Table of Contents
ISRN Probability and Statistics
Volume 2013, Article ID 851419, 12 pages
http://dx.doi.org/10.1155/2013/851419
Research Article

Multidimensional Structural Credit Modeling under Stochastic Volatility

1Ryerson University, Toronto, Canada M5B 2K3
2Technische Universität München, 85748 München, Germany
3RiskLab Toronto at the University of Toronto, Toronto, Canada M5S 2E4
4Chair of Mathematical Finance, Technische Universität München, 85748 München, Germany

Received 13 April 2013; Accepted 8 May 2013

Academic Editors: P. D'Urso, M. Galea, P. E. Jorgensen, and S. Sagitov

Copyright © 2013 Marcos Escobar et al. 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

This paper extends the structural credit model with underlying stochastic volatility to a multidimensional framework. The model combines the Black/Cox framework with the Heston model interpreting the equity of a company as a down-and-out barrier call option on the company's assets. This implies a combination of local and stochastic volatility on the equity as well as other stylized features. In this paper, we allow for a correlation between the asset processes of different companies to incorporate dependency structures. An estimator for the correlation parameter is derived and tested in a recovery framework. With the help of this model, we examine the default risk of the two mortgage lenders Fannie Mae and Freddie Mac before their actual placement into federal conservatorship and show that their default risk severely increased during the financial crisis.