Hedging Under Jump Diffusion with Transaction Costs

  • Date: 11/06/2006

Peter Forsyth (University of Waterloo)


University of British Columbia


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.

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