardsdatascience.com/efficient-frontier-in-python-detailed-tutorial-84a304f03e79)</center>\n",
    "\n",
    "**2) 윌리엄 샤프(William Sharpe), 존 리트너(John Lintner) & 잰 모신(Jan Mossin):**\n",
    "\n",
    "> - 1963년 `위험자산 가격결정 모형(Capital Asset Pricing Model, CAPM)`로 알려진 각 자산마다의 `가격을 결정`하는 단순한 모형 개발\n",
    "> - 마코위츠의 MPT와 달리 포트폴리오 선택의 `파라미터 갯수를 줄이고 실용성 높임`\n",
    "> - 각 자산별 `베터(Beta)`라는 개념을 도입하고 증권업계의 대표적 의사사통 도구로 사용\n",
    "\n",
    "<center><img src='Image/Basic/CAPM.png' width='400'>(https://www.bablomedia.com/finansy/model-capm-formula-i-raschyot-capm/)</center>\n",
    "\n",
    "**3) 유진 파마(Eugene Fama):**\n",
    "\n",
    "> - `주가는 예측 불가능하며 따라서 시장은 효율적이다`라는 `효율적 시장 가설(Efficient Market Hypothesis, EMH)` 창조\n",
    "> - 주식시장의 가격은 `시장의 접근 가능한 모든 정보`를 반영하고 있고 누구도 `수익을 낼 수 없음`을 주장\n",
    "> - 학자들과 실무자들이 받아들이는 금융공학 모델링의 `기본가정`이자 자산 가격이 `랜덤워크`라는 이론을 뒷받침 한 개념\n",
    "> - 2013년 노벨 경제학생을 수상했으나 훗날 `데이터분석`을 통해 `효율적 시장 가설이 맞지 않음을 스스로 인정`"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2de8dd95",
   "metadata": {},
   "source": [
    "## 수학적 접근의 금융상품 확장 및 시장 활성화\n",
    "\n",
    "**1) 피셔 블랙(Fisher Black), 마이런 숄즈(Myron Scholes) & 로버트 머튼(Robert Merton):**\n",
    "\n",
    "> - 1973년 두 편의 논문을 통해 `확률미적분`을 사용하여 `주식과 옵션`의 가격관계를 논문으로 제시하며 `블랙숄즈 방정식` 세상에 알림\n",
    "> - `피셔 블랙과 마이런 숄즈`가 `아인슈타인의 브라운 운동` 방정식으로부터 고안하였으며 이후 `로버트 머튼`이 참여하며 블랙-숄즈 방정식으로 명명\n",
    "> - `옵션의 가치`를 평가하는 최초의 모형으로 투자가치의 계산시간을 `100분의1`로 단축시켜 옵션시장 및 파생상품시장이 급속히 성장하게 된 계기\n",
    "> - `1997년` 사망한 블랙을 제외하고 숄즈와 머튼은 `노벨경제학상` 수상\n",
    ">\n",
    ">\\begin{align*}\n",
    "\\frac{\\partial V}{\\partial t} + \\frac{1}{2} \\sigma^2 S^2 \\frac{\\partial^2 V}{\\partial S^2} + rS \\frac{\\partial V}{\\partial S} - rV = 0\n",
    "\\end{align*}\n",
    "\n",
    "> - 옵션이라는 `파생상품의 위험`을 주식과 같은 기초자산들의 `포트폴리오로 완벽히 헷지(제거) 할 수 있음`을 발견하며 수상\n",
    "> - `옵션의 가격변화`를 `기초자산의 가격변화`를 통해 어떤 관계와 비율이 있는지 설명\n",
    "> - 당시 위험이 걱정되어 `거의 거래되지 않았던 옵션`을, 정상적인 시장에서 `95%까지 위험제거가 가능함`을 판명\n",
    "> - `금융상품의 가격 또는 가치`가 어떻게 결정되는지 `수학적으로 증명`하며, 경험과 직관에 의존하던 옵션가격의 판단기준을 좀더 `객관적이고 과학적`으로 만듬\n",
    "> - 금융산업을 혁명적으로 바꾼 `기술적 변화`로 이론이나 실무에서 가장 많이 이용\n",
    "> - 파생상품의 위험을 제거하는 방법을 제시하면서, `선물, 스왑 등` 각종 금융상품의 개발에 `수학적 계산`이 깊이 개입하게 된 계기\n",
    "\n",
    "**2) 로버트 머튼(Robert Merton):**\n",
    "\n",
    "> - 1974년 `기업의 순자산과 부채`를 기초자산과 파생상품으로 접근하여 `기업 파생 가능성` 예측\n",
    "> - `부도 위험 모델링(Default Risk Modelling)`을 위한 구조적 방법론 탄생\n",
    "\n",
    "**3) 올드리치 바시첵(Oldrich Vasicek):**\n",
    "\n",
    "> - 1977년 단기금리를 랜덤워크로 가정하고 `이자율 모델링(Interest Rate Modelling)` 창조하여 이자율 파생상품의 가치 산출 방법론 제시\n",
    "> - `채권 가격결정`을 위한 편미분방정식을 제시\n",
    "\n",
    "**4) 존 콕스(John Cox), 스티븐 로스(Stephen Ross) & 마크 루빈스타인(Mark Rubinstein):**\n",
    "\n",
    "> - `이항모형(Binomial Model)`이라는 단순한 도구를 사용한 `옵션 평가 방법` 개발하여 일반인들과 문과들에게 접근 문턱을 낮춤\n",
    "> - 오늘날 월스트리트에는 수학자과 물리학자들이 어렵지 않게 볼 수 있으나, 예전엔 대부분 문과출신들이 대다수다보니 이과들에겐 다소 간단한 `수리적 금융시장`을 이해하고 다루는데 어려움\n",
    "> - 문과생 및 MBA 학생들도 금융공학의 이해도를 갖게 된 계기\n",
    "\n",
    "<center><img src='Image/Basic/BinomialTree.png' width='400'>(https://www.bablomedia.com/finansy/model-capm-formula-i-raschyot-capm/)</center>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b3494a0f",
   "metadata": {},
   "source": [
    "## 기초자산이 여러개인 상품 성장 및 수학적 고도화\n",
    "\n",
    "**1) 마이클 해리슨(Michael Harrison), 데이빗 크렙스(David Kreps) & 스탠리 플리스카(Stanley Pliska):**\n",
    "\n",
    "> - 기존 방정식들과 접근들은 모두 `무위험 차익거래(No Arbitrage)` 이론에 기반\n",
    "> - 1979년 및 1981년 이산시간(Discrete) 및 연속시간(Continuous)에서의 `확률이론기반 가격결정방식`을 설명\n",
    "> - `수학적 및 통계적 연결고리`가 생성되고 확률적 접근의 `마킹게일 이론(Martingale Theory)`을 통해 프라이싱이 여러 관점으로 설명할 수 있는 길이 생성\n",
    "\n",
    "**2) 토마스 호(Thomas Ho) & 이상빈(Lee Sang-Bin):**\n",
    "\n",
    "> - 기존 바시첵 모형은 채권의 가격을 정확하게 산출하지 못하는 한계\n",
    "> - `1986년` 이자율 모형을 실제 시장 가격에 맞추기 위해, 이자율 모델링의 끝판왕으로 불리는 `캘리브레이션(Calibration) 또는 수익률 곡선 피팅(Yeild Curve Fitting)`의 시대를 등장\n",
    "\n",
    "<center><img src='Image/Basic/Calibration.ppm' width='800'>(The impact of macroeconomic news sentiment on interest rates)</center>\n",
    "\n",
    "**3) 존 헐(John Hull) & 앨런 화이트(Alan White):**\n",
    "\n",
    "> - 1990년 바시첵 모형의 확장판으로 `평균회귀(Mean-Reverting)` 성질을 지닌 모델 개발\n",
    "> - `금리가 음수(Negative Interest Rate)`인 경우도 적용 가능한데, 당시 현실과 맞지 않아 주목받지 못하다 `유럽과 일본의 마이너스 금리현상`으로 재조명받아 실무적으로 널리 사용 \n",
    "> - 선물옵션 수업에서 주로 사용되는 `교재 바이블`\n",
    "\n",
    "<center><img src='Image/Basic/VasicekMeanReversion.png' width='600'>(An Overview of the Vasicek Short Rate Model)</center>\n",
    "\n",
    "**4) 데이빗 히쓰(David Heath), 로버트 재로우(Robert Jarrow) & 앤드류 모톤(Andrew Morton):**\n",
    "\n",
    "> - 이전 이자율 모델들은 `단기금리`를 유일한 `독립변수`로 사용하는 한계\n",
    "> - 1992년 `수익률 곡선(Yield Curve)` 전체에 대한 모델링으로 `모든 선도 금리`를 독립변수로 사용하는 `HJM모델` 제안\n",
    "\n",
    "**5) 오렌 쉬옛(Oren Cheyette), 존 버렛(John Barrett), 제럴드 무어(Gerald Moore) & 폴 윌못(Paul Wilmott):**\n",
    "\n",
    "> - `2개 이상의 기초자산`을 가진 옵션(Multi-Asset Options)은 `다중 적분`이 필요한데 기초자산의 수가 늘어나면 다차원 적분이 쉽지 않은 현실\n",
    "> - 다중적분 문제를 `적분이 단지 전체 계산 영역에 함수 평균을 곱하는 것`이라는 기본적 아이디어를 활용하여 1990년대 `몬테카를로 기법`을 사용하여 수치 적분(Numerical Integration) 해결\n",
    "> - 다차원 금융에서 없어서는 안될 금융공학 기법으로 인식\n",
    "\n",
    "<center><img src='Image/Basic/VolumeAverage.png' width='700'></center>\n",
    "<center><img src='Image/Basic/MonteCalroIntegration.png' width='500'>(An Overview of the Vasicek Short Rate Model)</center>\n",
    "\n",
    "**6) 이매뉴얼 더만(Emanuel Derman), 이라쥐 카니(Iraj Kani), 브루노 두파이어(Bruno Dupire) & 마크 루빈스타인(Mark Rubinstein):**\n",
    "\n",
    "> - 블랫-숄즈 방정식의 최대 문제는 `변동성을 일정한 숫자`로 가정했다는 점이고, 실제로 옵션들은 내재 변동성값이 `행사가격과 만기`에 따라 달라짐\n",
    "> - 1994년 `변동성 모델링`을 반영한 `변동성 곡면(Volatility Surface)`를 개발\n",
    "> - 변동성을 기초자산과 만기의 함수로 표현 후, 각 변동성마다 블랙-숄즈 방정식에 입력하여 정확한 옵션가격 산출\n",
    "> - 이해하기 쉽지만 입력값에 예민하게 반응하기 때문에 실제 활용이 어려움\n",
    "> - 문제가 있음에도 불구하고 현실세계를 잘 반영했기 때문에 `변동성 모델의 대세`\n",
    "\n",
    "<center><img src='Image/Basic/VolatilitySurface.webp' width='800'>(Research on wave image analysis in the implied volatility of stock options)</center>\n",
    "\n",
    "<center><img src='Image/Basic/VolatilitySurface2.png' width='800'>(Which one is your volatility — Constant, Local or Stochastic?)</center>\n",
    "\n",
    "**7) 앨런 브레이스(Alan Brace), 다리우스 건타렉(Dariusz Gatarek) & 머렉 뮤즐리어(Marek Musiela):**\n",
    "\n",
    "> - 1997년 시장에서 `실제 거래되는 금리`와 시간에 따라 변하는 `변동성과 상관계수`를 내포한 `선도금리`를 몬테카를로 시뮬레이션을 통해 `독립변수`로 사용하는 `LIBOR 시장 모형(LIBOR Market Model, LMM)` 제시\n",
    "\n",
    "**8) 데이빗 리(David X. Li):**\n",
    "\n",
    "> - 폭발적인 기초자산이 여러개인 상품들의 성장을 통해 자연스럽게 `기초자산들의 부도(Default)`에 관심이 쏠리고 관련 파생상품들이 발전\n",
