Advanced Derivative Modeling 46-915
This course considers more advanced models. We start by revisiting the Fourier transform and discuss how to use this technique to price vanilla options in different standard Brownian-based models (Heston and Stein & Stein). We then study the theory of jump processes including Ito's lemma and Girsanov's theorem. We first focus on the Poisson process and the compounded Poisson. We then explain how to create the family of Cox-processes, which plays an important role in the credit derivatives' literature. Subsequently, we apply this theory to build asset pricing models, such as Bates' model (this is basically Heston's model with jumps added). We will not follow a textbook but one useful reference is: J. Gatheral, The Volatility Surface: A Practitioner's Guide, Wiley, 2006. Prerequisites: Stochastic Calculus for Finance II 46-945.
Deutsche MSCF Trading Competition 46-980
All first-year full and part-time students participate in a trading competition directed and underwritten by Deutsche Bank. Using equity and fixed income derivatives securities on a paper trading platform through Interactive Brokers, individuals trade and make markets during specified open market hours. Results of the competition are tallied and posted with the winners determined relative to the performance measurements specified in the trading cases. The top ten winners are recognized, with the top three winners awarded cash prizes (1st: $1,000; 2nd: $500; 3rd: $250). The winners will be honored in the company of all participants and members of the MSCF Steering Committee at a reception hosted by Deutsche Bank in New York on January 9, 2013.
Financial Computing I 46-901
This will be a "Survival Computing" course for MSCF students. We will cover the basics of C++, in the context of some elementary finance-related problems. The intent is to arm you with computing skills you can use in other MSCF courses, including Financial Computing II, III and IV. Reference texts (not required): "C++ Primer" by Lippman, et al, "Numerical Recipes in C++" by Press, et al. Prerequisite: Some experience in programming in a procedural or object-oriented language, or the Programming Prep course.
Financial Computing II 46-902
Throughout this course, we will be building a non-toy C++ application that uses genetic programming. Most of the concepts from the lectures will be used in this application. First, we look more deeply at the C++ standard library. Then some background on relational databases is given, so that the use of a database as a "back-end" to a C++ program will make sense. We look at the relational algebra, the relational calculus, and the query language SQL. Then we cover the construction of static and dynamically linked libraries. A few topics from Windows programming are briefly covered, and finally the idea of design patterns as object-oriented "building blocks" is discussed. Reference texts (not required): "C++ Primer" by Lippman, et al, "Database Modeling and Design" by Teorey, "The C++ Standard Library" by Josuttis and "Design Patterns" by Gamma, et al. (the "Gang of Four"), plus additional material available from the course Web site. Prerequisite: Financial Computing I 46-901.
Financial Computing III 46-903
This is a course in advanced O-O and C++ topics. We look at memory management, including overriding the new and delete operators, program design for other kinds of resource allocation, exception-safe code, profiling and optimizations, and other O-O topics as time permits. Also, we will consider additional ways of coupling Excel, VBA and C++, and the construction of Excel "add-ins". Several Excel/VBA/C++ projects will be assigned, as well as a "coding competition" amongst teams of students. Reference texts (not required): "Effective C++" by Meyers, "C++ Common Knowledge" by Dewhurst, and "The C++ Standard Library" by Josuttis. Prerequisite: Financial Computing I 46-901, Financial Computing II 46-902.
Financial Computing IV 46-904
The goal of this course is to refresh and expand your knowledge of several important topics of the Master Program, such as Object Oriented Programming with C++, theory of pricing and hedging of derivative securities, numerical analysis and stochastic calculus. The course is organized around a project of design and implementation of a powerful C++ library for pricing of derivative securities. You will learn important principles of implementation of financial models and master algorithms of evaluation of different types of derivative securities: European, American, standard, barrier and path dependent options on stocks and interest rates. Prerequisite: Stochastic Calculus II, Financial Computing III 46-903.
