simulation, laws of large numbers and the central limit theorem. Reference text (not required): Probability and Statistics, by Morris DeGroot, Fourth Edition, 2011. Prerequisite: None.
Simulation Methods for Option Pricing 46-932
This course initially presents standard topics in simulation including random variable generation, variance reduction methods and statistical analysis of simulation output. The course then addresses the use of Monte Carlo simulation in solving applied problems on derivative pricing discussed in the current finance literature. The technical topics addressed include importance sampling, martingale control variables, stratification, and the estimation of the "Greeks." Application areas include the pricing of American options, pricing interest rate dependent claims, and credit risk. Prerequisite: Intro to Probability 46-921, Intro to Statistical Inference 46-923, Statistical and Machine Learning Methods for Financial Data 46-926, Stochastic Calculus I 46-944, Options 45-885.
Statistical Arbitrage 46-936
This course will provide students with the basic concepts and techniques for statistical-based trading. It will present some of the standard approaches to statistical arbitrage including market neutral strategies such a pairs trading, value-based or contrarian methods, momentum-based strategies, cointegration-based trading, algorithmic and high-frequency trading. The course will address how to search for statistical arbitrage strategies based on short term and long-term patterns as well as multi-equity relationships. The course material will be drawn from the finance literature, and some material will be presented by professional hedge fund traders. Student will do projects that implement the statistical arbitrage concepts presented in the course. Prerequisite: Introduction to Probability 46-921, Introduction to Statistical Inference 46-923, Statistical and Machine Learning Methods for Financial Data 46-926, Financial Time Series 46-929.
Statistical Inference 46-923
The objective of this course is to introduce the basic ideas and methods of statistical inference and the practice of statistics, especially estimation and basic regression analysis. The statistical package R will be introduced. This package is used throughout the MSCF curriculum. Mathematical statistical theory will be supplemented by simulation and data analysis methods to illustrate the theory. This course will provide a solid foundation for subsequent MSCF courses in statistics. Reference text (not required): Probability and Statistics, by Morris DeGroot, Fourth Edition, 2011. Prerequisite: Introduction to Probability 46-921.
Statistical and Machine Learning Methods for Financial Data 46-926
This is an applied course in regression analysis and linear models focusing on the analysis of financial data. Basic methods taught in the course include simple and multiple linear regression, model selection, residual analysis, diagnostics, detection of multi-collinearity and nonstandard conditions. Principal components and factor analysis are also introduced. Examples will be taken from financial models, including the CAPM. Reference texts (not required): Campbell, J.Y., Lo, A.W. and MacKinlay, A.C. (1997). The Econometrics of Financial Markets, Princeton University Press; D. Ruppert (2010). Statistics and Data Analysis for Financial Engineering, Springer; R.A. Carmona (2004). Statistical Analysis of Financial Data in Splus, Springer. Lectures notes will be made available through the course web page. Prerequisite: Introduction to Probability 46-921, Introduction to Statistical Inference 46-923.
Stochastic Calculus for Finance I 46-944
This course introduces martingales, Brownian motion, Ito integrals and Ito’s formula, in both the uni-variate and multi-variate case. This is done within the context of the Black-Scholes option pricing model and includes a detailed examination of this model. Prerequisite: Multi-Period Asset Pricing 46-941 and knowledge of calculus-based probability theory. Text: S. Shreve, Stochastic Calculus for Finance II: Continuous-Time Models, Springer-Verlag, New York, 2004. Prerequisite: Introduction to Probability 46-921, Multi-Period Asset Pricing 46-941.
Stochastic Calculus for Finance II 46-945
This course treats the theory and implementation of interest-rate term structure models. The underlying methodology is change of measure. Both risk-neutral and forward measures are used. Models covered include Hull-White, Cox-Ingersoll-Ross, Heath-Jarrow-Morton, and Brace-Gatarek-Musiela. Texts: S. Shreve, Stochastic Calculus for Finance II: Continuous-Time Models, Springer-Verlag, 2004. C. Munk,Fixed Income Modelling 2011 (576 Pages) Oxford University Press ISBN 978-0-19-957508-4. Prerequisite: Stochastic Calculus for Finance I 46-944.
Studies in Financial Engineering 45-886
This is a course about using Financial Engineering to solve practical risk management and trading problems and about the sales process for selling derivative deals. The focus is on designing and pricing derivative securities to trade on and hedge customized risk exposures – particularly those involving non-linear, path-dependent, and/or multi-variable exposures to interest rates, equity prices, credit events, and commodity prices, –pitching these exotic securities to clients, and managing any associated risks. The valuation tools used to price these derivatives are Risk Neutral Valuation and Monte Carlo Simulation. The course also highlights practical issues about model calibration, model risk, and dynamic hedging. The highlight of the course is a series of in-class team case presentations. While pricing and hedging techniques are important, so too are practical issues such as deciding which risks to share contractually and knowing how to pitch a derivative deal. The in-class presentations are a chance to practice standing in front of a client or boss and sell/explain complicated structured products. Prerequisite: Capstone Course - Must be taken at the end of the program.
Topics in Quantitative Finance 46-955
This course is a collection of topics that vary from year to year. In 2011, the course will include both risk management and advanced topics in mathematical finance. Basic risk management including VaR, expected shortfall, coherent risk measures, and the Basel accords will be covered. More advanced risk management topics will include extreme value distributions, delta-gamma approximations to VaR, and the use of importance sampling for Monte Carlo simulation of VaR for portfolios of options and of bonds. Two guest lectures by a risk management professional will be given. The mathematical finance topics will include models for American options, foreign exchange, forward-futures spreads for interest rates, and volatility swaps. Texts: Glasserman, P., Monte Carlo Methods in Financial Engineering; S. Shreve, Stochastic Calculus for Finance II, Continuous-Time Models. Prerequisites: Stochastic Calculus for Finance II 46-945, Simulation Methods for Option Pricing 46-932.