Course Descriptions : Tepper School of Business at Carnegie Mellon
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COURSE DESCRIPTIONS Advanced Derivative Modeling 46-915 This course considers more advanced models. We start by revisiting the F ourier transform and discuss how to use this technique to price vanilla options in different standard vol 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, 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. Prerequisite: Stochastic Calculus for Finance II 46945, Simulation Methods for Option Pricing 46-932. Credit Derivatives 45-903 This course provides techniques for modeling credit risk. We will present the mathematical techniques which can be used to model credit prices. We w ill first focus on single name derivatives (mainly the CDS contract and variants hereof). Secondly, we will introduce the copulas and consider basket derivatives (mainly the first-to-default and CDO contracts). We will not follow a specific textbook and therefore it is recommended that you take notes. I will post the doc slides after the NY lecture. There are countless textbooks on credit derivatives: our main text will be the book by P. Sch"onbucher: Credit Derivatives Pricing Models: Models, Pricing and Implementation. Implementation. Prerequisite: Stochastic Calculus for Finance II 46-945, Simulation Methods for Option Pricing 46-932, Options 45-814, Advanced Derivative Modeling 46915. 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 t rading 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 5, 2011. Financial Computing I 46-901 This will be a "Survival Computing" course for MSCF students. We will cover the basics o f 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): "C++ Primer" by Lippman, et al, "Numerical Recipes in C++" by P ress, 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 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 Financial Computing I 46-901, Financial Computing II 46-902.
Course Descriptions : Tepper School of Business at Carnegie Mellon
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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 46903. Financial Economics for Computational Finance 45-848 Valuation Theoryis 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 This course provides a broad overview of the financial markets, its institutions, and the products they create and trade. Our focus is upon the pockets of quantitative finance found in the CMO, CDO, CDS, rates, commodities, and the equity derivatives markets. Industry practioners will teach five of the seven lectures, providing a v aluable "first-hand" overview of 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, the statement of cash flows (as well as a brief overview of the issues involved in accounting for derivative instruments) with the goal of helping you better appreciate how useful these disclosures may be in assessing a company's future performance. Required Texts: "Risk Management, Derivatives, and Financial Analysis Under SFAS No. 133," Gary Gastineau, AIMR Publications, 2001, ISBN 0-943205-51-4; "Financial Intelligence" by Karen Berman, 2006, ISBN 1-59139-764-2; "Capital Markets for Quantitative Professionals," by Alex Kuznetsov, McGraw-Hill, 2007, 0-07-146829-3. 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 v aluation 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. Corequisite: Multi-Period Asset Pricing. 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 is a macroeconomics class that is tailored for Masters students in a quantitative finance program. This
Course Descriptions : Tepper School of Business at Carnegie Mellon
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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 pr emise 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 a nd 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. Prerequisite: Intro to MSCF Finance 45-711, Options 45-814, Linear Financial Models 46-926, Multi Period Asset Pricing 46-941. MSCF Finance 45-711 Broadly speaking, there are three types of p layers 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, Noarbitrage 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: 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 BlackScholes, 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 peek 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, Co-requisite: Intro to Fixed Income 46-956, Multi-Period Asset Pricing 46941. 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 t arget key decision-makers’ needs, craft verbal and quantitative arguments, and provide problem-solving action-oriented content. Prerequisite: None. 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.
Course Descriptions : Tepper School of Business at Carnegie Mellon
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Quantitative Asset Management 45-908 This course covers quantitative techniques that are used in investment management. The essential elements of a quantitative investment management process include a model of risk and return, portfolio construction tools that find optimal trade-offs between risk and return, strategies for portfolio rebalancing and trading, and some attribution mechanism to measure performance. The course will place special emphasis on the algorithmic techniques for portfolio construction and trading. The first half of the course will deal with static models. These include conventional active management based on mean-variance optimization as well as modern techniques such as resampled efficiency, Bayesian approaches, robust, and scenario optimization. The second half of the course will be devoted to dynamic models. These include multi-period asset-liability management, optimal execution strategies, and dynamic portfolio choice. Representative Texts: Grinold and Kahn, "Active Portfolio Management." Cornuejols and Tutuncu, "Optimization Methods in Finance." Campbell and Viceira, "Strategic Asset Allocation: Portfolio Choice for Long-Term Investors." Prerequisites: Intro to MSCF Finance 45-711, Stochastic Calculus II 46-945, Simulation Methods for Option Pricing 46932, Financial Computing III 46-903. 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, 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 tr ading, valuebased 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. 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. 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 multivariate 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-IngersollRoss, 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 Analysis: Securities, Pricing, and Risk Management, Lecture Notes, 2005. Prerequisite: Stochastic Calculus for Finance I 46-944. 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 vary from year to year. In 2010, the course will include both risk management
Course Descriptions : Tepper School of Business at Carnegie Mellon
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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 t he use of importance sampling for Monte Carlo simulation of VaR for portfolios of options and of bonds. A guest lecture by a risk management professional will be given. The mathematical finance topics will include models for the spread between forward interest rates and interest rate futures, the Brace-Gatarek-Musiela model, and pricing and hedging volatility products. 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.