Financial Economics for Computational Finance 45-887
This course will focus on aspects of economics that can inform financial engineering, the design, valuation, and hedging of complex securities. We will consider the methods economists use in analyzing problems, the economic basis for evaluating risk premia, endogenous responses and the risks of over-fitting. We will consider information frictions, specifically adverse selection and moral hazard, and how they can distort valuations and interfere with efficient trade. The second half of the course will review the structure and evolution of the financial system, and sources of financial fragility. Prerequisites: Intro to MSCF Finance 45-785, Options 45-885, Macroeconomics for Computational Finance 45-986, Multi-Period Asset Pricing 46-941, Financial Time Series Analysis 46-929, Statistical Arbitrage 46-936.
Financial Optimization 45-988
Optimization models play an increasingly important role in financial decisions. Many computational finance problems ranging from asset allocation to risk management, from option pricing to model calibration, can be efficiently solved using modern optimization techniques. This course covers several classes of optimization models (linear, quadratic, integer, and dynamic programming) encountered in financial contexts. For each model class, after a survey of the relevant theory and solution methods, we will discuss problems in mathematical finance that are amenable to that problem class. Representative Texts: Cornuejols and Tutuncu, "Optimization Methods in Finance." Grinold and Kahn, "Active Portfolio Management." Campbell and Viceira, "Strategic Asset Allocation: Portfolio Choice for Long-Term Investors." Prerequisites: Intro to MSCF Finance 45-785, Stochastic Calculus II 46-945.
Financial Products and Markets 45-987
This course reviews four asset classes from the perspective of a quantitative finance practitioner: equities, rates and credit, foreign exchange and commodities. Individuals from industry will teach five of the seven lectures, providing a valuable “first-hand” overview of these markets and the desks they supervise. Two lectures will be offered toward developing a basic understanding of financial statement analysis and accounting for derivative instruments. Required Texts: "Financial Intelligence" by Karen Berman, 2006, ISBN 1-59139-764-2; Reference Text: "Capital Markets for Quantitative Professionals," by Alex Kuznetsov, McGraw-Hill, 2007, 0-07-146829-3. Prerequisite: Options 45-885, Fixed Income 46-956.
Financial Time Series Analysis 46-929
This course introduces time series methodology to the MSCF students. Emphasis will be placed on the data analytic aspects related to financial applications, with a view toward development of quantitative trading strategies. Topics studied in this course include univariate ARIMA modeling, forecasting, seasonality, model identification and diagnostics. In addition, GARCH and stochastic volatility modeling will be covered. At the end of the course, trading strategy development based on these models will be discussed. Reference texts (not required): Brockwell & Davis, Introduction to Time Series and Forecasting, 2nd edition, Springer (2002); N.H. Chan, Time Series: Applications to Finance, Wiley (2002). Prerequisite: Probability 46-921, Statistical Inference 46-923, Statistical and Machine Learning Methods for Financial Data 46-926.
Fixed Income 46-956
This course introduces the most important securities traded in fixed income markets and the valuation models used to price them. Payoff characteristics and quotation conventions will be explained for treasury bills and bonds, STRIPS, defaultable bonds, mortgage-backed securities like Collateraized Mortgage Obligations and derivative securities like swaps, caps, floors, and swaptions. Basic concepts will be explained such as the relation between yields and forward rates, duration, convexity, and factor models of yield curve dynamics. Key concepts for interest rate derivative valuation will be introduced using discrete time versions of the Ho-Lee and Hull and White models. Text: Bruce Tuckman, Angel Serrat. "Fixed Income Securities," 3rd ed., (University Edition) ISBN# 0-470-90403-8 (paperback contains exercises) 0-470-89169-6 (hardcover does not contain exercises, but will be posted on course site). Prerequisite: None.
Macroeconomics for Computational Finance 45-986
This course will provide students with tools to analyze the macroeconomic environment. Students will learn how to use economic theory in making short run forecasts of security prices and interest rates, and why particular attention is paid to economic variables such as initial jobless claims and inflation expectations. The course will provide the theory for evaluating how central bank and government policy affect the macroeconomy. Prerequisite: none.
MSCF Finance 45-785
Broadly speaking, there are three types of players in finance: ‘Individuals’ who save and invest to smooth consumption across time or smooth consumption across risk-outcomes, ‘Corporations’ who raise money by selling securities, invest in projects and pay investors cash-flows and ‘Financial Markets’ that match the saving/borrowing needs of individuals with the investing/cash-flow needs of corporations. We will look at Portfolio Theory, Capital Budgeting, Capital Structure, No-arbitrage Pricing, Efficient Markets, and the Capital Asset Pricing Model. Text: "Corporate Finance by Jonathan Berk & Peter DeMarzo ISBN 0135056551. Prerequisite: None.
