The Computational Finance Track emphasizes both financial quantitative theory and practice, bridging the two and using both the fundamental concepts of finance and the stochastic and optimization methods and software in finance. This track is meant for those individuals with a strong desire to become quantitative financial managers or to pursue applied finance research interests in cutting-edge investment science, trading and in financial risk management. Techniques such as quantitative finance, financial econometrics, stochastic modeling, simulation and optimization are part of a set of financial tools applied to the many problems of derivatives and options finance, arbitrage trading algorithms, asset pricing, credit risk and credit derivatives, developing new derivative products and the many areas where quant finance has a contribution to make.
Graduates of the Computational Finance Track will be qualified to work in pricing financial risk and their management, in credit risk and their derivatives, in cutting-edge institutions, in quant hedge funds and in research and advanced product development departments of financial and consulting firms. Graduates of the Risk Finance Track will have the qualification and abilities to become responsible specialists for positions in finance, credit granting firms, banks and insurance companies, as well as obtain the knowledge needed to face the upcoming complex problems arising by the increased use and centrality of financial insurance products (contributing to the development of complex financial products and a convergence) of finance and insurance. The complementary actuarial profession is a discipline that uses tools from statistics, probability theory and finance to analyze and solve practical problems in insurance and financial risk management. Actuaries assemble and analyze data to estimate the probability and likely cost of an event such as death, sickness, injury, disability or loss of property. Courses in risk finance provide the background for the first four actuarial examinations supervised by the Society of Actuaries and the Casualty Actuarial Society and cover additional educational experience requirements.
Required to Complete the Financial Engineering MS program:
- 5 core courses, each 3 credits totaling 15 credits
- Track-required courses totaling 7.5 credits
- 1 required applied lab worth 1.5 credits
- 6 credits of electives
- 1 capstone experience of 3 credits
- Capstone assessment (0 credits)
- Bloomberg Certification (0 credits)
Total # of credits: 33
- Options Pricing & Stochastic Calculus FRE-GY 6233
- This course provides the mathematical foundations of Option Pricing models. The techniques covered include arithmetic and geometric Brownian motion, first passage time, the reflection principle, the stochastic Ito integral, Ito differential Calculus, change of probability measure, martingales, Stochastic Differential Equations and Partial Differential Equations. Some of the pricing models considered are the European, Barrier, Asian and American options. These problems are either solved analytically by the martingale approach or numerically, by applying approximation and simulation methods. Since the same techniques allow the treatment of more complex financial products, examples of credit derivatives will be also presented. This course is a requirement in the Computational Finance Track
Prerequisite: FRE-GY 6083
3 of the following courses (4.5 Credits):
- Extreme Risk Analytics FRE-GY 6041
- The course covers failures of financial theory in risk management, deriving from fundamental definitions and assumptions in modeling, including pricing formulae; convexity; stochasticity and volatility; "fat tails"; and risk. Other topics: Portfolio robustness and extreme markets and moral hazard; data-mining biases and decision error; and decision-making with incomplete information.
Pre-Requisite: Graduate Standing
- Numerical & Simulation Techniques in Finance FRE-GY 6251
- Advanced numerical techniques for the solution of ordinary, partial and stochastic differential equations are presented. These techniques are analyzed both mathematically and using computer aided software that allows for the solution and the handling of such problems. In addition, the course introduces techniques for Monte Carlo simulation techniques and their use to deal with theoretically complex financial products in a tractable and practical manner. Both self-writing of software as well as using outstanding computer programs routinely used in financial and insurance industries will be used.
Prerequisite: FRE-GY 6083 and Graduate Standing
- Dynamic Assets and Options Pricing FRE-GY 6311
- The course focuses on inter-temporal assets pricing in discrete and continuous time. The course explores problems in complete and incomplete markets of both theoretical and practical interest that require an appreciation of financial economic theories and computational techniques. Financial-engineering techniques are introduced including Martingales, stochastic calculus and jump processes; these are applied to engineering problems in finance. Problems and cases are presented that span Stocks and Derivatives (options of various sorts), Bonds and Implied Risk-Neutral Pricing.
Prerequisites: FRE-GY 6083, FRE-GY 6123 and Graduate Standing
- Financial Risk Management and Optimization FRE-GY 6331
- This course provides solutions to the inter-temporal problems in financial management of portfolios, credit risks and market making. Dynamic and stochastic dynamic programming techniques as well as optimal control and stochastic control principles of optimality are presented, and their financial contexts emphasized. Both theoretical and practical facets of inter-temporal management of financial risks and risk pricing are also stressed. The course uses financial and optimization software to solve problems practically.
Prerequisites: FRE-GY 6083, FRE-GY 6123, and FRE-GY 6091 and Graduate Standing.
