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The prerequisites for the course are MATH 2403 and MATH 3215 (or the equivalent), knowledge of computer programming, and MS QCF standing or some previous exposure to the topics of stocks, bonds and options. Class notes are used for this course; these notes are at the level of The Mathematics of Financial Derivatives: A Student Introduction by P. Wilmott, S. Howison and J. Dewynne, published by Cambridge University Press.

The specific course topics are the following:

    * Solution of a single non-linear equation and its application in simulating geometric Brownian motion and computing implied volatility from the Black-Scholes formula.
    * Smooth interpolation and approximation of data by splines.
    * The heat equation and its solution, analytic properties and issues in its numerical solution.
    * The Black-Scholes equation for European options: derivatives, boundary conditions, the Black-Scholes formula, the binomial method, and finite-difference methods.
    * Solutions of the American option problem: boundary conditions implied by early exercise; numerical methods for the free boundary problem (finite differences with projection, the sweep method ??he method of lines); and barriers, jumps and transaction costs and their numerical treatment.
    * Pricing bonds: derivation of the diffusion equation, boundary conditions, and numerical considerations.
    * Path dependent options, stochastic volatility, options on multiple assets and other advanced models, and the need for Monte Carlo methods.

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Derivative Securities (MGT 6081)

This course provides an introduction to options, futures, and swaps. Concepts of arbitrage, index trading, and portfolio insurance are discussed.

The prerequisite for this course is MGT 6060, Financial Management, or MS QCF standing and MGT 6078. The course is at the level of the text Derivative Securities by R. Jarrow and S. Turnbull, published by South-Western College Publishing.

The specific course topics are the following:

    * Introduction to derivative securities.
    * Simple arbitrage relationships for forward and futures contracts.
    * Hedging, basis risk, and speculation.
    * Stock index futures.
    * Short-term interest rate futures.
    * Swaps.
    * Option markets.
    * Simple arbitrage relationships for options.
    * Trading strategies involving options.
    * Valuation of options using a binomial model.
    * The Black-Scholes analysis.
    * Options on stock indices, currencies, and futures contracts.
    * Hedging positions in options, and portfolio insurance.
    * Non-standard (exotic) options

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Design and Implementation of Systems to Support Computational Finance (ISYE/MATH 6767)

The prerequisites for this course are some knowledge of computer programming, and MS QCF standing or some previous exposure to the topics of stocks, bonds and options.

Course Description:
Introduction to large scale-system design to support computational finance for options, stocks, or other instruments. The course weaves together the tools to obtain Web-based financial data, store it in a data base, and use various mathematical toolkits to compute desired parameters. The course includes acquisition of functional literacy in Java and object-oriented programming, use of Java (1) to obtain data from the Web, and store and retrieve it from a data base, such as Oracle; (2) to interact with mathematical and computational finance tools as necessary, for example, MatLab; and (3) to design Java-based graphical user interfaces to manage individual applications. The course uses a sequence of examples, increasingly more challenging over time, to introduce various concepts. Students extend class examples and conclude with a final project that integrates the various concepts, principles, and skills the course contains.

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Fixed Income Securities (ISYE/MATH/MGT 6769)

The course will contain numerical work to implement the modeling; the prerequisites for this course are MGT 6060 or MGT 6078, MATH 3215 (or the equivalent), and some knowledge of programming.

Tentative Topics:

    * Introduction to Fixed Income Securities
    * Bond Calculations
    * Quantifying Interest Rate Risk
    * Floating Rate Notes and Interest Rate Swaps
    * Risk Management, Accounting, and Control
    * Stochastic Interest Rate Models
          o Bonds, Forward and Futures Contracts: Discrete- and Continuous-Time Models
          o Term Structure: Discrete- and Continuous-Time Models
          o Factor Spot Rate Models: Discrete- and Continuous-Time
          o Yield Curve Models and the Heath-Jarrow-Morton Model
    * Forwards, Futures and Options, caps and caplets, swaps
    * Credit Risk on Corporate Bonds
    * Emerging Market Debt
    * Mortgages and Mortgage Derivatives

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First Category Elective Courses
Stochastic Processes in Finance II         MATH 6235
Financial Optimization Models         ISYE 6673
Management of Financial Institutions         MGT 6090


Stochastic Processes in Finance II (MATH 6235)

This is the second of a two-semester sequence that develops basic probability concepts and models for working with financial markets and derivative securities. Continuous-time parameter stochastic processes are emphasized in this course. Mathematical concepts are introduced as needed.

