DEPARTMENT OF INDUSTRIAL AND
ENTERPRISE SYSTEMS ENGINEERING
GE/IE 590 SEMINAR
Modelling Credit Risk with Jumps
Associate Professor Steven Kou
Industrial Engineering and Operations Research
Columbia University
Abstract
We propose a two-sided jump model for credit risk by extending the Leland-Toft endogenous default model
based on the geometric Brownian motion. The model shows that jump risk and endogenous default can have
significant impacts on credit spreads, optimal capital structure, and implied volatility of equity options: (1)
Jumps and endogenous default can produce a variety of non-zero credit spreads, including upward, humped,
and downward shapes; interesting enough, the model can even produce, consistent with empirical findings,
upward credit spreads for speculative grade bonds. (2) The jump risk leads to much lower optimal
debt/equity ratio; in fact, with jump risk highly risky firms tend to have very little debt. (3) The two-sided
jumps lead to a variety of shapes for the implied volatility of equity options, even for long maturity options;
although in general credit spreads and implied volatility tend to move in the same direction under exogenous
default models, this may not be true in presence of endogenous default and jumps.
Biography
Professor Steven Kou joined Columbia University's Industrial Engineering and Operations Research
Department in 1998, and he teaches courses in financial engineering, stochastic models, and probability and
statistics. Prior to joining Columbia, Professor Kou was an assistant professor in the Department of Statistics
at the University of Michigan. Professor Kou's research interests include mathematical and computational
finance, and applied probability. He has published in numerous journals including Management Science,
Mathematical Finance, Advances in Applied Probability, Annals of Applied Probability, Statistica Sinica,
and Finance and Stochastics.
In terms of financial engineering, professor Kou is well known for his research on the double exponential
jump diffusion model, models for growth stocks, the numerical pricing of discrete path-dependent options,
market LIBOR models with jump risk, and option pricing in incomplete markets. His results have been
widely used on Wall Street, and have been incorporated into standard M.B.A. textbooks, such as the
textbook by John Hull.
Location:
Date:
Time:
206 Transportation Building
Tuesday, February 12, 2008
4-5 p.m.