- Econometrics and Time Series Analysis FRE-GY 6351
- Financial econometrics has matured into a necessary and essential part of financial engineering that provides opportunities to deal with real and practical problems in finance. For example, techniques such as ARCH and GARCH and their subsequent development are used to estimate the volatility of underlying financial processes; the analysis of intra-day trading data that requires particular models and techniques; memory-based and fractal stochastic processes to study complex markets behaviors and copulas applied routinely to model- and estimate-dependent risks. These financial and risk problems require the application of advanced financial-econometric techniques, which the course provides from both theoretical and empirical-applied viewpoints. Selected cases provide a real-world sense of financial engineering when it is faced with financial-market reality and complexity.
Prerequisite: FRE-GY 6083 and Graduate Standing
- Credit Risk & Financial Risk Management FRE-GY 6491
- This course provides a deep understanding of credit instruments from a qualitative and quantitative point of view. Students learn how to price credit derivatives and hedge credit risk. Both the structural and intensity models approaches are presented. Applications to a number of structured products are considered.
Prerequisites: FRE-GY 6411 and Graduate Standing
- Quantitative Portfolio Management FRE-GY 6711
- This course focuses on the quantitative foundations of portfolio management . It teaches the fundamental mathematical models such as the Markowitz, CAPM, and the Merton investment-consumption models, and discusses the issues related to the implementation of these models in practice to different types of portfolios. Finally, it also introduces some common portfolio construction and rebalancing techniques.
Prerequisites: Matriculation into a graduate program sponsored by the Department of Finance & Risk Engineering, or permission of the Department & FRE-GY 6083
- Special Topics in Financial Engineering FRE-GY 6971
- Current topics of particular importance in finance and risk engineering are analyzed and discussed. Selected topics will be emphasized and provide focus for further study. Examples might include urban finance engineering, environmental
finance, infrastructure and projects finance, real estate finance, insurance
finance and derivatives, macro hedge funds management, among others. Prerequisites: advanced standing and instructor’s permission and Graduate Standing
Recommended Electives (6 credits):
- Selected Topics in Financial Engineering FRE-GY 6961
- Current topics of particular importance in finance and risk engineering are analyzed and discussed. Selected topics are emphasized and provide focus for further study. Examples might include infrastructure and projects finance, international and global finance, economics and finance in developing countries, global finance in a global world, international investment strategies, finance and taxes, among others.
Prerequisites: advanced standing and instructor’s permission.
- Statistical Arbitrage FRE-GY 7121
- Statistical arbitrage refers to strategies that combine many relatively independent positive expected value trades so that profit, while not guaranteed, becomes very likely. This course prepares students to research and practice in this area by providing the tools and techniques to generate and evaluate individual trading strategies, combine them into a coherent portfolio, manage the resulting risks, and monitor for excess deviations from expected performance. It introduces theoretical concepts such as cointegration, risk capital allocation, proper backtesting, and factor analysis, as well as practical considerations such as data mining, automated systems, and trade execution. Programming languages such as R, Python, or C++ will be used to present applications to data at low, intermediate and high frequency.
Prerequisites: Matriculation into a graduate program sponsored by the Department of Finance & Risk Engineering, or permission of the Department & FRE-GY 6123 and FRE-GY 6083
- Topics in Risk Finance I FRE-GY 7821
- Current topics of particular importance in Actuarial Science are analyzed and discussed. Course topics may include for example: Pension Funds management, Actuarial Science and Social Security, Life Insurance, Insurance and Financial Products design and management.
Prerequisite: Advanced standing and instructor’s permission.
- Topics in Financial and Risk Engineering I FRE-GY 7831
- Current and selected topics of particular importance in finance and risk engineering are analyzed and discussed. Selected topics are emphasized and provide a focus for further study. Topics include Credit Risk and Credit Derivatives, Quantitative Methods in Rare Events, Energy, Oil and Water Finance as well as advanced topics in financial econometrics and computational finance.
Prerequisites: Graduate standing and instructor’s permission.
- Topics in Financial and Risk Engineering 2 FRE-GY 7851
- Current topics of particular importance in finance and risk engineering are analyzed and discussed. Selected topics are emphasized and provide a focus for further study. Examples can include urban finance engineering, environmental finance, infrastructure and projects finance, real-estate finance, insurance finance and derivatives, and macro hedge funds management.
Prerequisites: Graduate standing and instructor’s permission.
Recommended Labs (1.5 credits*):
- Computational Finance Laboratory FRE-GY 6831
- This course teaches students to use Matlab and GAMS.
Prerequisites: Graduate Standing
- Financial Computing FRE-GY 6883
- This course covers programming applications to financial engineering, including C++ and Java and the various common development environments for them. Topics include structured and object-oriented programming in C++ with applications to binomial options pricing, multi-threaded programming in Java with applets and graphical interfaces with applications to risk measurement tools, data-based manipulation and programming in SQL and standard database access libraries with applications to historical financial data series retrieval and management, and other advanced programming concepts important for financial engineering such as numerical techniques, trading systems, and large-scale software design.
Matriculation into a graduate program sponsored by the Department of Finance & Risk Engineering, or permission of the Department.
*FRE-GY 6883 counts both as a lab (1.5 credits) and as an elective (1.5 credits), totaling 3 credits.