    "> - 대표적으로 2008 글로벌 금융위기를 촉발시켰던 `부채 담보부 증권(Collateralized Debt Obligation, CDO)`이며 이를 프라이싱하기 위해서 여러 기초자산들의 `부도간 상호작용`을 설명할 수 있는 모델이 필요\n",
    "> - `2000년` 데이빗 리는 `가우시안 코풀라 함수(Gaussian Copula Function)`을 사용하여 설명할 수 있는 확률적 접근 제시하였고 서로 독립적인 회사들의 부도 모형을 결합시켜 `동시 부도 확률` 모델링\n",
    "> - `CDO 가격측정`이 가능해졌고 당시 저금리 상황에서 갈곳 없는 자금들이 CDO 시장으로 몰려들어 엄청난 속도로 성장하게 된 계기\n",
    "> - 2008 서브프라임 모기지 사태로 붕괴하였는데, `부동산 호황 데이터만 고려`하여 폭락 시나리오는 고려하지 못했기 때문에 단 하나의 수학 공식이 `엄청난 재앙 초래`\n",
    "\n",
    "**9) 팻 하간(Pat Hagan), 딥 쿠마르(Deep Kumar), 앤드류 레스뉴스키(Andrew Lesniewski) & 다이애나 우드워드(Diana Woodward):**\n",
    "\n",
    "> - `2002년` 변동성과 선도금리를 독립변수로 사용하는 `SABR모형(Stochastic, Alpha, Beta, Rho)` 개발\n",
    "> - 가격결정 방식에 `컴퓨테이션 기법`인 `점근적 근사화(Asymptotic Approximation)`를 사용하여 실무적으로 정확하면서 다루기 쉬움\n",
    "> - `점근 분석법(Asymptotic Analysis)`은 수치해석 문제를 간단하게 만들어주는 장점이 있고, 이러한 접근을 계량금융 분야의 `주류로 자리잡게 한 계기`\n",
    "\n",
    "<center><img src='Image/Basic/SABR.png' width='800'>(https://www.imperial.ac.uk/media/imperial-college/faculty-of-natural-sciences/department-of-mathematics/math-finance/Cheng_Luo-thesis.pdf)</center>\n",
    "\n",
    "---\n",
    "\n",
    "**10) 정리:**\n",
    "\n",
    "> **\"금융공학을 포함한 `인류의 역사`는 `무한루프`로 인류가 멸망하지 않는 한 멈출 일이 없음\"**\n",
    ">\n",
    "> **\"`새로운 문제`가 등장하면 `기술적 & 사회적 해결`을 하려 애쓰며 주류가 되다가, 시간이 흘러 `결함이 발견`되면 보완하기 위해 `새로운 해결법`이 등장하는 `무한반복`\"**\n",
    ">\n",
    "> **\"`미래`를 해결하기 위해선 `현재의 상태`를 정확히 이해해야 하고, `현재`를 이해하기 위해선 `과거의 상태`를 돌아볼 필요\"**\n",
    "\n",
    "<center><img src='Image/Basic/InputOutputFE.png' width='700'></center>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9d27edb4",
   "metadata": {},
   "source": [
    "# **금융공학 모델링 및 데이터사이언스**\n",
    "\n",
    "## 금융데이터분석의 목표와 도구\n",
    "\n",
    "**0) 모델링(Modeling):** \n",
    "\n",
    "> - (비수학적) `모형을 제작`한다\n",
    "> - (수학적/공학적) 어떤 현상 또는 특성을 `수학적/정량적으로 표현`하는 과정\n",
    "> - `모델링`을 통해 분석가들은 `사회현상이나 시스템특성`을 재현/대응 할 수 있는 `수학적 함수로 구현`하고 정교한 변화를 대응 및 반영하기 위해 `변수들(Variables) 또는 파라미터(Parameters)`를 통제\n",
    "\n",
    "---\n",
    "\n",
    "**1) 목적 및 필요성:** \n",
    "\n",
    "> - `인간의 뇌`는 복잡한 현실세계를 파악하는데 근본적인 `인지적 한계` 존재\n",
    "> - `현실 세계를 좀더 쉽고 직관적`으로 이해하기 위한 `추상화` 과정 필요\n",
    "\n",
    "- **금융공학에서의 모델링:** `높은 정확도`를 도출하는 `고도화 데이터사이언스 방법론`들이 결합되기 때문에 고급 `수학(특히 미분방정식), 컴퓨테이션` 사용이 필수적\n",
    "\n",
    "| **-** \t| **재무 모델링<br>(Financial Modeling)** \t| **금융공학 모델링<br>(Modeling in Financial   Engineering)** \t|\n",
    "|:---:\t|:---:\t|:---:\t|\n",
    "| **도구** \t| `엑셀(전통적)` \t| `엑셀(전통적)/C++&Python(최근)` \t|\n",
    "| **입력** \t| 기업의 과거성과, <br>미래상황 가정, <br>각종 재무제표 데이터 \t| 과거 성과 재무제표 등을 포함한 <br>`비즈니스 전반`의 모든 데이터 \t|\n",
    "| **출력** \t| `기업의 미래 재무성과` \t| `미래 재무성과`를 포함한 <br>`투자전략, 가치평가, 미래상황 시뮬레이션` \t|\n",
    "| **특징** \t| 한정된 분야 + 느린 속도 + 낮은 정확도 \t| `모든분야 확장 + 빠른 속도 + 높은 정확도` \t|\n",
    "\n",
    "---\n",
    "\n",
    "**2) 방향:** 금융시장의 현실 문제를 `수학적 도구`를 사용하여 우리가 이해할 수 있는 `단순한 가상의 모델`로 표현한 후, 다시 역으로 `단계별 구축`을 통해 `현실세계`를 검증하며 반복하는 `무한루프 싸이클`이 바로 `역사`\n",
    "\n",
    "<center><img src='Image/Basic/FE_TargetTraining.png' width='800'></center>\n",
    "\n",
    "---\n",
    "\n",
    "**3) 목표 달성을 위한 도구:** 이런 해결과정을 사람의 `말`로만 진행할 수 없고 `도구` 필요\n",
    "\n",
    "<center><img src='Image/Basic/DataAnalysisToolExample.gif' width='800'></center>\n",
    "\n",
    "- 효과적인 전투를 위해 토르에게는 `묠니르`가 캡틴에게는 `방패`\n",
    "- 집을 짓는데 `망치`가 필요하고 요리하는데 `칼`이 필요\n",
    "- 인류는 날개도 발톱도 이빨도 없어서 살아남기 위해서 `여러 도구`를 개발하였고 이를 사용해 `찬란한 문명 건설`\n",
    "- 금융공학 그리고 데이터사이언스도 당면한 문제 해결을 위해 `다양한 도구(확률,통계,컴퓨터,엑셀,파이썬 등)` 사용"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0a8c3f16",
   "metadata": {},
   "source": [
    "## 가상세계를 활용한 현실세계 해결 예시\n",
    "\n",
    "> **\"금융시장의 현실 문제를 `수학적 도구`를 사용하여 우리가 이해할 수 있는 `단순한 가상의 모델`로 표현한 후, 다시 역으로 `단계별 구축`을 통해 `현실세계`를 검증하며 반복하는 `무한루프 싸이클`이 바로 `역사`\"**\n",
    "\n",
    "<center><img src='Image/Basic/FE_TargetTraining.png' width='800'></center>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "a79f7583",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-07-04T11:28:37.039606Z",
     "start_time": "2022-07-04T11:28:35.261610Z"
    }
   },
   "outputs": [],
   "source": [
    "# 도구 불러오기\n",
    "import warnings\n",
    "warnings.filterwarnings('ignore')\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import scipy.stats as stat\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "31014787",
   "metadata": {},
   "source": [
    "\\begin{align*}\n",
    "dS &= \\epsilon \\sqrt{dt} \\\\\n",
    "\\text{기초자산의 변화} &= \\text{임의 숫자 } \\times \\text{ 시간변화 반영을 위한 스케일링 변수}\n",
    "\\end{align*}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "430092f6",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-07-04T11:28:40.172121Z",
     "start_time": "2022-07-04T11:28:39.994093Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 내부변수 \"시간 데이터\" 생성\n",
    "T = 1\n",
    "N = T*252\n",
    "dt = T/N\n",
    "t = [i for i in np.arange(0,T,dt)]\n",
    "plt.plot(t)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "0abaea90",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-07-04T11:28:49.739317Z",
     "start_time": "2022-07-04T11:28:49.626280Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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1P4d6fCHM8XXCa+LT04fGJmeyX/rV6zz4age/fb2bruEgVcUFrClzUl/qxKTg6787zPa//y3B8ei05081PDa+4E6OIruFve1DfPmRg7xpWzUfuHztgr4+obTQNqnk0jYQyNgkquQKkAus7SeUF9kXnaEHx6O8cKyfy5q9Mz6e2DTkhq1V8z5XVbEdrSe6kYRYDAnoOZK4mXde/GbZ5vhb9tQbo7GY5v6X2nBYzfT7wxzsGkmuV241m6gudnBqOEjfaHjOjZ0Tz+teYEAvtJuTdf2PXrsBm2Vx/13KXLZJJZd/fuwQd/7glYzMkuxLtGPOcH8gHeUuO72LzNB3HR8kFImxo3nmstWVZ1TwF5c2cdXGinmfy5Mys1SIxZKAniOJrPDNZ9fwgcubeOs5Rjkj9Qe622d0sVwar7/2jYapck9Mva9NmYY/V0ljPBojEI4uOEN32Y3zHVZzctnZxSgttCcz9FhM82xLH8HxGL7Q0ib0gJGhO23mZC//Qnlddvp8i6vv7zzSi81s4sK1pTM+XlVcwOfevHlaS+hMEvc3ZNMLsRQS0HMkUT+vL3HwmTdtTs7ATM3QT8TXEX/DxsrksdQdhc6u9yQ/7p+jLTAxA3XhAd0IRJuqi5KlocUoK7Ql2xYPdfuS2fpS+7/B6J5ZbHYORsmlbzTE8T4/t/3PSzx+IL1S0MsnBnjwlQ62N5Ys+pdJqsTELtn0QiyFBPQcSXS4JHb7SQTb1ICe2BjiknUTizpVpgT0T9+wkac+cRUw88SdAX+YrZ9/LLl58oIDenw9l80zdHAsRGmhDV8oQigS5ZmWifVqMhHQjRUgF35DNKG8yE4kprnm357kdwd6uP/Ftnm/ZjQU4d33vojDZuIzb9o07/npSAT0IcnQxRJIl0uOJDL0xISY4vgP9HBKhnZiwI/ZpKgrcdDkLeRgl29Shp5Yhxwmuj1StQ8GGA1FeLrFmFnqdizs5U50bmyunt5jvRDJtcH94zzT0keB1URwPJaRgN4/Gp62D+pC3LitmraBMcwmY5GtXScG5t3UuqVnlLHxKJ9902a2zDBDdDE8jol/IyEWSzL0HOnxhbCaVbJ2WmS3YDapaSWXWo8Di9nEuvhKfqlraoMxfb+owJJcfCtVYtr+kW5jBuJiulxg6Rl6ogOlbzTErhODXLmhIvn5UiV2YVqsSrdR5/7MmzZz47ZqhgLjfPrB17jma09yLL7z0lSJ45lcd8VmMeGyW6SGLpZEAnqOdA8HqSgqSGaCSincBZZJbYsn47MzAbbVFuOyW5IlmlRel33GkktiFcFj8T0+FxrQr9pYwW2XNc04aWYhEhn688f68QUjXL2pAqt5+oSeI90+7n3qWNrPm9iFqWyGXZQW44L46pM/3NXGkZ5R/vTbzyd/wR7p9rGnbQgw/j3NJrXgvv75eJzWtBdoE2ImEtBzpG0wMG2zCI/TxvDYROfHif5AMmi8/9JGfvPXO2ZsHSwrtM1YcklsgByOGuu9LLRtsa7Eyd/etBmreWn/Tc6oKsJqVnx7pxGsz28sxeua3v993zOt/P2vDxAIp9f9MjIWMXZhWmQP+lQNZU7Ki+yYTYrP3bSZvtEQ++MbYHzhl/v5yA93A3Csb5Q1pc5Ft3HOpsRpkwxdLIkE9BxpGxijfkqGV+K0sqdtiPbBAMOBcYbHxpMZemJlxJmUFtpm7HLxTVnne6bVEJeDx2njjZsq6fUZW9g1lDnxuux0jQS57+nW5I3AV+PrhqfbRpiYhDPTPqeLoZTizivX8ekbNnJ9fDJQa7/x7uZgp4/j/X4C4QjHev2s9S6+jXM2HqdVulzEkkhAz4HgeJSukeC0t+wffuMGBv1h3vHt59nfaWSGqbvgzKbMZZ9xhmHq9nF2iymtfuhs+ZPtRp/9eQ0lKKUoL7Lz3NF+vvir1/n1a534QxEOx2v96U70Sa7jsoQa+lTvv7SJ2y5fS5W7ALvFxIn+AH2jIfr9YbQ2NrNo7fOztjzzAb3EaZMuF7EkEtBzILG6Yn3p5Iz7ig3lfPamzXQMjfHgKx0AnFXnmff5vC5jav3UHW8SJRdYeP0803Y0l3N5s5e3nFMLGDM0I/Hxdg8H2ds+TGL46d4sTZSZltK2OBuTSdFQ5qS1z8/hlGVtnzjYQygSy8pGFCXx9dOFWCwJ6DmQWAa3foYdfC6IL7P6i90d1Jc60rrhV1ZoI6bh1v95Kbn5BUwuueQ6oFvMJr5/64XcuK0aYNKGFF0jQV5tG0x+nm5AT9TgvRnM0FM1lBVyot/Pofg7B4tJ8dP4L9rmNN45LZTHaWMkGCESzd7+qyK/SUDPgfZ4QJ+pSyJxY248qtPKzoFk0H/iUC+P7e9KHk+dWp/rgD7V5IAeYk/bUPImcbo19B5fCJMiY10uUzWWOTnRH+BA5wilhTa21LjpGBpjbXkh58bX4MmkxOQi6XQRiyUBPQdODgSwW0wzbpumlOL8RiNYpE7tn0vqOuedwxPL6fqCkWQv+UI7XLLt7HoPDWVOzq730D0c5EjPKFtriil2WNPO0HtGQpS57EtalmAujd5CQpEYOw/3saHSxcYqo33zL3esnXPi0WIlXsf5tiIUYjbzBnSl1H1KqR6l1L5ZHn+XUmpv/M+zSqmzMj/M/JLocJltI4vz4/3QZ6UZ0M9t8PDnFzewudpNV8qqi77gOGvjpYHTLUM/q97Dk//3KrbVFnNqaIyT/QGayguTa6uko8cXpHIROxWlK7EgWddIkPMaSrh+W9Wk+wCZJtP/xVKlMxf8u8A3gO/N8ngrcIXWelApdQNwD3BhZoaXn9oGA9SXzNyCCPAn2+uxWUzJpXXn47RZ+Lubt/KJn+zhD4d6k8d9wQjNFS7aBmyL2qJtOVQVFyRLQ2u9hXgXsOFEjy8040SrTGmudGE2Ka7fWsWHrm7GbjFz1RnzL4W7WIlrmW8pZCFmk84WdDuVUo1zPP5syqfPAwvf1maVOTkQ4LyG2YO1y27hXRc2LPh5q4sd9I2GCEdi2CwmRoMRigos/PiOizPWq51pqZs7ry134XXZ096KrXskxLYZ9vLMlIqiAp771BsoL7IveC/VxUjMOUissinEQmW6hn4r8EiGnzOvDAfG8QUjGZ82DlDjKUDriYW/fMFxXHYr68pdp13JJaEqZWEtI0NPbwehSDRGvz806RdCNlS4C5YlmIPxTquiyE5rn39Zvp/IPxkL6EqpqzAC+ifnOOd2pdQupdSu3t7e2U7La4mWxboZWhaXqrrYKOOcGhojGtP4w1GKCk7vBTUTi42VOK2UFNooL7IzGorMu6VeYqJPeRZLLrnQ6C3kuAR0sUgZCehKqTOBe4Gbtdb9s52ntb5Ha71da729vHz23ebzWdvg7C2LS1XjMYLb0y19/PSVdoDTPqAn1ndvik+lT/SUz5el94wYj2c7Q19uTWWFHJeSi1ikJf+0K6XWAA8C79FaH176kPJbclJR6ew3RRcrkaH/5+9bksdO94BeZLdQZLewLj7zMnENLx0fmLbWTaoen1FWyuZN0Vxo8DrpGw3hC45TlKO1d8TKNe9Pu1LqfuBKwKuUagc+D1gBtNZ3A58DyoBvxWuNEa319mwNeKVrGwjgcVqz8sNaaLfgLrAkl80FTvugoJTi7vecl3zHcsm6Ms6q9/DFX73OZc1eKopmDtjdeZyhg3FjdGsWb/iK/DRvyUVrfYvWulprbdVa12mtv6O1vjsezNFa36a1LtFanx3/I8F8Dm2DY1kptyTUlTipSbnReLpn6ACXrvcms3GL2cS//smZDAXGeWj3qVm/JpGhn67dO4vVEA/ox/ulji4WTmaKLrO2gcCMa7hkylfeto3vvO/85Ocu++kf0KdaX1FEUYGF9sGxWc/pHglRWmjL+JrkudboNf5vyI1RsRj59dNwmovGNB2D09dBz6Qz6zxsqnZzebMXAIctd0vmLkWtxzFnQO8cHlvSXqKnK6fNQqXbLjdGxaKsvPRtBTvQOUI4GmNDZeZX6pvqG7ecy893d3BGZVHWv1c21HocyWWGZ9I5FMzqL8ZcaiiT1kWxOJKhL6PnjxkdnRevK8v69yp2WvnzSxqXbVJMptWWOOgYnD1LPTU8lmzTzDdG66IEdLFwkqEvo+eO9tPkLUy25onZ1XgcjAQjvNY+TPtggNJCGz99pZ2PX3sGTrsFXzCSt/+Ojd5C+kbD0rooFkwC+jKJRGO82DrATWfV5HooK0JtfP/U2773UrJFEcBqNvG+SxoB8jZDb0xZ00VaF8VCSEBfJgc6ffhCkWUpt+SD2vhqlN0jIa7bUskl67zsbR/mx7vaObPOCHL5nKEDtPb5JaCLBZGAvkyO9o4CsLnaneORrAx1nolgfetla7mgqZT2wQA/393Bv/32CEBedrlA6qqLUkcXCyM3RZfJxKJc+ZlVZprXZcdmNuEusHDuGg9gTJq6ZF0ZXSNBlJq8UmM+SbQutvZJ66JYGAnoy+TkQIBKt50C68rsC19uJpOiudLFtVuqsJgn/pvedKaxyXRFkR2rOX//+26scrOnfSjXwxArTP7+RJxmTg4EsjrlPx/df/tF/P1btk46du3mKswmlbf184SL15XR0jOaXOJAiHRIQF8m7QOBvJ0Iky3uAuu0dzQlhTbee3ED122pytGolscl8Zvnzx2ddTVqIaaRm6LLIBSJ0jkSlAw9Qz7/5i25HkLWbakppqjAwvPH+rn57OxsSi3yj2Toy6BjcAyts7OphchPZpPiwqYyydDFgkhAXwYTm1pIQBfpO2eNh+P9AYYD47keilghJKBnWI8vyIfuf5VrvvYkL58YBIwlc0EydLEwiUlF+zuHczwSsVJIQF8irTUfeeBVHtvfBcCXfnWAR/d30dI7ypOHjY2wj/X5cdrMlOfZZgwiu7bUGJPQXj81kuORiJVi3oCulLpPKdWjlNo3y+NKKfUfSqkWpdRepdS5mR/m6Wv/qRF+vvsUj7zWycsnBvnlnlPcccU61pQ6OdpjzA5t6RllXbkLk2llrnwocsPrslPptrNfArpIUzoZ+neB6+d4/AagOf7nduC/lj6slePh1zoBaO0P8LNX23HZLdxxxVrWl7uS0/1bekZZX5H9NdBF/tlSU8z+U1JyEelJZ0/RncDAHKfcDHxPG54HPEqp6kwN8HQQjWnuf/Ek49HYpONa62RAP97n53DXKBurinDaLKyrcHGsz89IcJzO4aAEdLEoW2vctPSMMhaO5nooYgXIRA29FmhL+bw9fmwapdTtSqldSqldvb29GfjWy+OF1n4+/eBrPHFo8phP9Ac43h9grbeQ4bFx9rQPsaHK2CFoXXkh4UiMJ+Nfs65cArpYuEZvITENXSMyY1TMLxMBfabCsJ7pRK31PVrr7Vrr7eXl5Rn41suja9j4YUq0HyZ0x3/IrjjDuJZQJJbc8i2RkT8av1kqGbpYjML4Jt/+UCTHIxErQSYCejtQn/J5HXAqA8972ujxGRsstE/ZEm0w3h98zpqS5LEN8YC+1msE8N8f6MFqVsklUYVYCFc8oI9KQBdpyERAfwh4b7zb5SJgWGvdmYHnPW0kMvG2gcmbFg8FwgCcWVtMooElsQF0SaGNSredsfEozRVFeb0yoMgeydDFQsy7lotS6n7gSsCrlGoHPg9YAbTWdwMPAzcCLUAAeH+2Bpsr82XoFW47tSUOxsIxylJ6zX9w20W0DQbYGK+rC7FQLruxOJlk6CId8wZ0rfUt8zyugQ9mbESL1DMS5NMPvsY/vf1MvBmewNM7kgjoY2itUcpIx4cCYWwWEw6rmUvXeQlP6YJZX+GS2rlYkokMXbpcxPzyZrXF51sHePxgD4/u6+LdFzVk9Lm742tSj4YifP6h/RRYzXzs2g0MBsKUOK0opfjK287M6PcUAqTkIhYmbwq7p4aM+vazR/uSxx7d18n2v/8dgfDifxi01vSMhJLrsHzvuRPcs/MYf/n9lxkMjFPitC1t4ELModAmN0VF+vIwoPcTixldk7/YfYq+0RCnhhbfwzsaijA2HuW8BqOTxWxSvPmsGp460kffaAiP07r0wQsxC7NJ4bCaJUMXacm7gD4UGOf1zhEi0RhPtxjZem/8puZidMfr5+fGA/oNW6u4fL2XaExzqMsnGbrIukK7Bf8S3mWK1SNvaugdQ0G21rrZ1zHCS8cHCI5H8QWNH4Le0cUF9INdI/zslQ7AmPn5jT87h/MbS2nt8wMQCEfxSEAXWeaymxmVm6IiDXkT0DuHx7jpzGoOd4/SNRJk0B9OPrbYDP1fHjvE7w70AFBRVMAl67yAsbZLQomUXESWFdotUnIRacmLkos/FGEoME6tx0m5y06vL8TBLh/rK1zYzKZFB/REJg5QXVyQ/LjSXYAtPlFISi4i2wrtFrkpKtKSFwG9c9ion9d4CigvMgJ690iQGo8j+TnA3/1yP//6m0NpPWc0pmkbGOMDlzfx4meuTraPgXGjqq7EAUCxZOgiy4okQxdpyouA3hHvYqlNCeCdw0Gq3Ha8RfZkDf0PB3uSJZT5dI0ECUdjNHldVBQVTHs8sT+oZOgi26TkItKVFwE90eGSyMg7h4P0jYaochckSzBgTOHvmDJ9fzYn4uWWxlkW1UostiU1dJFtRslFboqK+eVFQH/iUA9FdgsVRXbKXXaGx8aJaagqnsjYR0MRAuEoI8EIvuD8u6gf7zcCf4O3cMbHExONpMtFZJvLLn3oIj0rvstlT9sQj+3v5q/fuAGL2UR50cQ6LlXFdrqGbQz4Q3QNT6yU2DE0xsaquTPrEwN+bGYTVe7p5RaAG7dV0zkcpGmWgC9EphTaLYyNR4nGNGbZl1bMYcVn6Hc/eZTSQhu3Xt4EMCmgV7qNm6QxDQe7fMnjLT2j/M3PXuOcL/6GXcdn3l3vRF+A+lLHrD9ANR4Hn71ps/yAiaxLrIkuk4vEfFZ0hh6Jxnj6SB83nVWT/E+fGtCrix2UFxmlk9Sd0//lsUPJksoLrQNsbyyd9tzH+/00lkn2LXIvdYEud4HcsxGzW9EZ+t6OYXyhCJet9yaPlceXzrVZTJQ4rZTHO1Reazd2TlfKqI+vLS+kyl3AsV4/L58Y5Lmj/cnn6B4JcrDLx1n1nuW7GCFmISsuinSt6ID+bHytlovXlSWPJTL0SrcdpRQbKl0oBS+2DmAzm2iI38zc0VxOk7eQY32jfOGh/Xzhof3J53gsvg/oDVurlutShJjVxCYX0uki5pZWQFdKXa+UOqSUalFKfWqGx4uVUr9USu1RSu1XSi3LrkVPt/SxpcZNaeFEp0mB1Yy7wEK125j4U1RgpbnCRTgao7zITl2JEdAvW++lqbyQlu5RDnSO0D4YwNirAx5+rZP1FS6aK2WnIZF7iSV0JUMX85k3oCulzMA3gRuAzcAtSqnNU077IPC61vosjO3q/lUpldV+vkA4wisnhiaVWxKaK4s4I2Xbt7PjpZPyIjv1pQ4sJsVF68pY6y3EF4oQiWn84SjDY+MM+sO82Dog2bk4bSRKLonF5hK01tz3dCt9i1x8TuSfdG6KXgC0aK2PASilHgBuBl5POUcDRcrYm80FDABZTSdeOj5IOBrjkhkC+vdvvWBS98lZ9R5+tKud8iI7f7ljHVdvrMRlt0xrOWwfHONEf4CYhivPqMjm8IVIW0W8jNjjm7yu//H+AF/81esM+MN8/LozcjE0cZpJp+RSC7SlfN4eP5bqG8Am4BTwGvBhrXWMLHqmpQ+b2cT5jSXTHnPaLNgt5uTniQy9oshOo7eQN26uBEgG9ETsbx8M8MzRPlx2C2fVFWdz+EKkrbzIjsNq5njf5FnOnfEZ0juP9OZiWOI0lE5An6nRWk/5/DpgN1ADnA18QynlnvZESt2ulNqllNrV27u4/4THekd5970v8Jv9XZzb4MFpm/9NxhmVRawpdXLmlCBdX+o0yi9rjZuq7YNjPNPSx0VrS7GYV/T9YpFHlFI0lDk50e+fdPzUsJGxv9YxzEDKctFi9UonarUD9Smf12Fk4qneDzyoDS1AK7Bx6hNpre/RWm/XWm8vLy9f1IDbBsfYf2qY4/0BLl03vdwyE4vZxM5PXMU7zl8z6bjVbOILf7SFT16/EZfdwgutA5zoD3DpDGUcIXKpsayQ4/1+vvN0K/c+dQwgOftZa5K7c4nVLZ2A/hLQrJRqit/ofCfw0JRzTgJXAyilKoEzgGOZHGjCFRvK+cPHr+SzN23mvRc3Lvn53n1RA2fVe6grcfD4ge7k9xDidNLgddI2MMZ/PdHCvU+1AkaG7nFa8Tit7DwsZReRxk1RrXVEKXUX8BhgBu7TWu9XSt0Rf/xu4EvAd5VSr2GUaD6ptc5ayuBx2rj1sqaMPmddiYODXT52bChnbbkro88txFI1lhUSjsboGzVKK13DQTqHxqj1OGj0FvLUkV601hh9CWK1Smvqv9b6YeDhKcfuTvn4FHBtZoe2vBL96R+4PLO/KITIhIYpyzjvaR+iczhIXYmTHc1efr23k0PdPjZWTbt1JVaRFb2WSya95Zxa7FbTjH3tQuRaYl2hWo+D7pEge9qMgH5+Yyk74iXCpw73SUBf5aSVI+7seg+fvmGTvGUVp6UqdwFFdgtXb6pgY3URzx3rZ3hsnGpPAdXFDporXNK+KCSgC7ESmEyKB++8hI9fdwbn1Jfw6skhAGqKjSUuzlnjmbREtFidJKALsUI0VxbhLrByW8p9nupiYzXRNaVOen0hxsKygNdqJgFdiBWmoayQRz58OW85u4attcZkucSm5W3xReb+e+cxDnaNzPU0Ig9JQBdiBdpU7ebr7zwnuXBXYo/bk/0B9rYP8w8PH+C933mRrvhs0mhM84vdHQTHJYPPZxLQhcgDDfEumJMDAR7e14nFpBgNRfjyIwcAeOClk3z4gd08fqAnl8MUWSZti0LkgRKnFZfdwsmBAH841MMl670UO6y81DrAWDjKv//uCGAsQCfyl2ToQuQBpRT1pU5++3o3J/oD3LC1irPqijk1HOTuJ4/S4wthNik64is0ivwkGboQeWJNqYPH9o/gcVq5cVs1LT1GG+M9O4+xvsKF1Wzi1NAYsZhGKWTORR6SDF2IPJG4MXrXVespdljZUlOM2aQYG49yw9Yqaj0FtA+O8cH/fYWP/XhPjkcrskEydCHyxLVbqjg1HOQ9FzcAxv66G6uK2H9qhBu2VjM8Ns4LxwZoGwjIAnR5SgK6EHni/MZSzm8snXTs6k2VWMwmNlUXUeNx4ItvND00Jhti5CMJ6ELksY9es4GPXrMBMBb2ShgKjOdqSCKLpIYuxCpRkxLQfcEI0djUnSTFSicBXYhVIjVDBxgZkyw930hAF2KVqCiy4y6wJLthhiSg5520ArpS6nql1CGlVItS6lOznHOlUmq3Umq/UurJzA5TCLFUJpPi0Y/s4G9uNPZvHwrIjdF8M+9NUaWUGfgmcA3QDryklHpIa/16yjke4FvA9Vrrk0qpiiyNVwixBDUeB10jxoJdkqHnn3Qy9AuAFq31Ma11GHgAuHnKOX8GPKi1PgmgtZYVgIQ4TXkcVgCGpdMl76QT0GuBtpTP2+PHUm0ASpRSTyilXlZKvXemJ1JK3a6U2qWU2tXbK9tlCZELHqcNkJJLPkonoM+04MPUficLcB7wJuA64LNKqQ3Tvkjre7TW27XW28vLyxc8WCHE0rkLjEqrlFzyTzoTi9qB+pTP64BTM5zTp7X2A36l1E7gLOBwRkYphMgYi9lEUYFFJhfloXQy9JeAZqVUk1LKBrwTeGjKOb8ALldKWZRSTuBC4EBmhyqEyBSP08qwZOh5Z94MXWsdUUrdBTwGmIH7tNb7lVJ3xB+/W2t9QCn1KLAXiAH3aq33ZXPgQojF8zhsUkPPQ2mt5aK1fhh4eMqxu6d8/lXgq5kbmhAiWzxOq9TQ85DMFBViFSp2WKVtMQ9JQBdiFfI4rfT6QhzsGuHjP97D8T5/rockMkACuhCr0I1bqwlFYlz/9af4ycvtPHFI5gLmAwnoQqxCl6z38t2/OJ83bDRW6ej3yw3SfCABXYhV6pJ1Xu573/l4XXb6RkO5Ho7IAAnoQqxyXpeNXp9k6IsRikQB+MgDr3L/iydzPBoJ6EKseuVFkqEvxssnBtn2+d/w/eeO8/Pdp/jd6925HpIEdCFWOym5LM7+U8OEozE++4v9AHQMjeV4RBLQhVj1jJJLCK1lj9GF6BicHMBPSUAXQuSa12UnFIkxGorkeigrSsfQGHUlDv7qDet590VrGAlG8AVzO1lLAroQq5zXZQegb1RujC5Ex9AYDWVOPnbtGVzYVAbAqaFgTsckAV2IVa68KBHQpY6+EB2DY9R6HICxtR/kvuwiAV2IVS6ZofskoKcrFInS4wslA3kisLdLQBdC5JK3yNiSTjL09HUNG6WVRCCvKLJjNSvJ0IUQuVXqtKEU9EqGnrZEh0ttiRHQTSZFVXGBBHQhRG5ZzCbqShz8+rVOWVI3TYnSSiJDB6gpdkxrZVxuaQV0pdT1SqlDSqkWpdSn5jjvfKVUVCn19swNUQiRbf/8trM4ORDgb37+Wq6HsiKc7A+gFFQVFySPbap2s+/UMP4ctn/OG9CVUmbgm8ANwGbgFqXU5lnO+yeMreqEECvIxevKeNO2anafHMr1UFaE3x3o5rw1Jdgt5uSxG7dVExyP8bsDuVsCIJ0M/QKgRWt9TGsdBh4Abp7hvL8CfgrIwspCrEA1HgfdI0FiMZkxOpeWHh8Hu3zcdGb1pOPbG0qochfwyz2dORpZegG9FmhL+bw9fixJKVULvBWYtM+oEGLlqC4uIBLT9Pnl5uhcfrmnE6WMjDyVyaS4cVs1Ow/3EhyP5mRs6QR0NcOxqb/Cvw58Ums951UopW5XSu1SSu3q7e1Nc4hCiOVQVWzc4Eu05ImZPXWkl3PXlFDhLpj22OYaN+FoLGf/hukE9HagPuXzOuDUlHO2Aw8opY4Dbwe+pZR6y9Qn0lrfo7XerrXeXl5evrgRCyGyojp+g68zHowCYVnbZSqtNUe6R9lS457x8Zop/4bLLZ2A/hLQrJRqUkrZgHcCD6WeoLVu0lo3aq0bgZ8Ad2qtf57pwQohsifRsdE1HKTHF+TCf3icj/94j9TUU3QOB/GFIjRXFs34ePLfcCQ37YuW+U7QWkeUUndhdK+Ygfu01vuVUnfEH5e6uRB5oNRpw2Y20Tkc5Nd7O/GFIvzk5XbCkRhfunkrxU5rroe4rP7x4QOYlOJTN2xMHjvc7QOgucI149ckAnquFumaN6ADaK0fBh6ecmzGQK61ft/ShyWEWG4mk6Ky2E7X8BjPHetnc7WbG7dV8W+/O8Lzx/r5i8uaONEf4OPXbqAsvv5LPrtn5zEA7rhiLR6nsTxCS88oABtmydCdNgvFDutpXUMXQqwS1W4HzxztZ0/bEG85p4a73tDMz++8lNJCG1955CD3v3iSn7zcnuthLqvU6z3c7cPrslFaaJv1/OrigtO6hi6EWCUqiwvo9YUotJl5yzlGd/K2umIeuusyfv+xK9hc7ea3p8HemdmmtcZiMhr8Ujd/Ptw9SnPFzNl5QnVxQc5q6BLQhRBJ0VgMgE9cv5GKoom2PJvFxNpyF9duqeTlk4N5vzJjIBwlEtOUFdo42utn0B9Ga83RnlGaK2eunydUFTvozFENXQK6ECLprquaueuq9bz7ooYZH792cxVaw2P7u5Z5ZMtraMxYpOyyZi8Ar3UMM+AP4wtFaCwrnPNrq4sL6PeHczK5SAK6ECJpc42bj193BmbTTPMJYVN1Edtqi/mPx4/k9R6kiVUnL103EdBPDgQAWFPqnPNrE/38PSPL/y5GAroQIm1KKb548xZ6fCG+8fuWXA8na4bjGXpdqYMmbyF724cmAnrZ3AE9sYvRiQF/dgc5AwnoQogFOWdNCZeu8/J0S2aX7+gZCXLdv+3kBy+cyOjzLsbwmLFhdrHDytbaYvZ1jNAWD+j1JXMH9LPqPVjNiqeO9GV9nFNJQBdCLNj6ChetvX60zsws0vFojNu+t4tD3T4eeS339flEhl7ssHJmbTEdQ2O8fGKQiiI7Dpt5zq912S1ctLaMx3OwjK4EdCHEgq0rL8QfjtKdoTrx3vYh9rYPU+tx8MrJQSLRWEaed7ESAd3jtHHJ+jIAnjjcO2/9POENGys42uvneN/yll0koAshFmxtudG6d6x3NCPPd7zPKGe88/x6AuEor3eOZOR5F2soMI7ZpCi0mdlc7aauxIHW89fPE67eWAnA7w8u7/YQEtCFEAu2ttxo3TuaoQz0eL8fs0klJzO9dHwwI8+7WMNj4xQ7rCilUEpx/ZYqYP4Ol4Q1ZU6aK1wS0IUQp78qdwFOm5mjPRnK0PsD1Hoc1Jc6qS918NzR/ow8bzq+99xxnjg0OfAOjY3jcUwsRnbDNiOgJ96ZpOMNmyp4obUfX3D5Nt6WgC6EWDClFGvLCzmWoQz9RL+fhng544at1fz+YPekcs7xPn+yN3yq/3z8CO/5zguLukEbicb4x4cPcN8zxycdHxkbx50S0M9rKOVHf3kxN2ytSvu5r95YyXhU8/QydrtIQBdCLMparysjNXStNa19fpq8Rhnn9h1rsVvMfO23h9Fao7XmHfc8x9/+Yt+0rx2Pxvjus8d56kgfu9uGFvy9D3ePEhyPTbuORMkl1QVNpVjN6YfMc9d48Dity1p2kYAuhFiUhjInncPBJXekDAbG8QUjNMSn1Htddm69rIlf7e3kzh+8QvdIiO6REI8f6J40nf7RfV3c/+JJ+v1Gz/iPdrURiixsuv2e9iEAOobGGAtPfO1QYBzPEtd/t5hNnFnn4WCXb0nPs6DvuWzfSQiRV2o8DqIxTY8vlJwdmY5oTPOue58nFoPbLm/CW2Ssrd6Y0kHy0Ws2YDIp/uPxI8nMPRCO8uThXq7bUsWgP8wd/9/LgNErfsWGcu5/sY37X2yjrsTBl/94G5c3T9/m8r93HsMXivDRazYAsCee1WsNrX1+Nse3lpspQ1+MdeWF/PD4AFprlDKWU3ixdYDGMueMe5IulWToQohFqU7uzrOwpWJb+/w8f2yAF48P8J2nWznRb9ThG70Ti16ZTIpbL2sCJtYjd1jNPLrPmHTUNTKxmuHtO9by19ds4JYL1vChq5vpGQnxxKHps1i11tz3TCs/fbmdSDTGL3Z38OLxASrdxi+UXScG+JfHDvHBH7zC8Nh4clOLpVhX7iIQjibHG41p3v2dF7j36dYlP/dM0srQlVLXA/+OsQXdvVrrr0x5/F3AJ+OfjgL/R2u9J5MDFUKcXmrjWfmpBW7mcCDeY35GZRHtg2O09gUwKagrmZzlFzusNFe4ONIzSrHDyqXry3j1pNHO2B0PkD/9PxdzXkMpAF/+420A/HhXW3JiUKqTAwE6h4OYFPzm9W4+/MBuAD5weRP3Pt3Kl371OtGYpspdwC0X1HPLBfULuq6ZrIt3xRzt8VNd7KB9MEA4EmNd+dwrNi7WvBm6UsoMfBO4AdgM3KKU2jzltFbgCq31mcCXgHsyPVAhxOmlOhHQF5ihH+gcwWJSXLWxglPDY7T0+KjxOLBbpk+pP3dNCQAbKl1UFzvo8YXQWicDeuqa7QnFDitDM3TEJFohYxqeOmJk8P/3ujP4wOVrqfU4GI9q3ndJE89++mq+/MdnUl2cfhlpNusq4v368Zuuib/Xz7In6VKlU3K5AGjRWh/TWoeBB4CbU0/QWj+rtU7MBHgeqMvsMIUQpxuX3YK7wLLggH6wy8e6chfrK1xobQTa2dYYP7fBA0BzZRGVbjuBcJTRUCS55ECFe/repsUOKyMzZOjPH5vobX/yUC+VbjsfvGo9Fe4C1pW7MJsUf3FZ44KuZT7lLjtFBZZkIE/sSbpuAf3sC5FOQK8F2lI+b48fm82twCMzPaCUul0ptUsptau3N7MrtQkhll+Nx7GoDH1TdRH18RLLYGCcRu/MMzAT5ZRN1W4q4zcRja6XIKWFthmz+mKHdcaSy0vHBzmr3gMYZaK13omgescV6/jyW7dRN89Kigtl9Ou7JgV0r8uWkfr8TNIJ6DOtdD9jB79S6iqMgP7JmR7XWt+jtd6utd5eXj79DrQQYmWp9Tg4tYDt1oYCYTqHg2yqdk9aF2W2DH19hYsf3HYhf3JeXbK80jMSpHskREXR9OwcwOO0MhRf/jZBa02vL8SFTaXJzTvWptSxL15Xxp+ev/Sa+YzXUO7iUNcoWmtaekazlp1DegG9HUi90jrg1NSTlFJnAvcCN2utl2/erhAiZ6o9BZwaTj9D39dh3BDdVO2msqgAW3yiTsMc27pdut5LgdWc7Ebp9gXp8QWTGftUM2XowfEY4WiMEqeNGo/xdQuZxr8UZ6/x0Dca4uRAgKO9/qzVzyG9gP4S0KyUalJK2YB3Ag+lnqCUWgM8CLxHa30