CMU MSCF curriculum(Course Descriptions)

Course Descriptions

Our innovative curriculum is made possible by the close collaboration of four colleges on campus that together have designed a course of study specifically tailored for the computational finance program:

Advanced Derivative Modeling 46-915
This course treats models in which underlying asset prices jump and/or have stochastic volatility. There is a computational component, based on Fourier analysis and the fast Fourier transform. Basic processes considered are Poisson and compound Poisson. Stochastic calculus and change-of-measure techniques will be developed for these processes. Equity derivative models considered are local vol, Hull-White and Heston. Reference: J. Gatheral, The Volatility Surface: A Practitioner's Guide, Wiley, 2006. Prerequisite: Stochastic Calculus for Finance II 46-945.   

Credit Derivatives 45-903
This course provides techniques for modeling credit risk. In the literature there exist two basic frameworks for doing this. The first framework is known as the 'structural approach' and here the key object is the value of the firm's assets. The fundamental idea is that if this value falls below some threshold, the firm defaults. The second framework is known as the 'intensity based' or 'reduced form' approach. This approach models the default time as the first jump time for a counting process and allows this jump time to be influenced by certain background variables. More time will be spent on the latter approach since this framework allows us to use many results from the default-free term-structure theory. Indeed, one main result is that the intensity can be interpreted as a default premium. Reference text: "Credit Risk: Pricing, Measurement, and Management," Duffie, D. and K. Singleton (2003); Princeton University Press. Prerequisite: Stochastic Calculus II 46-945, Options 45-814, Simulation Methods for Option Pricing 46-932, Advanced Derivative Modeling 46-915.

Deutsche MSCF Trading Competition 46-980
In 1989, Carnegie Mellon's Financial Analysis and Security Trading Center (FAST) was the first initiative on the part of an educational institution to successfully replicate the live international data feeds and sophisticated software of Wall Street's top trading firms. While no longer dedicated to the trading floor "look," this proprietary, real-time, trading software developed by MSCF Professors Sanjay Srivastava and John O'Brien (now licensed to over seventy-five universities worldwide) continues to be employed in the annual MSCF Deutsche Trading Competition. All first-year full and part-time students are required to participate (all other MSCF degree students are eligible to participate). Using fixed income and derivatives instruments, 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 5, 2009.

Dynamic Asset Management 45-908
This course covers the theoretical and quantitative tools that are used in dynamic asset management. After a review of static portfolio selection models including mean-variance optimization and multiple factor models, the course focuses on multi-period models with careful consideration of frictions such as transaction costs and taxes. Additional topics may include stochastic optimization, resampled efficiency, Bayesian approaches, robust optimization, active management techniques, and dynamic performance evaluation. Students will also be exposed to industry standard asset management software. Representative Text: Grinold and Kahn, Active Portfolio Management. Prerequisite: Financial Computing III 46-903, Stochastic Calculus II 46-945, Simulation Methods for Option Pricing 46-932, Intro to MSCF Finance 45-711.

Financial Computing I 46-901
This course covers the fundamentals of programming in C++. We start with a discussion of the differences between procedural and object-oriented programming, and then cover syntax and programming techniques from the core "C" subset of C++. We then discuss C++ classes, along with inheritance and polymorphism. Considerable attention is paid to heap memory management. Finally, we introduce parametric programming with templates, along with a look at the C++ standard libraries (especially the STL). The use of Excel as an alternative to C++ in solving some types of problems is also explored. 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.

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: Numerical Methods 46-950, Stochastic Calculus II, Financial Computing III 46-903.

Financial Products and Markets 45-906
This course provides a broad overview of the financial markets, its institutions, and the products they create and trade. Our focus will be upon the structures underlying the mortgage, credit derivatives, commodities and fixed income and equity derivatives markets, looking at the participants in these markets and the role of the "quant" desks in these institutions. Two lectures will be devoted to developing a basic understanding of financial accounting - the balance sheet, the income statement, the statement of cash flows, and the statement of retained earnings - and a brief overview of the issues involved in accounting for derivative instruments. Guest speakers from industry will present three of the seven lectures. Prerequisite: None.

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. 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, along with related applications to finance including option pricing. 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: Introduction to Probability 46-921, Introduction to Statistical Inference 46-923, Linear Financial Models 46-926.

Introduction to MSCF Finance 45-711
An introduction to the financial problems faced by firms and the models used to address them. Topics include: time value of money and compounding, capital budgeting, portfolio theory and diversification, risk and return, capital structure and dividend policy. Reference text:  Brealey, Myers, Allen "Principles of Corporate Finance," 8th ed.,ISBN 0-07-295723-9 Prerequisite: None.

Introduction to 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, "Fixed Income Securities," 2nd ed., ISBN# 0-471-06322-3 (paperback) 0-471-06317-7 (hardcover). Prerequisite: None.

Introduction to Probability 46-921
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 distribution, expected values, moment generating functions transformations of random variables and vectors, simulation, laws of large numbers and the central limit theorem. Reference text (not required): Probability and Statistics, by Morris DeGroot, Third Edition, 2002. Prerequisite: None.

