Journal of Applied Mathematics and Stochastic Analysis
Volume 2009 (2009), Article ID 695798, 33 pages
doi:10.1155/2009/695798
Research Article
Defaultable Game Options in a Hazard Process Model
1Department of Applied Mathematics, Illinois Institute of Technology, Chicago, IL 60616, USA
2Département de Mathématiques, Université d'Évry Val d'Essonne, 91025 Évry Cedex, France
3Europlace Institute of Finance, Palais Brongniart-28 Place de la Bourse, 75002 Paris, France
4School of Mathematics and Statistics, University of New South Wales, Sydney, NSW 2052, Australia
5Faculty of Mathematics and Information Science, Warsaw University of Technology, 00-661 Warszawa, Poland
Received 22 October 2008; Accepted 4 April 2009
Academic Editor: Salah-Eldin Mohammed
Copyright © 2009 Tomasz R. Bielecki 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
The valuation and hedging of defaultable game options is studied in a hazard process model of credit risk. A convenient pricing formula with respect to a reference filteration is derived. A connection of arbitrage prices with a suitable notion of hedging is obtained. The main result shows that the arbitrage prices are the minimal superhedging prices with sigma martingale cost under a risk neutral measure.