The prerequisites for this course are MATH 2403 and ISYE/MATH 6759.

The specific course topics are the following.

    * Background on integration and on simulation
    * Brownian Motion, and Continuous-Time Martingales and their Variation.
    * The Ito Stochastic Integral and its Properties, and Ito's Change-of-Variable Formula.
    * Stock Prices as Geometric Brownian Motions.
    * Black-Scholes Option Pricing.
    * Ito Processes and Stochastic Differential Equations.
    * Continuous-Time Markov Processes and the Kolmogorov Equations.
    * Additional Results on Black-Scholes Option Pricing
    * Girsanov's Theorem for Change of Measure, and Martingale Representation Theorems
    * Asset Pricing theory, Risk Neutral Measures (Equivalent Martingale Measures), and Hedging
    * Pricing Specific Exotic Options
    * Continuous-Time Optimal Stopping and Pricing American Style Options

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Financial Optimization Models (ISYE 6673)

Financial optimization models are indispensable tools for managing risk, structuring portfolios and customizing financial products in the banking, insurance, corporate, and financial service sectors of our economy. This course will introduce different applications of optimization models, with special emphasis on formulation, analysis and implementation obtained by hands-on experience with computer modeling languages and cutting-edge optimization software. The prerequisites are ISYE 6225 or the MGT 6078 Finance and Investments course. ISYE 6669 or its equivalent is strongly recommended.. The course uses a text at the level of Operations Research, 3rd ed., Wayne L. Winston, Duxdury Press, and course handouts.

The specific course topics are the following.

    * Portfolio Selection Models
    * Asset Allocation Models
    * Index Construction Models for Equity and Bond Portfolios
    * Immunization Models to Manage Interest-Rate Risk
    * Cash Matching Models for Asset-Liability Management
    * Models to Structure Collateralized Mortgage Obligations
    * Firm Valuation Models
    * Valuation Bound Models on Financial Options
    * Dynamic Hedging Models for Risk Management

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Management of Financial Institutions [Risk Management] (MGT 6090)

This course provides an introduction to the various risks faced by financial institutions and a detailed analysis of the tools used to manage these risks.

The prerequisite for this course is MGT 6060, Financial Management, or MS QCF standing and the MGT 6078 Finance and Investments course . The course is at the level of the text Management of Financial Institutions by A. Saunders.

The specific course topics are the following.

    * Introduction (depository institutions)
    * Unique characteristics of financial institutions
    * Management of interest rate risk
    * Mortgage backed securities
    * Option adjusted spread analysis
    * Management of credit risk
    * Management of off-balance-sheet risk.
    * Management of foreign exchange risk.
    * Management of liquidity risk.
    * Deposit insurance.
    * Security underwriting.
    * Role of investment banks in treasury and municipal markets

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Second Category Elective Courses
Empirical Finance         MGT 7061
Statistical Techniques of Financial Data Analysis         ISYE/MATH 6783
The Practice of Quantitative and Computational Finance         ISYE/MATH/MGT 6785


Empirical Finance (MGT 7061)

The material and level of this course will be similar to that of the book Campbell, J., Lo, A. and MacKinlay, C. (1997) The Econometrics of Financial Markets. Princeton University Press, Princeton, N.J.

