IEOR 298

IEOR 298: Selected Topics in Financial Engineering

(Spring 2008)

3:30pm – 5:00pm, TTh, 89 Dwinelle.

Instructor
Xin Guo
Department of IEOR

Room: #4173 Etcheverry Hall
Office Hours: T Th 5:00pm ~ 6:00pm
Email: xinguo AT ieor.berkeley.edu
Phone: 510-642-3615

Announcements

02/01/2008: Homework 1 posted.
02/09/2008 Homework 1 solution and lecture materials posted.

Course Information

The course aims at graduate students who are interested in Financial Engineering and would like to know the state-of-art topics in this area. It will start with a gentle review of the basic finance and mathematical concepts needed for the course, summarizing key notions such as no-arbitrage, complete market, pricing/hedging, and martingales. The course will move on to credit/default risk, one of the most active research topics in financial engineering. Default risk is critical in many areas such as portfolio management, mortgage, and insurance; a proper understanding requires some beautiful theory from stochastic processes, semi-martingales, and filtration expansions. This course will cover the fundamentals, including the classical structural approach, the reduced-form approach, and the current information-based approach, as well as issues of pricing credit derivatives and modeling correlated default. Finally, it will cover another important and relevant topic, namely, risk measure.

Solid background in either stochastic processes or finance will be helpful, especially for students without FE I. Talk to the instructor with further inquiries.

Main references

In addition to recent papers on the topics for the course, which will be distributed in class, the following references will be used throughout the semester.

S. Shreve. Stochastic Calculus for Finance II, 2004
D. Lamberton. Introduction to Stochastic Calculus Applied to Finance, 1996
T. Bielecki and M. Rutkowski. Credit Risk: Modeling, Valuation, and Hedging, 2002.
D. Duffie and K. Singleton. Credit Risk, 2003.
D. Lando. Credit Risk Modeling: Theory and Applications, 2004.
H. Follmer and A. Scheid. Stochastic Finance: An Introduction in Discrete time, 2002.
P. Schonbucher. Credit derivatives pricing models, 2003.

Lecture Summary

Preliminaries

Homework

Homework 1(solutions)

Reading Material

Review paper on American put
Numerical simulation for American put
Lando's paper on Cox processes and credit derivatives
Duffie and Lando's paper with incomplete accounting information

Final Projects

Longstaff, F.A, E. S. Schwartz (2001). Valuing American Options by Simulation: A Simple Least-squares Approach. Review of Financial Studies, 14: 113-147.
Myneni, R. (1992) The Pricing of the American Option. The Annals of Applied Probability, 2(1):1-23.
Jarrow, R.A, F. Yu (2001). Counterparty Risk and the Pricing of Defaultable Securities. Journal of Finance, 56: 1765-1799.
Collin-Dufresne, P, R. Goldstein, J. Helwege (2003). Are jumps in corporate bond yields priced? Modeling contagion via the updating of beliefs. Working Paper.
Leland, H.E. and K.B. Toft (1996). Optimal Capital Structure, Endogenous Bankruptcy, and the Term Structure of Credit Spreads. The Journal of Finance, 51: 987-1019.
Jarrow, R.A, D. Lando, S.M.Turnbull (1997). A Markov Model for the Term Structure of Credit Risk Spreads. Review of Financial Studies, 10: 481-523.
Guo, X, R.A. Jarrow, Y. Zheng (2008). Modeling the Recovery Rate in a Reduced-Form Model. Mathematical Finance, to appear.
Dembo, A, J. Deuschel, D. Duffie (2004). Large Portfolio Losses. Finance and Stochastics, 8: 3-16.
Elliott, R.J, M. Jeanblanc, M. Yor (2000). On Models of Default Risk. Mathematical Finance, 10: 179-195.
Duffie, D, N. Garleanu (2001). Risk and Valuation of Collateralized Debt Obligations. Financial Analysts Journal, 57: 41-60.
Altman, E. I, B. Brady, A. Resti, A. Sironi (2005). The Link between Default and Recovery Rates: Theory, Empirical Evidence, and Implications. The Journal of Business, 78: 2203-2228.
Duffie, D, M. Schroder, C. Skiadas. Recursive valuation of defaultable securities and the timing of resolution of uncertainty. Annals of Applied Probability, 6(4): 1075-1090.