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development based on these models will be discussed. Reference texts (notrequired): 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.

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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: Richard A Brealey, Stewart C Myers, Franklin Allen "Principles of Corporate Finance" 9th edition (2007) ISBN 0072957239

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 jWww Savings2ndmortgage Tag Travel Savings 2nd Mortgage 排名5：Carnegie Mellon Computational Finance - 国外金融教育项目 - 学习交流 - 风险视界-风险管理与金融工程专业交流平台 - Powered by Discuz!o g Savings 2nd Mortgage Savings 2nd Mortgage gWww Savings2ndmortgage Tag Travel Savings 2nd Mortgage 排名5：Carnegie Mellon Computational Finance - 国外金融教育项目 - 学习交流 - 风险视界-风险管理与金融工程专业交流平台 - Powered by Discuz!a y Savings 2nd Mortgage Savings 2nd Mortgage Savings 2nd Mortgage