### 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).