488MUQpyOajwOhgLj+NPcju75Y/2YTYpzG0owmRR1pUbZpTGNVQwrppRcKmeon4MR0IPjsUmTjEbi66m4HZbkBhVrvdnpNJnqgkajbPTovi6Gx8Zzm6FrrSPAXcBjwAHgR1rr/UqpO5RSd8RP+xxQBnxLKbVbKbUrayMWQpw2ahfY6fLs0T7OrCvGZTc6putLnCgF9WmsYuiyW3DZLXQOjdHrC82eocfr06lZeuqGFcmAnqXWwamaK1wUO6x864mjAJyzxpO175VWH7rW+mHg4SnH7k75+DbgtswOTQhxuksE4rbBAM2VRXOe6w9F2Ns+zO071iaPXbi2lEA4QoF17l2AEircdl7vHCGmmXWmZWKG53BgPFl3T3S9uAusnNdYwrPH+jJ+A3Q2JpNie0MJjx/s4fzGEs6Jt2Jmg0z9F0IsWiLbPdkfmPfcl44PEIlpLl5Xljx255XrufPK9Wl/v8qiAl6OTy6qnOWmaDKgz5Kh79hQzp9uz84N0Nmc31TK4wd7uPOq9K91MSSgCyEWzeuy4bCaOTkwf8llX8cwMDFZaDEq3HbCkRgWk2JTtXvGczwzBPSJGvrS12dZjHdduIbGMidXbshud5+s5SKEWDSlFGtKnZwcMDJ0rTW/2nuKe586Nu3czuEgHqeVQvvi88jx+MqOt17eNGvdfcYMPZAoueQmhy0qsHL91urkAl3ZIhm6EGJJ6kudyTVKPvzAqzwSX0DrXRc24LBN1Ma7R4JULXGFwT+7oAFfMMKH3tA86zmJgJ46/X8kaHTh5CpDXy6SoQshlqS+1MHJgQAf+aERzC9db9TIO6f0p3eNzN47nq7Lmr18/9YL58zy3bPU0J0284I2qFiJ8vvqhBBZt6bUSSAc5eHXuvjYNRv4YPzGX9eUVRi7hkNLztDTYTYpigosk2voGVrf/HQnJRchxJKsideyvS47H9ixls54IO9MCejj0Rj9/hBVxdkP6DB9tujw2DjugvwP6JKhCyGWJDHz8fYdTRRYzcmNL1I3oTCWvWXZArrHaaW1z08sZiw7NRJcHRm6BHQhxJI0egt5+EOXc9tlxoShAquZEqd10uzRRPllOUouAG87t47dbUN86devAzA8FsHtyP+ChAR0IcSSba5xYzJNtORVFTsm1dATG1Is9aZout5/aRNvP6+O7z13gnAkxsjYeN53uIAEdCFEFtQUFyRr6L2+EK19xr6hy1VyAbi82Us0pmnt8zMSXB019Px/DyKEWHZVxQW82jYEwDvueY5jvUZAL3EuX1BtrjDWljnYNYIvGJEauhBCLEZ1cQED/jDDgfFkMAeyPlMy1dryQkwKXjlhrP2yGkoukqELITIuscHy863GXjd3XrmOHVlex2SqAquZhrJCdh7pA5b33UGuSIYuhMi4hviGFb97vRuA67dWcdHasrm+JCuaK1y09vmxWUxceUbFsn//5SYBXQiRcZtr3JhNikfj67o0LtPuQFNtiK/R/kdn1VBamJ2NmU8naQV0pdT1SqlDSqkWpdSnZnhcKaX+I/74XqXUuZkfqhBipXDaLDRXuPCFIpQV2nLWYXJ2vQezSfH+Sxtz8v2X27wBXSllBr4J3ABsBm5RSm2ectoNQHP8z+3Af2V4nEKIFeasOg+Qu+wc4OpNFTz/6avZUlOcszEsp3Qy9AuAFq31Ma11GHgAuHnKOTcD39OG5wGPUqo6w2MVQqwgZ9V7AGgsy11AV0pRPsvORvkonYBeC7SlfN4eP7bQc4QQq8iZdUZW3ORdnr07RXoBfabGUb2Ic1BK3a6U2qWU2tXb25vO+IQQK9Smajd3XbWem8+W3G65pBPQ24HUHVXrgFOLOAet9T1a6+1a6+3l5cvbkyqEWF5mk+Lj150x61ZxIvPSCegvAc1KqSallA14J/DQlHMeAt4b73a5CBjWWndmeKxCCCHmMO9MUa11RCl1F/AYYAbu01rvV0rdEX/8buBh4EagBQgA78/ekIUQQswkran/WuuHMYJ26rG7Uz7WwAczOzQhhBALITNFhRAiT0hAF0KIPCEBXQgh8oQEdCGEyBMS0IUQIk8oo0ElB99YqV7gxCK/3Av0ZXA4K4Fcc/5bbdcLcs2L0aC1nnFmZs4C+lIopXZprbfnehzLSa45/6226wW55kyTkosQQuQJCehCCJEnVmpAvyfXA8gBueb8t9quF+SaM2pF1tCFEEJMt1IzdCGEEFOsuIA+34bV+UApdVwp9ZpSardSalf8WKlS6rdKqSPxv0tyPc6lUErdp5TqUUrtSzk26zUqpT4df80PKaWuy82ol2aWa/6CUqoj/lrvVkrdmPLYir5mpVS9UuoPSqkDSqn9SqkPx4/n7es8xzUvz+ustV4xfzCW7z0KrAVswB5gc67HlYXrPA54pxz7Z+BT8Y8/BfxTrse5xGvcAZwL7JvvGjE2J98D2IGm+P8Bc66vIUPX/AXg4zOcu+KvGagGzo1/XAQcjl9X3r7Oc1zzsrzOKy1DT2fD6nx1M/A/8Y//B3hL7oaydFrrncDAlMOzXePNwANa65DWuhVj3f0LlmOcmTTLNc9mxV+z1rpTa/1K/GMfcABjr+G8fZ3nuObZZPSaV1pAXy2bUWvgN0qpl5VSt8ePVer4LlDxvytyNrrsme0a8/11v0sptTdekkmUH/LqmpVSjcA5wAusktd5yjXDMrzOKy2gp7UZdR64VGt9LnAD8EGl1I5cDyjH8vl1/y9gHXA20An8a/x43lyzUsoF/BT4iNZ6ZK5TZziWL9e8LK/zSgvoaW1GvdJprU/F/+4BfobxFqxbKVUNEP+7J3cjzJrZrjFvX3etdbfWOqq1jgH/zcTb7by4ZqWUFSOw/UBr/WD8cF6/zjNd83K9zistoKezYfWKppQqVEoVJT4GrgX2YVznn8dP+3PgF7kZYVbNdo0PAe9UStmVUk1AM/BiDsaXcYnAFvdWjNca8uCalVIK+A5wQGv9tZSH8vZ1nu2al+11zvVd4UXcRb4R487xUeAzuR5PFq5vLcZd7z3A/sQ1AmXA48CR+N+luR7rEq/zfoy3nuMYWcqtc10j8Jn4a34IuCHX48/gNX8feA3YG//hrs6XawYuwygf7AV2x//cmM+v8xzXvCyvs8wUFUKIPLHSSi5CCCFmIQFdCCHyhAR0IYTIExLQhRAiT0hAF0KIPCEBXQgh8oQEdCGEyBMS0IUQIk/8/8FRgW8F8YFcAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 기초자산 \"주식(Stock)\" 움직임 생성\n",
    "dS = np.random.randn(N) * np.sqrt(dt)\n",
    "S = np.cumsum(dS)\n",
    "S = S - S.min()\n",
    "plt.plot(S)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "708cb4b8",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-07-04T11:30:44.115967Z",
     "start_time": "2022-07-04T11:30:44.009966Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "array([0.40291098, 0.43612543, 0.57616603, 0.48850084, 0.51540617,\n",
       "       0.50156568, 0.45826883, 0.37012942, 0.20520508, 0.1748504 ,\n",
       "       0.26008803, 0.18966076, 0.15320123, 0.28432068, 0.26859918,\n",
       "       0.2060214 , 0.32035091, 0.30360969, 0.36840497, 0.3920704 ,\n",
       "       0.43283445, 0.52651278, 0.61357706, 0.60035713, 0.62914192,\n",
       "       0.62677584, 0.63912204, 0.62582578, 0.7083094 , 0.73354251,\n",
       "       0.79289299, 0.75101911, 0.68976734, 0.72070527, 0.69318243,\n",
       "       0.80357568, 0.88503127, 0.82481979, 0.88279637, 0.87875371,\n",
       "       0.83651875, 0.76760235, 0.81267159, 0.71130452, 0.74423573,\n",
       "       0.8486449 , 0.84866012, 0.75561526, 0.71130062, 0.59140868,\n",
       "       0.6825812 , 0.58593354, 0.58136499, 0.54829518, 0.4796851 ,\n",
       "       0.33968409, 0.28517307, 0.28610395, 0.3291914 , 0.42039914,\n",
       "       0.51502288, 0.54533978, 0.45305557, 0.4470682 , 0.41264307,\n",
       "       0.3888866 , 0.35183368, 0.27030064, 0.20106881, 0.21197052,\n",
       "       0.3118236 , 0.33646549, 0.3210766 , 0.36549943, 0.42803725,\n",
       "       0.45221833, 0.48499178, 0.57291409, 0.64790224, 0.61846496,\n",
       "       0.65633692, 0.58155645, 0.56597314, 0.5994173 , 0.56781506,\n",
       "       0.54268707, 0.45833332, 0.44357764, 0.44529244, 0.44051607,\n",
       "       0.51017044, 0.43917733, 0.45049228, 0.41729461, 0.4155724 ,\n",
       "       0.43641488, 0.3933703 , 0.35717663, 0.32909663, 0.28651355,\n",
       "       0.2802063 , 0.27200875, 0.30422045, 0.37092861, 0.29970121,\n",
       "       0.28188191, 0.2908678 , 0.26963431, 0.2929095 , 0.33204747,\n",
       "       0.35775406, 0.3054746 , 0.37079115, 0.30428626, 0.21622932,\n",
       "       0.2606735 , 0.24437474, 0.20876799, 0.20143244, 0.20671264,\n",
       "       0.19169513, 0.20734904, 0.22732603, 0.1071867 , 0.04135971,\n",
       "       0.09082141, 0.03161721, 0.04472772, 0.        , 0.12407351,\n",
       "       0.09216699, 0.06805444, 0.16485705, 0.1734812 , 0.27697129,\n",
       "       0.24372705, 0.30923009, 0.25942641, 0.15334713, 0.28749419,\n",
       "       0.30211696, 0.31942572, 0.33793357, 0.39355131, 0.4015013 ,\n",
       "       0.36111192, 0.31728131, 0.36245295, 0.28708831, 0.20145977,\n",
       "       0.18782271, 0.286586  , 0.34789095, 0.44796325, 0.42386123,\n",
       "       0.39570195, 0.35123896, 0.46499487, 0.51973202, 0.49526192,\n",
       "       0.50180103, 0.62646523, 0.73618413, 0.75223267, 0.71685016,\n",
       "       0.81745132, 0.7400411 , 0.76498865, 0.79193736, 0.79882611,\n",
       "       0.80942611, 0.63146052, 0.74524927, 0.77029466, 0.88970277,\n",
       "       0.91369609, 0.85427754, 0.85107819, 0.93119904, 0.85090763,\n",
