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Applied Mathematics Seminar
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Marek Rutkowski
School of Mathematics and Statistics, The University of Sydney

Arbitrage pricing of defaultable game options

Wednesday 5th May 14:05-14:55pm, New Law School Seminar 030 (Building F10).

The valuation and hedging of defaultable contracts with game option features within the hazard process approach to credit risk is examined. We first formally introduce the concept of a defaultable game option, that is, a financial contract that can be seen as an intermediate case between a general notion of a game option and a convertible bond with credit risk. We then concentrate on developing a general framework for valuing such contracts. In particular, building on results of Kallsen and Kuehn (2005), we show that the arbitrage pricing of a defaultable game option can be reduced to the study of the value process under some risk-neutral measure for the primary market model of the associated Dynkin game. A general result on hedging strategies in a hazard process set-up can be informally summarised as follows: under the assumption that the doubly reflected BSDE associated with the Dynkin game admits a solution under some risk-neutral measure, the state-process of the solution represents the minimal super-hedging price up to a local martingale cost process. More explicit results can be obtained for defaultable game options within particular setups, for instance, a jump-diffusion model.

This is the joint work with T. Bielecki (Illinois Institute of Technology), S. Crepey (University of Evry) and M. Jeanblanc (University of Evry).