Financial Engineering with Stochastic Calculus I 1 / 20 Financial Engineering with Stochastic Calculus I Andreea Minca Cornell University Fall 2019
Financial Engineering with Stochastic Calculus I 2 / 20 Introduction 0. Introduction
Financial Engineering with Stochastic Calculus I 3 / 20 Introduction Course syllabus I: Introduction: financial engineering, binomial model II: Background in probability: information and σ -algebras, independence, general conditional expectations, martingales, fundamental theorem of asset pricing III: Brownian motion (BM): scaled random walks, definition of BM, distribution of BM, filtration for BM, martingale property of BM, quadratic variation IV: Stochastic calculus: stochastic integral, Itˆ o processes, Itˆ o formula, Black-Scholes-Merton equation, multivariable stochastic calculus V: Risk-neutral pricing: Girsanov’s theorem, risk-neutral measure, martingale representation, fundamental theorems of asset pricing, dividend paying assets. VI: Miscellaneous topics (if time permits): dividends, forwards and futures.
Financial Engineering with Stochastic Calculus I 4 / 20 Introduction August 29, 2019 Outline Overview of financial markets Overview of main types of financial derivatives and their use in the market Size of the derivative market Modeling financial markets - the main assumptions: efficiency and absence of arbitrage Pricing derivatives: the philosophy
Financial Engineering with Stochastic Calculus I 5 / 20 Introduction Financial markets Throughout the course, we assume that there is exists a financial market , where securities are traded. In a primary financial market , securities are issued. For example, the debt of a company, government, etc., initial public offerings (IPO) for equity. On a secondary financial market a large number of investors trade securities through an exchange. E.g. New York Stock Exchange, Nasdaq, American Stock Exchange and all major exchanges in the world. These are the closest to the markets we consider in theory in this course. We call e fficiency of the market the capacity of the market to determine a ”fair value” for the traded securities. When the market is efficient, the market forces (supply and demand) determine the price of the primary assets, e.g., stocks, bonds. There are also over-the-counter markets, in which a (small) number of large investors trade directly, without passing through an exchange. When pricing a security traded in this markets, special attention must be given to counterparty risk .
Financial Engineering with Stochastic Calculus I 6 / 20 Introduction Derivative contracts Contrary to primary assets (such as commodities, stocks, interest rates, foreign exchange), derivative contracts depend on the performance of these primary assets.
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