       "       0.84712776, 0.78845417, 0.73472688, 0.7207788 , 0.8068321 ,\n",
       "       0.85166439, 0.89421057, 0.96565499, 1.07441782, 1.05480366,\n",
       "       1.09548974, 1.07425386, 1.22899795, 1.07479117, 1.12330068,\n",
       "       1.05005928, 1.02968971, 0.93591475, 0.92471185, 0.94267696,\n",
       "       0.98831365, 1.03289095, 1.01111336, 1.00161733, 0.93432522,\n",
       "       0.87494661, 0.82841446, 0.86145573, 0.97361094, 1.10418797,\n",
       "       1.0910886 , 1.04331105, 1.04039558, 0.96756819, 0.96910314,\n",
       "       0.98320205, 0.90327458, 0.80276747, 0.79868991, 0.77906403,\n",
       "       0.68672921, 0.70864051, 0.70112134, 0.68229448, 0.78672018,\n",
       "       0.75965515, 0.93823992, 1.02036074, 0.96516629, 0.99902543,\n",
       "       1.00272469, 0.97248013, 0.89720759, 0.82976009, 0.81030446,\n",
       "       0.74261148, 0.68942612, 0.65886885, 0.76604214, 0.8068959 ,\n",
       "       0.74027046, 0.71946527, 0.6972423 , 0.80447097, 0.8182353 ,\n",
       "       0.8604879 , 0.94409449, 1.00514599, 0.92985168, 0.8019501 ,\n",
       "       0.90195508, 0.80960637])"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 내부변수를 입력으로 기초자산을 출력으로하는 함수생성 및 실행\n",
    "def stock_movement(T):\n",
    "    N = T*252\n",
    "    dt = T/N\n",
    "    dS = np.random.randn(N) * np.sqrt(dt)\n",
    "    S = np.cumsum(dS)\n",
    "    S = S - S.min()\n",
    "    plt.plot(S)\n",
    "    plt.show()\n",
    "    \n",
    "    return S\n",
    "\n",
    "T = 1\n",
    "S = stock_movement(T)\n",
    "S"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4a72aaf7",
   "metadata": {},
   "source": [
    "\\begin{align*}\n",
    "dS &= \\epsilon \\sqrt{dt} \\\\\n",
    "\\text{기초자산의 변화} &= \\text{임의 숫자 } \\times \\text{ 시간변화 반영을 위한 스케일링 변수} \\\\\n",
    "F &= Se^{(r-d)T} \\\\\n",
    "\\text{선물가격} &= \\text{기초자산 가격 } \\times \\text{ 만기까지 남은 시간에 따른 이자 반영} \\\\\n",
    "\\end{align*}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "e582ef5d",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-07-04T11:32:42.227791Z",
     "start_time": "2022-07-04T11:32:42.111791Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 주식가격을 입력으로 선물가격을 출력으로하는 함수생성 및 실행\n",
    "def future_price(S, r, d):\n",
    "    F = []\n",
    "    for time, S_day in enumerate(S):\n",
    "        t_ramain = S.shape[0] - (time +1)\n",
    "        F_day = S_day * np.exp((r-d)*t_ramain)\n",
    "        F.append(F_day)\n",
    "        \n",
    "    return F\n",
    "\n",
    "F = future_price(S, 0.02, 0.015)\n",
    "SF = pd.concat([pd.DataFrame(S, columns=['Stock']), \n",
    "                pd.DataFrame(F, columns=['Future'])], axis=1)\n",
    "plt.plot(SF)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "426fbb0b",
   "metadata": {},
   "source": [
    "\\begin{align*}\n",
    "dS &= \\epsilon \\sqrt{dt} \\\\\n",
    "\\text{기초자산의 변화} &= \\text{임의 숫자 } \\times \\text{ 시간변화 반영을 위한 스케일링 변수} \\\\\n",
    "C &= S N(d_1) - K e^{-rT} N(d_2) \\\\\n",
    "P &= -S N(-d_1) + K e^{-rT} N(-d_2) \\\\\n",
    "\\end{align*}\n",
    "\\begin{align*}\n",
    "\\text{(주식을 살수/팔수 있는 권리인 콜옵션/풋옵션 가격)}\n",
    "\\end{align*}\n",
    "\n",
    "<span style=\"color:red\">$\\Rightarrow$ **\"블랙-숄즈 방정식은 1) 구매가, 2) 현재가, 3) 기간, 4) 이자율, 5) 유동성으로 예상 가격을 계산\"**</span>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "73eb7bed",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-07-04T11:36:32.324765Z",
     "start_time": "2022-07-04T11:36:32.095795Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 주식가격을 입력으로 콜옵션&풋옵션을 출력으로하는 함수생성 및 실행\n",
    "def option_price(S, K, r, sigma, option_type):\n",
    "    OV = []\n",
    "    for time, S_day in enumerate(S):\n",
    "        t_remain = S.shape[0] - (time +1)\n",
    "        d1 = (np.log(S_day/K) + (r+0.5*sigma**2) * t_remain) / (sigma*np.sqrt(t_remain))\n",
    "        d2 = d1 - sigma * np.sqrt(t_remain)\n",
    "        \n",
    "        if option_type == 'call':\n",
    "            OV_day = S_day * stat.norm.cdf(d1) - K * np.exp(-r*t_remain) * stat.norm.cdf(d2)\n",
    "        else:\n",
    "            OV_day = -S_day * stat.norm.cdf(-d1) + K * np.exp(-r*t_remain) * stat.norm.cdf(-d2)\n",
    "        OV.append(OV_day)    \n",
    "    \n",
    "    return OV\n",
    "\n",
    "C = option_price(S, 1, 0.01, 0.25, 'call')\n",
    "P = option_price(S, 1, 0.01, 0.25, 'put')\n",
    "SFCP = pd.concat([pd.DataFrame(S, columns=['Stock']), \n",
    "                  pd.DataFrame(F, columns=['Future']),\n",
    "                  pd.DataFrame(C, columns=['Call Option']), \n",
    "                  pd.DataFrame(P, columns=['Pup Option'])], axis=1)\n",
    "SFCP.plot()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "2f62f03d",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-07-04T11:38:53.863733Z",
     "start_time": "2022-07-04T11:38:53.565769Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 수십년간 수많은 학자들의 노고로 탄생한 노벨경제학상 결과물을\n",
    "# 코드 몇줄로 지금 바로 완성 가능!\n",
    "T = 1\n",
    "S = stock_movement(T)\n",
    "F = future_price(S, 0.02, 0.015)\n",
    "C = option_price(S, 1, 0.02, 0.25, 'call')\n",
    "P = option_price(S, 1, 0.02, 0.25, 'put')\n",
    "\n",
    "SFCP = pd.concat([pd.DataFrame(S, columns=['S']), \n",
    "                  pd.DataFrame(F, columns=['F']),\n",
    "                  pd.DataFrame(C, columns=['C']), \n",
    "                  pd.DataFrame(P, columns=['P'])], axis=1)\n",
    "SFCP.plot()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d434876d",
   "metadata": {},
   "source": [
    "## 빅데이터 및 데이터사이언스 시대\n",
    "\n",
    "> **\"인터넷과 정보통신, 그리고 관련 기기장치들의 발달로 인간이 남기는 `모든 것들이 데이터로 측정되어 저장`되는 시대\"**\n",
    ">\n",
    "> - 투자자들이 `방대한 양의 시장 움직임 데이터`를 `실시간`으로 획득 가능\n",
    "> - 아마존에서 판매되는 `수백만가지 상품 가격 데이터를 실시간 획득` 가능하고 `실시간 인플레이션` 추정 가능\n",
    "> - 온라인 쇼핑몰의 `고객들 방문과 활동들을 모두 데이터`로 얻을 수 있고 기업의 `매출을 정확하게 추정` 가능\n",
    "> - 인공위성의 `이미지 데이터`들을 통해 `농작물 작황 상황`, `원유 생산 상황`, `기후 변화 상황`을 추정 가능\n",
    "\n",
    "---\n",
    "\n",
    "**0) 비즈니스와 시장의 변화:**\n",
    "\n",
    "- 인플레이션을 알기 위한 `월간CPI`, 농작물이나 원유상황을 알기 위한 `USDA 농작물 리포트나 주간 원유 쿨착장비 수`, 그리고 매출상황을 알기 위한 `소매판매, 도매판매, 분기실적` 등의 데이터를 위해 과거에는 오랜시간이 소요되었고 `사후적으로 평가`되기 때문에 `효용이 체감되지 않고 신뢰성도 떨어짐`\n",
    "> - 국가가 발표하는 인플레이션 데이터보다 국민들은 `시장에서 이미 체감`함\n",
    "> - 농작물이나 원유 상황 리포트를 읽기도 전에 이미 `가격 폭등을 경험`함\n",
    "> - 리서치사들이 발행하는 기업들의 비즈니스 현황을 기다리기도 전에 `온라인 상에서 기업들의 이슈`를 더욱 빠르게 느끼고 있음\n",
    "\n",
    "<center><img src='Image/Basic/FE_Evolution_ToDS.png' width='600'></center>\n",
    "\n",
    "- `빅데이터와 컴퓨팅 파워` 덕분에 투자자/퀀트/분석가들은 더이상 전통적이고 느린 `저빈도 데이터가 불필요`\n",
