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

37 Pages Posted: 20 Sep 2016

See all articles by Ovidiu Costin

Ovidiu Costin

Ohio State University (OSU)

Michael B. Gordy

Federal Reserve Board

Min Huang

City University of Hong Kong (CityUHK)

Pawel Szerszen

Board of Governors of the Federal Reserve System

Multiple version iconThere are 2 versions of this paper

Date Written: October 2016

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 Lévy. 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.

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

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 (October 2016). Mathematical Finance, Vol. 26, Issue 4, pp. 748-784, 2016. Available at SSRN: https://ssrn.com/abstract=2841045 or http://dx.doi.org/10.1111/mafi.12082

Ovidiu Costin (Contact Author)

Ohio State University (OSU) ( email )

Michael B. Gordy

Federal Reserve Board ( email )

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

HOME PAGE: http://https://www.federalreserve.gov/econres/michael-b-gordy.htm

Min Huang

City University of Hong Kong (CityUHK)

83 Tat Chee Avenue
Kowloon
Hong Kong

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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