Introduction to 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 S-PLUS 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, Third Edition, 2002. Prerequisite: Introduction to Probability 46-921.

Linear Financial Models 46-926
This is a course in regression analysis and linear models with application to equity portfolio management. Basic methods taught in the course include simple and multiple linear regression, model selection, residual analysis, diagnostics, detection of multi-collinearity, nonstandard conditions and transformations. Principal components and factor analysis are also introduced. Examples will be taken from financial models, including the CAPM and multi-factor with applications to portfolio selection and asset allocation. Reference text (not required): Campbell, J.Y., Lo, A.W. and MacKinlay, A.C. (1997). The Econometrics of Financial Markets. Princeton University Press; Modern Applied Statistics with Splus, by Venables and Ripley, Third Edition Springer-Verlag (0-387-98825-4); and handouts available through the course web page. Prerequisite: Introduction to Probability 46-921, Introduction to Statistical Inference 46-923.

Macroeconomics for Computational Finance 45-905
This course provides students with a working knowledge of the economic models and concepts which underlie many of the mathematical and statistical tools that are taught elsewhere in the MSCF program. The first half of the course develops the microeconomics which underlie classical valuation theory: arbitrage-free pricing, equilibrium pricing and decision-making under uncertainty. The second half goes through a variety of topics in international macroeconomics, including  interest rate determination and monetary policy, foreign exchange rates, money and banking, and international capital flows and financial crises. A key aspect of the course is that the topics and tools from the first half of the course are extensively used in the second half. For example, a discrete-time, lognormal pricing kernel model (from the theory of arbitrage-free valuation) will be used to understand currency risk premiums and, therefore, the relationship between  interest rates and exchange rates. The course will make explicit the linkages between its own material and that of other MSCF courses, thereby providing students with an economics-based foundation for many of the valuation tools which form the core of the MSCF curriculum. Prerequisite: Intro to MSCF Finance 45-711, Options 45-814, Linear Financial Models 46-926, Multi Period Asset Pricing 46-941.

 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: Intro to Probability 46-921.

Numerical Methods 46-950
This course covers numerical methods relevant to solving the partial differential equations, which arise in finance. Both the theoretical background and practical issues are treated. Topics include: 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 far boundary conditions, the connection with binomial models, interest rate models, early exercise, and the corresponding free boundary problems, techniques for calibration of Hull and White interest rate models, and a brief introduction to additional difficulties of the multi-factor models. Prerequisite: Stochastic Calculus I 46-944, Financial Computing II 46-902.

Options 45-814
The primary focus of this course is on pricing and hedging contingent claims, that is, assets with option-like features. Examples include calls, puts, warrants, bank loans and underwriting contracts. The models to be studied include Black-Scholes, binomial and risk-neutral Monte Carlo pricing. Specific topics include simple no-arbitrage pricing relations (most notably put-call parity); delta, kappa and gamma hedging; implied standard deviations and their statistical properties; exotic options; portfolio insurance and other dynamic option replication trading strategies; and futures and forward contracts. The course employs much math and statistics -- of all subjects in finance, the area of derivatives securities has used these tools to the greatest profit. Our goals are (1) to become proficient at the fundamental option calculations and (2) to take a peak inside the "black box" so as to understand the pros and cons of the most widely used models. Prerequisite: Intro to MSCF Finance 45-711, Intro to Fixed Income 46-956, Multi-Period Asset Pricing 46-941, Stochastic Calculus I  46-944.

Presentations for Computational Finance 45-795
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.

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, Linear Models 46-926, Stochastic Calculus I 46-944, Stochastic Calculus II 46-945, Options 45-814.

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, and technical analysis. The course will address how to search for statistical arbitrage strategies based on intra-day patterns, longer-term patterns, and multi-equity relationships. The course material will be drawn from the finance research literature. The work for the course will involve implementation and evaluation of some of these approaches using historical equity data. The topics covered are particularly relevant for proprietary trading, such as in the context of hedge funds. Prerequisite: Introduction to Probability 46-921, Introduction to Statistical Inference 46-923, Linear Financial Models 46-926, Financial Time Series 46-929.

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, New York 2004. C. Munk, Fixed Income Analysis: Securities, Pricing, and Risk Management, Lecture Notes, 2005. Prerequisite: Stochastic Calculus for Finance I 46-944. Co-requisite: Simulation Methods for Option Pricing 46-932.

Studies in Financial Engineering 45-816
This course is about using financial engineering and derivative securities to solve practical business problems. Students will work through business cases and give in-class simulated sales pitches to hypothetical clients. The cases highlight the design, valuation and hedging of structured products on stock prices, interest rates, FX, and exotic "underlyings" such as volatility, credit, and energy. Reference text: Option, Futures and Other Derivative Securities, 2nd Ed., John Hull, Prentice-Hall, 1993. 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 can vary from year to year. Typical topics include the application of heavy-tailed distributions and simulation methods to financial risk management, models for the spread between forward interest rates and interest rate futures, the theory of American options, models for exchange rates, and pricing and hedging exotic options. Texts: P. Glasserman, 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.



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