EXPECTATIONS OF FUNCTIONS OF STOCHASTIC TIME WITH APPLICATION TO CREDIT RISK MODELING. (15th December 2014)

• Record Type: Journal Article
• Authors: Costin, Ovidiu; Gordy, Michael B.; Huang, Min; Szerszen, Pawel J.
• Is Part Of: Mathematical finance. Volume 26:Number 4(2016:Oct.)
• Page Start: 748
• Page End: 784
• Publication Date: 2014-12-15
• Subjects: time change -- default intensity -- credit risk -- CDS options; Business mathematics -- Periodicals; 332
• DOI: 10.1111/mafi.12082
• Languages: English
• ISSNs: 0960-1627

Abstract

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 ( X t ) is Lévy. Maintaining the assumption that the business clock ( T t ) and the background process are independent, we develop two different series solutions for the Laplace transform of the time‐changed process X ̃ t = X ( T t ) . 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.