This webpage describes future Quantitative Finance courses that are not now offered but are under development for the future. These courses under development have not yet been approved by the Graduate School.

• AMS 518 - Advanced Portfolio Optimization (under development)
• AMS 519 - Advanced Options Theory (under development)
• AMS 520 - Interest Rate Sensitive Securities (under development)
• AMS 521 - Credit Risk Modeling and Credit Derivatives (under development)

AMS 518 - Advanced Portfolio Optimization (under development)

Development and formulation of portfolio optimization problems in single and multi-period settings. Exploration of the geometry and economic significance of problems of portfolio selection in an advanced setting. Formulation and solution of optimization problems via a variety of approaches such as vector space and interior point methods. The stability and sensitivity of mathematical programs in portfolio management will be explored. There will be extensive coverage of the analysis of data required to parameterize practical problems. Prerequisites: AMS 540 and AMS 513. 3 credits.

Suggested texts:

• Campbell, John Y., & Luis M. Viceira, Strategic Asset Allocation, Oxford University Press, 2002.
• Luenberger, David G., Linear and Nonlinear Programming (2nd ed.), Kluwer Academic Publishers, 2003.
• Luenberger, David G., Optimization by Vector Space Methods, Wiley, 1969.
• Markowitz, Harry M., Mean-Variance Analysis in Portfolio Choice and Capital Markets, Blackwell, 1987.
• Nocedal, Jorge, & Stephen J. Wright, Numerical Optimization, Springer-Verlag, New York, 1999.

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AMS 519 - Advanced Options Theory & Valuation Methods (under development)

Advanced topics in the pricing of options. Detailed study of such exotics as lookback options, ladder options, tigger or knock-in options, basket options, and multi-asset options. Development and pricing of customized structured products. Parameter estimation and pricing under conditions of stochastic volatility, including mixture distributions, GARCH models, and the failure of traditional pricing approaches under volatility explosions. Prerequisite: AMS 514. 3 credits.

Suggested texts:

• Cont, Rama, and Peter Tankov, Financial Modelling with Jump Processes, Chapman & Hall, 2004.
• Lewis, Alna L., Option Valuation under Stochastic Volatility, Finance Press, 2000.
• Schoutens, Wim, Lévy Processes in Finance: Pricing Financial Derivatives, Wiley, 2003.
• Shaw, William, Modeling Financial Derivatives with Mathematica, Cambridge University Press, 1998.

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AMS 520 - Interest Rate Sensitive Securities Theory and Valuation (under development)

Organization and operation of the LIBOR and Swap Markets. Theory and implementation of interest rate models including no arbitrage pricing, change of numeraire, and short rate factor models such as Heath-Jarrow-Morton. Advanced techniques in pricing interest rate sensitive securities including numerical methods and the estimation of parameters required to calibrate models to current market rates and implied volatilities. Pricing of equity derivatives under stochastic interest rates. Prerequisites AMS 512 and AMS 513. 3 credits.

Suggested text:

• Brigo, Domiano, and Fabio Mercurio, Interest Rate Models - Theory and Practice, Springer, 2001.

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AMS 521 - Credit Risk Modeling and Credit Derivatives (under development)

Development of credit derivatives and their markets. Credit risk modeling, including factor model and copulas for default correlation models. and recovery modeling. Pricing models using a variety of approaches. Prerequisites AMS 512 and AMS 513. 3 credits.

Suggested texts:

• Bluhm, Christian, Ludger Overbeck and Christoph Wagner, An Introduction to Credit Risk Management, Chapman and Hall, 2002.
• Schonbucher, Philipp J., Credit Derivatives Pricing Models: Models Pricing and Implementation, Wiley, 2003.
• Tavakoli, Janet M., Credit Derivatives and Synthetic Structures, 2 Ed., Wiley, 2001.

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