Applied Maths Seminar: Rutkowski -- Arbitrage pricing of defaultable game options

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

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).

http://www.maths.usyd.edu.au/u/AppliedSeminar/abstracts/2010/rutkowski.html