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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: Duffie, D. and K. Singleton, Credit Risk: Pricing, Measurement, and Management, Princeton University Press, 2003. 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 4, 2010.

Course Descriptions-2
Financial Computing I 46-901
This will be a "Survival Computing" course for MSCF students. We will cover the basics of C++, MATLAB and VBA, all 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): Lippman et al., C++ Primer; Press et al., Numerical Recipes in C++. 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): Lippman et al., C++ Primer; Teorey, Database Modeling and Design; Josuttis, The C++ Standard Library; and Gamma et al. (the "Gang of Four"), Design Patterns, 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): Meyers, Effective C++ ; Dewhurst, C++ Common Knowledge; and Josuttis, The C++ Standard Library. 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.

Course Descriptions-3
Financial Economics for Computational Finance 45-848
Valuation Theory is the branch of economics that studies the pricing of uncertain cash flows. Specific examples include CAPM, Black-Scholes, term-structure models and the real-options brand of corporate finance. This course focuses on the economics underlying valuation theory. The course begins by developing the basic microeconomic framework of arbitrage-free pricing, decision-making under uncertainty and competitive equilibrium. The basic framework is then used to understand time series and cross-sectional variation in the risks and the expected returns on equities, bonds and currencies. The associated implications for portfolio choice are modeled and analyzed. The course places a strong emphasis on using data to understand and implement theory. The overall idea behind the course is that coherent economic intuition makes for more effective application of the quantitative finance tools that are the bedrock of the MSCF program. Prerequisite: Intro to MSCF Finance 45-711, Options 45-814, Macroeconomics for Computational Finance 45-905, Multi Period Asset Pricing 46-941, Financial Time Series Analysis 46-929.

Financial Products and Markets 45-906
The focus of this course is upon the pockets of quantitative finance found in the CMO, CDO, CDS, rates, commodities, and equity derivatives markets. Industry practioners will teach five of the seven lectures, providing a valuable "first-hand" look at these markets and the desks they supervise. Two lectures will be devoted to developing a basic understanding of financial accounting - the balance sheet, the income statement and the statement of cash flows - and the issues involved in accounting for derivative instruments. Required Texts: Berman, K., Financial Intelligence, 2006, ISBN 1-59139-764-2; Chisholm, A., An Introduction to Capital Markets, John Wiley & Sons, 2008, 978-0471-49866-7 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, 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: Introduction to Probability 46-921, Introduction to Statistical Inference 46-923, Linear Financial Models 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: Tuckman, B., Fixed Income Securities, 2nd edition, ISBN 0-471-06322-3 (paperback) 0-471-06317-7 (hardcover). Prerequisite: None.

Linear Financial Models 46-926
This is a course in regression analysis and linear models with application to modeling equity and portfolio price processes. 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, heavy-tailed distributions and nonlinear regression are also introduced. Examples will be taken from financial models, including the CAPM and multi-factor with applications to portfolio selection and term structure. Reference text (not required): Campbell, J.Y., A. W. Lo, and A. C. MacKinlay, The Econometrics of Financial Markets, Princeton University Press, 1997; Venables and Ripley, Modern Applied Statistics with Splus, 3rd 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.

Course Descriptions-4
Macroeconomics for Computational Finance 45-905
This course is a macroeconomics class that is tailored for Masters students in a quantitative finance program. This means that the class will emphasize the intersection between macroeconomics, financial markets and financial valuation theory. For example, a representative topic is the relationship between exchange rates and interest rates. Both are obviously macroeconomic variables. Equally obvious is that they are (basically) the prices of random future cash flows, the purview of valuation theory. The basic premise of the class is that one cannot understand exchange rates and interest rates without bringing together macroeconomics and valuation theory. A good way to communicate the course's content and goals is by considering a common job-interview question; "what determines interest rates?" A weak answer would be "the Fed." Interest rates in the Soviet Union were determined by the government, but in the market economy that we live in it's not so simple. Interest rates are yields on bonds. Bond yields are simple functions of bond prices. Bond prices are determined in a competitive marketplace just like the price of orange juice. The Fed certainly has an influence on interest rates, but the word "determines" is too strong. A better answer is as follows. Nominal interest rates have three components: real interest rates, inflationary expectations and risk premiums. Inflationary expectations are the only component that the Fed has (somewhat) direct control over. Real interest rates are determined by people's preferences for saving versus consuming and by real macroeconomic variables like productivity and demographics. Risk premiums are determined by people's attitudes toward uncertainty and involve complex interactions between inflation, real interest rates and the time-to-maturity of the particular interest rate. Students who take this class will understand the theory and the evidence underlying each of these components.

MSCF Finance 45-711
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: Berk, J. and P. DeMarzo, Corporate Finance, 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: 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.

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