    "- 각종 `대체 데이터`를 실시간 수집하여 `실시간 비즈니스 정보` 또는 `투자전략 및 의사결정 등`을 즉각적으로 반영\n",
    "- 빅데이터 더미 속에서 의미있는 정보인 `숨겨진 보석/인싸이트/아이디어`를 인간의 직관으로 발견하긴 어려워졌으나, 수학과 컴퓨터의 결합으로 고도화 된 `머신러닝/딥러닝`은 인간의 한계를 넘어 `매우 빠르고 의미 있는 결과물` 출력\n",
    "\n",
    "---\n",
    "\n",
    "**1) 빅데이터기반 데이터사이언스 반영을 위한 2가지:** 요리를 위한 `재료(빅데이터) 준비` 및 `레시피(통계추론/머신러닝/딥러닝) 연구`\n",
    "\n",
    "> **\"`현재 시장의 상황/트랜드`를 면밀히 파악하여 `어떤 전략을 생성`할 수 있을까?\"**\n",
    ">\n",
    "> **\"우리의 전략에 따라 `미래에는 어떤 매출이? 또는 어떤 일들이 일어날까?`\"**\n",
    ">\n",
    "> **\"만약 미래 결과가 좋지 않다면, `지금 우린 어떤 전략으로 방향을 수정`해야 최적의 효과가 나타나게 될까?\"**\n",
    "\n",
    "<center><img src='Image/Basic/DataScienceHowTo.png' width='800'></center>\n",
    "\n",
    "**(1) 빅데이터 수집:** 시장 트랜드를 가장 빠르게 파악할 수 있는 방법은 `실시간 수집되는 다양한 소스의 빅데이터`를 오랜시간 수집하고, 빠른 적용과 활용을 위해 `미리 데이터를 전처리 및 가공 필수`\n",
    "\n",
    "<center><img src='Image/Basic/BigData.png' width='500'>(LOTAME / DMP에서 수집 & 분석하는 이용자 데이터 예시)</center>\n",
    "\n",
    "> - `Web, CRM, Mobile, IoT, Social, Purchasing, Real-time Log 등` 의지만 있다면 다양한 경로를 통해 실시간 고객과 시장 변화 데이터 수집 가능\n",
    "> - `인공위성 이미지, 교통정보, 사물인터넷(IoT) 등` 각종 기기장치에서 고객과 사회가 `무의식적 행동 및 의사결정 변화 등`을 스스로 제공하고 있음\n",
    "> - `소셜 미디어, 평가 및 후기, 검색 기록 등` 실시간 고객 의견을 쉽게 확인 가능\n",
    "> - `거래내역, 신용카드 사용기록 등` 상품별 수요나 고객들의 현재 행동패턴들로 비즈니스 변화 쉽게 확인 가능\n",
    "> - 사람들을 사회에 적응시키기 위해 오랜시간 교육과정을 운영하듯, `천문학적 가치`로 커지고 있는 빅데이터를 다루고 `새로운 기술`들을 적용하기 위해선 `빅데이터를 사람이 이해할 수 있게` 미리 처리/가공 필요하고 단기간 수집이 어렵기 때문에 `오랜기간 인내심을 가지고 수집` 필요\n",
    "\n",
    "**(2) 분석 방법론 사용:** 수집된 빅데이터에서 보석을 찾기 위한 `통계추론/머신러닝/딥러닝 등`을 활용하여 분석할 수 있는 능력\n",
    "\n",
    "> **\"수집한 데이터가 많을수록 `더욱 정확하게 고객과 시장의 트렌드를 추적`할 수 있지만, 모든 데이터를 하나하나 다 들여다볼 수는 없는 노릇\"**\n",
    ">\n",
    "> **`경험 및 직감`** $\\rightarrow$ **`데이터집계`** $\\rightarrow$ **`통계추론`** $\\rightarrow$ **`기계학습/딥러닝`**\n",
    "\n",
    "- **데이터집계(Cross Table):** \n",
    "\n",
    "<center><img src='Image/Basic/CrossTableExample1.png' width='700'>(https://www.qualtrics.com/au/experience-management/research/cross-tabulation/)</center>\n",
    "<center><img src='Image/Basic/CrossTableExample3.png' width='600'>(https://www.qualtrics.com/design-xm/cross-tabulation/)</center>\n",
    "<center><img src='Image/Basic/CrossTableExample2.png' width='600'>(Measurement Of Customer Satisfaction On Demographic Variables Of Banking Sector In National Capital Region - An Empirical Analysis)</center>\n",
    "\n",
    "> - 정량적인 `하위 집단의 특성`을 파악하기 위해 `2차원` 형식으로 데이터를 요약하는 것\n",
    "> - 데이터집계는 다차원의 특성을 `2차원으로 축약`하여 해석하기 때문에 해석이 왜곡될 수 있고 `자의적인 해석`이 가능하도록 조작도 가능하며, `과거 특정시점에서의 특성 스냅샷(Snapshot)`이기 때문에 사실 `현재와 미래에는 맞지 않는 해석`을 가능성 높음\n",
    "> - `최근`에는 통계추론/기계학습/딥러닝을 사용하기 위한 `데이터 전처리 용도 또는 보고서 작성`용도로만 사용하는 편\n",
    "\n",
    "- **통계추론(Statistical Inference):** 소수의 데이터를 통해 `다수의 정보`를 추정\n",
    "\n",
    "<center><img src='Image/Basic/StatisticalInference.jpg' width='700'>(https://www.playnexacro.com/#show:techtip:268)</center>\n",
    "\n",
    "> - `적은 비용과 시간`으로 `전체 시장의 변화`를 파악하는데 도움 (ex. 출구조사)\n",
    "> - `실제 비즈니스 제도, 전략 또는 의사결정`을 생성하거나 변경할 때는 통계추론으로 `거시적 변화`도 필요하지만 `미시적 고객 변화`가 더욱 중요\n",
    ">> - 어떤 고객의 보험 가입을 승인?\n",
    ">> - 어떤 프로모션이나 이벤트가 고객들의 반응을 높일지?\n",
    ">> - 특정 상품이 어떤 조건에서 잘 팔리는지?\n",
    ">> - 비용을 최소화 하기 위해 재고량을 얼마나 확보?\n",
    ">> - 제조 공정상 데이터로 불량품 검출?\n",
    "\n",
    "- **기계학습(Machine Learning)/딥러닝(Deep Learning):** 데이터집계나 통계추론으로 분석하기 까다로운 `방대하고 복잡한 데이터`를 효과적으로 분석하여, 빅데이터 속에 숨겨진 인간이 발견하기 힘든 `다양한 고객과 시장의 변화 패턴 포착`\n",
    "\n",
    "<center><img src='Image/Basic/StatisticsMachinelearning.png' width='800'>(루이, 다빈치랩스)</center>\n",
    "\n",
    "> **\"어떤 문제가 나와도 당황하지 않고 시험을 잘 보기 위해서는..\"**\n",
    ">\n",
    "> **1. 작년도 기출문제(`스몰데이터`)가 도움이 될 수 있지만 문제의 특성과 범위가 매년 달라질 수 있으니 과거 20년치처럼 많은 기출문제(`빅데이터`)를 `학습`하는 것이 좋을 수 있습니다.**\n",
    ">\n",
    "> **2. 많은 기출문제를 풀어서 단순히 정답을 통째로 학습(`데이터집계 or 통계추론`)하는 것도 좋을 수 있지만, 적은 기출문제라도 풀이 방법과 과정을 학습(`기계학습`)하면 새로운 문제도 잘 풀어 시험을 잘 풀수 있습니다.**\n",
    ">\n",
    "> <center><img src='Image/Basic/HumanLearningMachineLearning.png' width='800'>(루이, 다빈치랩스)</center>\n",
    ">\n",
    "> - 인간의 암기력(`빅데이터`)은 물론이고 학습방식(`통계추론/기계학습/딥러닝`)을 모방한 수리통계와 컴퓨터의 융합으로 개발된 `알고리즘 기술`을 사용하여 시험문제 해결\n",
    ">\n",
    "> | **인간/엑셀** \t| **알고리즘 기술** \t|\n",
    "|:---:\t|:---:\t|\n",
    "| 스몰데이터 \t| 빅데이터 \t|\n",
    "| 느린정리 \t| 빠른정리 \t|\n",
    "| 비정확한정답 \t| 정확한정답 \t|\n",
    ">\n",
    ">\n",
    "> - 인간이나 데이터정리 도구인 엑셀과 달리 `알고리즘 기술`은 고도화되어 `통계추론/머신러닝` $\\rightarrow$ `딥러닝` $\\rightarrow$ `인공지능`으로 발전중\n",
    "\n",
    "<center><img src='Image/Basic/DigitalEconomy_DataScience.png' width='900'></center>\n",
    "\n",
    "---\n",
    "\n",
    "**2) 데이터사이언스(Data Science):**\n",
    "\n",
    "> **\"데이터사이언스는 `빅데이터를 활용하는 것`으로 `알고리즘 기술`을 사용하여 기계에게 `데이터에서 패턴을 학습`하도록 하여 인간을 대신하여 `문제를 해결`\"**\n",
    ">\n",
    "> **\"데이터사이언스를 통해 고객과 시장의 변화를 실시간으로 분석하여 `기업의 성장 및 제품 품질 향상`에 도움이 되는 `의사결정 전략 적용 가능`\"**\n",
    "\n",
    "<center><img src='Image/Basic/BigDataTechDataScience.png' width='900'></center>\n",
    "\n",
    "> - 비즈니스와 인류는 `신중한 결정`을 내리는 데 도움이 되는 `데이터가 필요`하고 원시데이터에서 `의미 있는 통찰력`을 파악하기 위해 `데이터과학` 필요\n",
    "> - `데이터사이언티스트/애널리스크/분석가 등`은 데이터를 사용하여 마법을 만드는 방법을 아는 `마법사` 어떤 데이터에서든 `의미 있는 정보(인싸이트)`를 캐내어 비즈니스 또는 인류의 삶을 올바른 방향으로 도움을 줌\n",
    "> - `빅데이터 전문가`는 방대한 양의 데이터를 수집, 처리, 관리하며, `데이터사이언티스트`는 데이터를 `분석, 시각화, 통찰력, 스토리텔링 등`으로 신뢰성 높은 설득 진행\n",
    "> - 아직은 `인간 능력 일부분만`이 알고리즘 기술을 갖춘 `자동화 기술 또는 로봇`이 대체하고 있지만 빠르게 영역을 넓히는 중 (인간은 말도 많고 탈도 많고 합리적이지 않으나 기계는..)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "49f25e72",
   "metadata": {},
   "source": [
    "## 데이터사이언스 활용사례\n",
    "\n",
    "> **\"데이터 사이언스는 `오늘날 가장 인기 있는 분야`\"**\n",
    ">\n",
    "> **\"데이터는 어디에나 기하급수적인 속도로 생성되고 있으며 `다양한 정보/통찰력`을 포함\"**\n",
    "\n",
    "---\n",
    "\n",
    "**0) 어떤걸 풀수 있는가?**\n",
    "\n",
    "- 전체적으로 `지도학습/비지도학습/강화학습`이라는 3가지 종류의 알고리즘으로 해결중\n",
    "\n",
    "<center><img src='Image/Basic/ML_Type_CategoryKorean.png' width='800'></center>\n",
    "\n",
    "- 각 알고리즘은 인간이 해결하고 싶어하는 `특정 세부문제 맞춤해결` 방식으로 진화중\n",
    "\n",
    "| **알고리즘 종류** \t| **해결문제 종류** \t| **해결 예시** \t|\n",
    "|:---:\t|:---:\t|:---\t|\n",
    "| **지도학습 알고리즘** \t| **예측문제** \t| 주관식 문제의 숫자형태의 정답을 해결 \t|\n",
    "|  \t| **분류문제** \t| 객관식 문제의 보기들 중 정답을 해결 \t|\n",
    "| **비지도학습 알고리즘** \t| **군집문제** \t| 시험문제에 어떤 유형들이 있는지 해결 \t|\n",
    "|  \t| **차원변환문제** \t| 시험문제의 풀이법을 다양한 관점으로 변환 \t|\n",
    "| **강화학습 알고리즘** \t| **-** \t| 공교육/사교육 없이 스스로 지도학습/비지도학습 문제를 해결하고<br>오답노트도 스스로 만들고 학습하여 성적을 계속 끌어올림 \t|\n",
    "\n",
    "---\n",
    "\n",
    "**1) 예시 사례 5종:**\n",
    "\n",
    "<center><img src='Image/Basic/ML_Type_Application_Upgrade.png' width='700'></center>\n",