The topics of the course will be as follows:

    * Overview of Econometrics
    * Testing of Models Related to the Following Topics and Areas
    * Capital Asset Pricing Model
    * Arbitrage Pricing
    * Conditional Asset Pricing
    * Market Efficiency
    * Information and Volatility Issues
    * Option Pricing
    * The Course also covers some topics involving
    * Time Series Analysis and Prediction
    * Market Microstructure Issues
    * Event Studies
    * Investment Performance Evaluation

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Statistical Techniques of Financial Data Analysis (ISYE/MATH 6783)

Fundamentals of statistical inference are presented and developed for models used in the modern analysis of financial data. Techniques are motivated by examples and developed in the context of applications.

The prerequisites for the course are MATH 3215 (or the equivalent), some knowledge of programming, and MS QCF standing or some previous exposure to the topics of stocks, bonds and options.

The specific course topics are the following.

The following probability topics are covered in the models that are presented:

    * Distributions such as the normal (Gaussian), lognormal, geometric, binomial, Poisson, Student's t, F, chi-square, gamma, and Pareto
    * Characteristic functions, sums of independent random variables, a-stable random variables
    * Limit Theorems for sums
    * order statistics
    * Limit Theorems for extremes
    * Elementary stochastic processes such as Markov chains
    * Dynamic linear models
    * Time series models

The following topics in statistical inference are covered in the models that are presented:

    * Likelihood functions
    * Estimation
    * Testing Hypotheses via Neyman-Pearson tests, likelihood ratio tests, and Wald tests
    * Tests of fit
    * Markov chain and time series inference
    * Regression
    * Principal components analysis
    * Non-parametric analyses

Applications to financial data are made throughout and include the topics such as the following:

    * Testing hypotheses of independence, normality, homoscedascticity, and symmetry for returns, and the Bachelier and Mandelbrot models
    * Efficient frontier in portfolio analysis under short selling and riskless borrowing and lending, optimal portfolio under single index and multi-index models, principal components analysis, stability tests of betas from auxiliary data
    * simulation and Monte-Carlo, estimation and assessment of accuracy of path integrals arising in option pricing
    * Hill's estimator of the Pareto index, application to solvency analysis and ruin probabilities, connections with a-stability
    * Analysis of ar, ma, arma, arima, arch, garch, and stochastic volatility time series models applied to exchange rates, indexes, interest rates, and returns.

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The Practice of Quantitative and Computational Finance (ISYE/MATH/MGT 6785)

This course is jointly listed with the College of Management, the School of Mathematics and the School of Industrial and Systems Engineering. The course will consist of case studies, visiting lecturers from financial institutions and student group projects of an advanced nature - all centered around quantitative and computational finance. The group projects deal with applicable problems in areas such as portfolio management and optimization, pricing of derivatives, and data analysis and testing of models. The groups will be required to formulate and analyze the project problem, and implement and present their solutions to the problems. The prerequisite for the course is MS QCF major, or consent of the instructor. Normally the course is taken during the student's third semester in the QCF program.

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Additional QCF Elective Courses

For the Third Category Elective Courses Requirement there are many possible Elective Choices. Here is one of the courses directly related to quantitative and computational finance.
Advanced Topics in QCF

ISYE/MATH/MGT 6793

This course is jointly listed with the College of Management, the School of Mathematics and the School of Industrial and Systems Engineering. The course will deal with advanced research material in quantitative and computational finance. The prerequisite for the course is graduate standing, and consent of the instructor. Normally the course is taken during the student's third semester in the QCF program. The course will also be suitable for students pursuing Ph.D eWww Mortgagedealslending Tag Sans Serif Mortgage Deals Lending 排名12：Georgia Institute of Technology QCF(页 1) - 学习交流 - 国外金融教育项目 - 风险视界-风险管理与金融工程专业交流平台 - Powered by Discuz! Archiverr n Mortgage Deals Lending Fast Lending qWww Mortgagedealslending Tag Sans Serif Mortgage Deals Lending 排名12：Georgia Institute of Technology QCF(页 1) - 学习交流 - 国外金融教育项目 - 风险视界-风险管理与金融工程专业交流平台 - Powered by Discuz! Archivera Mortgage Deals Lending Mortgage Deals Lending Return