Finance and Economics Discussion Series (FEDS)
February 2013
Expectations of functions of stochastic time with application to credit risk modeling
Ovidiu Costin, Michael B. Gordy, Min Huang, and Pawel J. Szerszen
Abstract:
We develop two novel approaches to solving for the Laplace transform of a time-changed stochastic process. We discard the standard assumption that the background process is Levy. Maintaining the assumption that the business clock and the background process are independent, we develop two different series solutions for the Laplace transform of the time-changed process. In fact, our methods apply not only to Laplace transforms, but more generically to expectations of smooth functions of random time. We apply the methods to introduce stochastic time change to the standard class of default intensity models of credit risk, and show that stochastic time-change has a very large effect on the pricing of deep out-of-the-money options on credit default swaps.
Full paper (Screen Reader Version)Keywords: Stochastic time change, default intensity, credit risk, CDS options
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