    "\n",
    "> **(1) 지도학습 예측문제:** 예측 타겟이 `명확한 숫자` 추정\n",
    ">\n",
    "> <center><img src='Image/Basic/Example_Prediction.png' width='700'></center>\n",
    ">\n",
    "> **(2) 지도학습 분류문제** 분류 타겟이 `명확한 그룹` 추정\n",
    ">\n",
    "> <center><img src='Image/Basic/Example_Classification.png' width='700'></center>\n",
    ">\n",
    "> **(3) 비지도학습 군집문제:** 특징을 규명하기 힘든 기존과 다른 `이상 행위/패턴` 추정\n",
    ">\n",
    "> <center><img src='Image/Basic/Example_Clustering.png' width='700'></center>\n",
    ">\n",
    "> **(4) 실제 비즈니스 적용:** 현실에는 멀티버스나 닥터스트레인지가 없기 때문에, `시간흐름`을 반영하여 `지도학습/비지도학습/강화학습` 사용하여 문제 해결\n",
    ">\n",
    "> <center><img src='Image/Basic/Example_TimeSeries.png' width='700'></center>\n",
    ">\n",
    "> **(5) 실제 비즈니스 적용:** 현실에는 `모든 알고리즘 방법론`을 `모든 업무 과정` 내 반영되어 유기적으로 교류하며 `효율화/고도화` 달성\n",
    ">\n",
    "> <center><img src='Image/Basic/Example_Relation.png' width='700'>(루이, 다빈치랩스)</center>\n",
    "\n",
    "---\n",
    "\n",
    "**2) 주 활용사례:**\n",
    "\n",
    "> **(1) 실시간 분석**\n",
    ">\n",
    "> - 과거에는 데이터 처리를 실시간으로 할 수 없었고 그럴 필요도 없었으나, `비즈니스 경쟁력`을 높이기 위해 `실시간 데이터를 확보해 현황을 파악`해야 하는 문제가 생겼으며, `기술의 진보`를 통해 가능해짐\n",
    "\n",
    "<center><img src='Image/Basic/DSBusinessUsage1.jpeg' width='900'>(FineReport)</center>\n",
    "<center><img src='Image/Basic/DSBusinessUsage3.png' width='900'>(https://www.octoboard.com/dashboards/ecommerce-analytics)</center>\n",
    "\n",
    "---\n",
    "\n",
    "> **(2) 소비자 분석**\n",
    ">\n",
    "> - 점점 생산자 중심에서 `소비자 중심`으로 비즈니스가 확산되고 있고, `소비자의 개인화` 분석이 주 업무였던 서비스분야를 벗어나 `다양한 비즈니스 영역`에서도 활용하기 위해 애쓰고 있고, 데이터사이언스를 통해 `소비자 생동으로부터 정보를 얻어 적절한 의사결정` 가능해짐\n",
    "\n",
    "<center><img src='Image/Basic/DSBusinessUsage4.webp' width='900'>(https://www.pointillist.com/blog/how-to-successfully-implement-customer-journey-analytics/)</center>\n",
    "\n",
    "---\n",
    "\n",
    "> **(3) 비즈니스 운영 효율화**\n",
    ">\n",
    "> - 기업들은 `디지털전환`을 통해 비즈니스 `운영방식을 완전히 바꾸었음`\n",
    "> - `말, 의지` 기반 업무방식에서 `정량화된 수치`를 제시하지 못하는 의견은 받아들이기 어려움\n",
    "> - 고객의 필요에 따라 `차별화된 서비스`를 제공하기 위한 비즈니스 방향 전환\n",
    "> - `미래 위험 관리`를 통해 전략적 의사결정 및 `기업의 신뢰성과 보안 강화`\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d3e84eff",
   "metadata": {},
   "source": [
    "## 데이터사이언스를 알아야 하는 3가지 이유 및 현실\n",
    "\n",
    "**1) 미래의 시장과 우리의 삶의 방식 더 나은 방향으로 변화**\n",
    "\n",
    "<center><img src='Image/Basic/Programming_4thIndustry.PNG' width='600'></center>\n",
    "\n",
    "- 새로운 형태의 산업혁명에 따라 기존의 구체제들이 몰락해왔던 역사적 싸이클처럼 `구시대적 데이터를 과거의 유물`로 취급하게 될 것이고 `빅데이터는 점점 더 정형화된 모습`을 갖추게 될 것\n",
    "- 분석가들은 `고빈도 데이터`를 찾기 위한 끊임없는 노력을 하게 될 것이고, 기존의 `전통적 데이터를 개량하거나 보강하기 위한 시도`를 계속할 것\n",
    "- `빅데이터와 데이터사이언스`가 야기할 업계 내의 변화는 매우 크고 광범위할 것으로 예상\n",
    "- `데이터 자체`가 비즈니스를 위한 `새로운 연료`로써 작용하고 `데이터 없이 어떠한 의사결정도 내릴 수 없는 시대`\n",
    "- 점점 더 많은 투자자들이 새로운 형태의 `대체 데이터`를 받아들이게 될 것이고 시장은 지금보다 `더 빠르게 반응`하게 될 것\n",
    "- `새로운 형태의 데이터와 분석 방법론`을 배우고 받아들이려는 분석가들에게 보다 나은 우위를 제공하게 될 것\n",
    "\n",
    "<center><img src='Image/Basic/DigitalEconomy_SocialChange.png' width='900'>(디지털전환의 가속화 이유인 미래 사회변화 전망)</center>\n",
    "\n",
    "- 우리는 대략적인 `데이터가 어떻게 의미 있는 제품으로 전환`되는지를 배워야 하며 내포된 `도구와 기술을 활용한 분석방법`을 배워야 함\n",
    "- `빅데이터 & 데이터사이언스`는 각종 자선 및 사회조직이 데이터를 활용해 `효율적인 이익생성으로 기부나 봉사력을 높이고 있음`\n",
    "- `의료단체`는 의사들이 환자의 건강 상태를 더 잘 파악할 수 있도록 데이터를 활용\n",
    "- 많은 사람들이 `인터넷과 상호작용`하면서 더욱 많은 데이터를 스스로 만들어내고 `데이터 지식 습득이 필수조건`이 된 세상이기 떄문에 데이터사이언스는 `미래의 일반화된 직업`이 될것 \n",
    "\n",
    "---\n",
    "\n",
    "**2) 국가 및 기업의 발전 동력**\n",
    "\n",
    "- 21세기에 데이터 사이언스는 `발전을 촉진하는 새로운 동력`으로 `금융경제 및 비즈니스 전반에서 일반적인 분석 도구로 자리매김`\n",
    "\n",
    "<center><img src='Image/Basic/DigitalEconomy_GlobalProcess.png' width='900'></center>\n",
    "<center><img src='Image/Basic/DigitalEconomy_Evolution.png' width='900'>(디지털생태계에 따른 국가의 수익구조 진화)</center>\n",
    "\n",
    "- 기업들은 그들의 `실적을 향상`시켜 그들의 `업무 효율성을 증가`시키고 그들의 `고객에게 더 좋은 제품 및 서비스를 제공`\n",
    "\n",
    "> - 퀀트 투자자들뿐만이 아니라 기존의 `펀더멘털 방식의 투자자들`에게도 이러한 머신러닝은 `필수적인 스킬셋`이 되어가고 있음\n",
    "> - 위험 프리미엄, 추세추종, 주식 롱숏과 같은 각종 `계량투자전략(Quantitative Investment Strategies)`들은 다른 누구보다 `머신러닝 도구 및 방법론들을 빠르게 받아들임`\n",
    "> - `단기 분석에선 이미 사람이 맡고 있는 역할은 거의 없는 상황`이고 중기 분석도 그 영향력을 넓히며 사람보다 우위에 있음\n",
    "> - 사람은 할 수 없지만 `기계`는 매우 빠르게 뉴스 기사와 트위터를 분석하고, 각종 데이터를 처리하며, 웹사이트를 `실시간` 스크래핑하고 즉각적으로 이를 반영해 `의사결정`하기 때문\n",
    "\n",
    "- 전통적 제조업인 자동차 업계조차 `자동차 자율성과 안전성 제고`를 위해 데이터를 활용\n",
    "- `매출을 극대화`하기 위해 매출 배후에 있는 `데이터를 철저히 분석`해 `고객의 구매 패턴`을 파악하고, 그들의 조언을 활용해 `제품을 개선`하는 `데이터사이언티스트 필요`\n",
    "\n",
    "<center><img src='Image/Basic/DigitalEconomy_BusinessChange.png' width='900'>(디지털전환의 가속화 이유인 미래 기업비즈니스 전망)</center>\n",
    "\n",
    "---\n",
    "\n",
    "**3) 고임금직업 및 필요수요**\n",
    "\n",
    "- `Glassdoor의 연구`에 따르면 데이터 사이언티스트의 `평균 연봉은 117345달러`로 평균인 44564달러보다 `약3배 높은 수준`\n",
    "- 데이터 사이언스는 `통계학·수학·컴퓨터과학 등 몇몇 분야에서 숙련과 지식을 요구`하기 때문에 데이터 사이언티스트의 가치는 시장에서 높음\n",
    "- 데이터 사이언티스트는 `기업에서 중요한 역할`을 담당하기에 전문지식과 데이터를 바탕으로 `기업을 효율적이고 올바른 방향으로 항해`하도록 가이드를 하기 때문에 `고임금에도 수요 높음`\n",
    "\n",
    "<center><img src='Image/Basic/DSSalary.jpeg' width='900'>(https://www.finereport.com/kr/)</center>\n",
    "<center><img src='Image/Basic/Programming_Type.png' width='900'></center>\n",
    "\n",
    "---\n",
    "\n",
    "**4) 우리의 현실(두려움?불편함?위험?):** `기존의 방식`으로 살아가는 사람들에겐 이러한 변화는 생소하고 받아들이기 `불편함과 언짢음` 느낄 수 있음\n",
    "\n",
    "- `1950년대` 월마트 창업자 샘 월튼은 비행기를 타고다니며 주차장의 자동차 갯수를 기반으로 `투자부지 선정 의사결정`에 활용하였고, `최근` 인공위성 이미지 데이터 기반 의사결정과 `아이디어는 다를게 없고 단기 기술만 달라진 것`\n",
    "- `머신러닝`도 수리통계적 방법론의 연장선으로 과거엔 이를 구현할 컴퓨터가 없었을 뿐이고, 오늘날엔 `빅데이터와 컴퓨팅 파워의 도움`으로 단지 실제로 구현 및 적용을 해본것 뿐\n",
    "- 컴퓨팅 비용이 저렴해지고 발전하며 이를 활용해 `비즈니스 전반에서 수익을 창출하는 토대`가 마련되고 나타나고 있을 뿐\n",
    "\n",
    "> - 아직은 `알고리즘 기술`들은 인간의 직관과 통찰력을 완벽하게 대체할 수는 없음\n",
    "> - 비즈니스 현장의 `문제가 무엇인지 정확하게 인지`하고 `어떻게 비즈니스 문제를 해결한 것인가에 대한 통찰력을 발휘`하는 것이 빅데이터 및 데이터사이언스 전문가에게 가장 중요한 능력\n",
    "> - 아주 복잡한 테크니컬 솔루션을 제시할 수 있는가가 아니라, `데이터 패턴 이면에 있는 경제적 함의`를 이해할 수 있는가\n",
    "> - 많은 빅데이터, 머신러닝, 인공지능 관련 분석이 겉보기에는 번지르르하지만 실제 성과가 좋지 못한 이유는 바로 시장 또는 시스템이 가지고 있는 `비이성성과 그로 인한 비정상성`을 심각하게 고려하지 않은 채 `기교와 테크닉에만 집중`하기 때문\n",
    "\n",
    "<center><img src='Image/Basic/DigitalEconomy_DataScience.png' width='900'></center>\n",
    "\n",
    "> - 빅데이터와 머신러닝은 결국 `문제를 해결하기 위한 도구`일 뿐, 본질은 `문제를 해결하고자 하는 것`이기에 데이터 과학자는 본질에 집중하여 `누가 먼저 양질의 데이터를 찾고 분석하여 그 속에서 보석을 창출하는지 선착순 싸움`의 출발점에 서야할 때\n",
    "> - 결국 좋던 싫든 간에 `빅데이터와 기계학습 그리고 인공지능`은 향후 인간의 삶과 비즈니스 의사결정에 새로운 세계를 열게 될 것임은 자명한 사실\n",
    "> - 관련된 모든 사람들은 이제 `빅데이터 그리고 데이터사이언스 방식을 활용하는 삶의 방식과 비즈니스에 익숙해져야만 살아남을 수 있을 것`"
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