Perturbations Methods in Default Modeling

  • Date: 09/28/2006

Jean-Pierre Fouque (University of California, Santa Barbara)


University of British Columbia


Stochastic volatility has played a central role in modeling equity
derivative markets. In the recent years the market in credit-linked
derivative products has grown tremendously and had generated a need for
more sophisticated models of default. We show that stochastic
volatility incorporated in first passage models can create reasonable
default probabilities over a wide range of maturities. To achieve that,
one has to carefully calibrate the time scales of volatility. Regular
and singular perturbation techniques associated to slow and fast time
scales can be used to make this approach tractable. We then address the
multi-name case and we show that default correlations created by
stochastic volatility give interesting loss distributions. Perturbation
techniques are again used to compute these distributions and the
related CDO tranche prices.

Other Information: 

MITACS Math Finance Seminar 2006