## 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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