Time-Changed Birth Processes and Multi-Name Credit Derivatives

Operations Research, Forthcoming

32 Pages Posted: 5 Jan 2007 Last revised: 15 Jun 2016

See all articles by Kay Giesecke

Kay Giesecke

Stanford University - Department of Management Science & Engineering

Xiaowei Ding

Stanford University

Pascal Tomecek

Cornell University

Date Written: February 28, 2008

Abstract

A credit investor such as a bank granting loans to firms or an asset manager buying corporate bonds is exposed to correlated corporate default risk. A multi-name credit derivative is a financial security that allows the investor to transfer this risk to the credit market. In this article, we study the valuation and risk analysis of multi-name derivatives. To capture the complex economic phenomena that drive the pricing of these securities, we introduce a time-changed birth process as a probabilistic model of correlated event timing. The self-exciting property of a time-changed birth process captures the feedback from events that is often observed in credit markets. The stochastic variation of arrival rates between events captures the exposure of firms to common economic risk factors. We derive a closed-form expression for the distribution of a time-changed birth process, and develop analytically tractable pricing relations for a range of multi-name derivatives valuation problems. We illustrate our results by calibrating a tranche forward and option pricer to market rates of index and tranche swaps.

Keywords: Self-affecting point process, birth process, event feedback, time change, portfolio credit derivative

JEL Classification: C63

Suggested Citation

Giesecke, Kay and Ding, Xiaowei and Tomecek, Pascal, Time-Changed Birth Processes and Multi-Name Credit Derivatives (February 28, 2008). Operations Research, Forthcoming, Available at SSRN: https://ssrn.com/abstract=1100334

Kay Giesecke (Contact Author)

Stanford University - Department of Management Science & Engineering ( email )

475 Via Ortega
Stanford, CA 94305
United States
(650) 723 9265 (Phone)
(650) 723 1614 (Fax)

HOME PAGE: http://https://giesecke.people.stanford.edu

Xiaowei Ding

Stanford University ( email )

Stanford, CA 94305
United States

Pascal Tomecek

Cornell University ( email )

Ithaca, NY 14853
United States

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