# Analytics of Financial Engineering

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1 Andrew W. Lo MIT Sloan School of Management Spring 2003 E Course Syllabus Analytics of Financial Engineering Course Description. This course covers the most important quantitative methods of financial engineering and computational finance. These methods include: (1) static and dynamic optimization; (2) Monte Carlo simulation; (3) stochastic (Itô) calculus; (4) financial econometrics; and (5) statistical inference for financial applications. Each of these techniques will be covered in some depth along with its computer implementation however, the emphasis will be on financial-engineering applications, not on methodology. In particular, quantitative methods are developed within the context of specific problems in financial engineering, problems that fall into one of the following four areas: (1) derivatives; (2) portfolio management; (3) risk management; and (4) proprietary trading. The correspondence between methods and applications is given in the following table: Quantitative Method Derivatives Portfolio Management Risk Management Proprietary Trading Optimization Monte Carlo Simulation Stochastic (Itô) Calculus Statistical Inference Financial Econometrics To ensure that the focus of the course is properly directed towards the practical application of these quantitative methods, the material will be presented in a unique way. The entire course will be devoted to solving successively more complex versions of a single problem: how should a rational investor decide to allocate his wealth among a collection of risky investments? By starting with a relatively simple static version of this problem (basic portfolio theory), and then adding more realistic features incrementally (dynamics, trading costs, securities with nonlinear payoffs, stochastic interest rates, non-gaussian returns, etc.), students will have seen each of the five quantitative methods in the context of the four application areas listed above. In this way, the motivation for each method and how the method is applied follows naturally and immediately. Pre-requisites. This course is intended for second-year Sloan Master s students in the Track in Financial Engineering (TFE). Therefore, the pre-requisites include and all other requirements of the TFE; in particular, is a recommended co-requisite. Some rudimentary programming skills will be necessary projects will make use of Matlab and eviews programming languages (though prior exposure to these languages is not expected). Non-TFE students may enroll only with the permission of the instructor by Andrew W. Lo, All Rights Reserved Page 1 of 5

5 Readings 1. Black, F., 1993, Beta and Return, Journal of Portfolio Management 20, Bodie, Z., 1995, On the Risk of Stocks in the Long Run, Financial Analysts Journal 52, Boyle, P., Broadie, M. and P. Glasserman, 1997, Monte Carlo Methods for Security Pricing, Journal of Economic Dynamics and Control 21, Ibbotson, R. and P. Kaplan, 2000, Does Asset Allocation Explain 40, 90, or 100 Percent of Performance?, Financial Analysts Journal 56, Jagannathan, R. and E. McGrattan, 1995, The CAPM Debate, Federal Reserve Bank of Minneapolis Quarterly Review 19, Kao, D., 2000, Estimating and Pricing Credit Risk: An Overview, Financial Analysts Journal 56, Lo, A., 1994, Data-Snooping Biases in Financial Analysis, in H. Russell Fogler, ed.: Blending Quantitative and Traditional Equity Analysis. Charlottesville, VA: Association for Investment Management and Research. 8. Lo, A., 2001, Risk Management for Hedge Funds: Introduction and Overview, Financial Analysts Journal 57, Lo, A., 2002, The Statistics of Sharpe Ratios, Financial Analysts Journal 58, Lo, A. and C. MacKinlay, 1990, When Are Contrarian Profits Due to Stock Market Overreaction?, Review of Financial Studies 3, Merton, R., 1994, Influence of Mathematical Models in Finance on Practice: Past, Present, and Future, Philosophical Transactions of the Royal Society of London A 347, Sharpe, W., 2002, Budgeting and Monitoring Pension Fund Risk, Financial Analysts Journal 58, Treynor, J. and F. Black, 1973, How to Use Security Analysis to Improve Portfolio Selection, Journal of Business 46, by Andrew W. Lo, All Rights Reserved Page 5 of 5

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