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Expectations of Functions of Stochastic Time with Application to Credit Risk Modeling

40 Pages Posted: 9 Apr 2013  

Ovidiu Costin

Ohio State University (OSU)

Michael B. Gordy

Board of Governors of the Federal Reserve

Min Huang

University of Chicago

Pawel Szerszen

Board of Governors of the Federal Reserve System

Multiple version iconThere are 2 versions of this paper

Date Written: February 26, 2013

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 (Xt) is Levy. Maintaining the assumption that the business clock (Tt) and the background process are independent, we develop two different series solutions for the Laplace transform of the time-changed process X-tildet=X(Tt). 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

Keywords: Stochastic time change, default intensity, credit risk, CDS options

JEL Classification: G12, G13

Suggested Citation

Costin, Ovidiu and Gordy, Michael B. and Huang, Min and Szerszen, Pawel, Expectations of Functions of Stochastic Time with Application to Credit Risk Modeling (February 26, 2013). FEDS Working Paper No. 2013-14. Available at SSRN: https://ssrn.com/abstract=2245641 or http://dx.doi.org/10.2139/ssrn.2245641

Ovidiu Costin

Ohio State University (OSU) ( email )

Michael B. Gordy (Contact Author)

Board of Governors of the Federal Reserve ( email )

20th & C. St., N.W.
Washington, DC 20551
United States
202-452-3705 (Phone)

Min Huang

University of Chicago ( email )

Pawel Szerszen

Board of Governors of the Federal Reserve System ( email )

20th Street and Constitution Avenue NW
Washington, DC 20551
United States

HOME PAGE: http://www.federalreserve.gov/research/staff/szerszenpawelj.htm

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