Multi-Period Asset Pricing 46-941
This course introduces the concepts of arbitrage and risk-neutral pricing within the context of multi-period financial models. Key elements of stochastic calculus such as Markov processes, martingales, filtration and stopping times will be developed within this context. Prerequisite: Probability 46-921.
Numerical Methods 46-950
This course covers numerical methods relevant to solving the partial differential equations of mathematical finance. Theoretical and practical issues are treated. Topics include (but are not limited to): background material in partial differential equations, examples of exact solutions including Black Scholes and its relatives, finite difference methods including algorithms and question of stability and convergence, treatment of near and far boundary conditions, the connection with binomial models, interest rate models, early exercise, and the corresponding free boundary problems, and a brief introduction to numerical methods for solving multi-factor models. Prerequisite: Stochastic Calculus I 46-944.
The goal of the Options course is to develop tools to price and hedge and understand the risk exposures of any contingent claim on any underlying variable. The types of options considered include exchange-traded calls and puts, OTC exotic options, interest rate options, volatility derivatives, corporate securities such as callable bonds and warrants, and “real options” like power plants and mines. The option pricing techniques to be studied include binomial option pricing, Black-Scholes, Hull and White, and the option pricing super-theory known as risk-neutral valuation. Some specific topics are Geometric Brownian Motion and the mathematics of continuous-time stochastic processes; put-call parity and other arbitrage-free price option restrictions; Greeks; Monte Carlo Simulation; implied standard deviations and their statistical properties; exotic options; static and dynamic option replication trading strategies; and implied stochastic processes. Prerequisite: MSCF Finance 45-785, Fixed Income 46-956, Co-requisite: Multi-Period Asset Pricing 46-941.
Presentations for Computational Finance 45-789
This course provides practical, usable, and relevant practice and study in oral communications strategies critical for professional managerial success. Students will enact non-verbal and vocal techniques that support a professional attitude and will study how their appearance and demeanor are indeed contributors to the messages they send. Assignments will enable students to target key decision-makers’ needs, craft verbal and quantitative arguments, and provide problem-solving action-oriented content. Recommended textbook: How Audiences Decide by Richard O.Young, New York: Routledge, 2011. Prerequisite: None.
The objective of this course is to introduce the basic ideas and methods of calculus-based probability theory and to provide a solid foundation for other MSCF courses based on probability theory. Topics include basic results on probability and conditional probability, random variables and their distributions, expected values, moment generating functions, multivariate distributions, transformations of random variables and vectors, laws of large numbers and the central limit theorem. Required text: Statistics and Data Analysis for Financial Engineering by David Ruppert, 2011. Prerequisite: None.
Risk Management I 46-954
Risk Management II 46-955
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: Probability 46-921, 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: Probability 46-921, 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, including methods and theory of estimation, quantifying uncertainty, Bayesian inference, and hypothesis testing. 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. Required text: Statistics and Data Analysis for Financial Engineering by David Ruppert, 2011. Prerequisite: Introduction to Probability 46-921.
Statistical and Machine Learning Methods for Financial Data 46-926
This is an applied course in the modeling and discovery of relationships between multiple variables. Topics include parametric and nonparametric regression, classification, and clustering. Specific methods covered will include linear models, LASSO, basis expansions, kernel methods, support vector machines, and classification and regression trees. There will also be a discussion of the need for and the implementation of dimension reduction techniques, including principal components and factor analysis. There will be a focus on model selection, residual analysis, diagnostics, detection of multi-collinearity and nonstandard conditions. Examples will be taken from financial models, including the CAPM. Required text: Statistics and Data Analysis for Financial Engineering by David Ruppert, 2011. Reference texts (not required): Campbell, J.Y., Lo, A.W. and MacKinlay, A.C. (1997). The Econometrics of Financial Markets, Princeton University Press. 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: 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.
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.