Journal of Applied Mathematics
Volume 2011, Article ID 158020, 20 pages
http://dx.doi.org/10.1155/2011/158020
Credit Risky Securities Valuation under a Contagion Model with Interacting Intensities
1Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200240, China
2School of Jiashan Guangbiao, Shanghai 201209, China
3School of Business Information Management, Shanghai Institute of Foreign Trade, Shanghai 201620, China
Received 13 April 2011; Revised 20 June 2011; Accepted 20 June 2011
Academic Editor: Mark A. Petersen
Copyright © 2011 Anjiao Wang and Zhongxing Ye. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
We study a three-firm contagion model with counterparty risk and apply this model to price defaultable bonds and credit default swap (CDS). This model assumes that default intensities are driven by external common factors as well as other defaults in the system. Using the “total hazard” approach, default times can be generated and the joint density function is obtained. We represent the pricing method of defaultable bonds and obtain the closed-form pricing formulas. By the approach of “change of measure,” analytical solutions of CDS swap rate (swap premuim) are derived in the continuous time framework and the discrete time framework, respectively.