Hedging Under Jump Diffusion with Transaction Costs

In this talk, we consider the problem of hedging a contingent claim, where the underlying asset follows a jump diffusion process. The no-arbitrage value of the claim is given by the solution of a Partial Integro-Differential Equation (PIDE), which in general must be solved numerically. By constructing a portfolio consisting of the underlying asset and a number of liquidly traded options, we devise a dynamic hedging strategy. At each hedge rebalance time, we minimize both the jump risk and the cost of buying/selling due to bid-ask spreads. Simulations of this strategy show that the standard deviation of the profit and loss of the hedging portfolio is greatly reduced compared with the standard hedging strategy.

After graduating in 1979, Peter Forsyth was a Senior Simulation Scientist at the Computer Modelling Group (CMG) in Calgary, where he developed petroleum reservoir simulation software. After leaving CMG, Peter was the founding President of Dynamic Reservoir Systems (DRS), also in Calgary. DRS produced reservoir simulation software for PC's, using the then enormous amount of memory available (640K). DRS had three employees: a president and two vice-presidents. After selling out his shares in DRS (now owned by Duke) in 1987, Peter joined the University of Waterloo. In recent years, he has also carried out research-related consulting for such organizations as: SunLife of Canada, NOVA, the Electric Power Research Institute, Smithville Bedrock Remediation Corporation, Los Alamos National Laboratory, Oak Ridge National Laboratory, and HydroGeoLogic. Peter is currently a member of the Editorial Boards of Applied Mathematical Finance and the Journal of Computational Finance.