Approximate hedging with proportional transaction costs in stochastic volatility models with jumps

We study the problem of option replication under constant proportional transaction costs in models where stochastic volatility and jumps are combined to capture market's important features. In particular, transaction costs can be approximately compensated applying the Leland adjusting volatility principle and asymptotic property of the hedging error due to discrete readjustments is characterized. We show that jump risk is approximately eliminated and the results established in continuous diffusion models are recovered. The study also confirms that for constant trading cost rate, the results established by Kabanov and Safarian (1997) and Pergamenshchikov (2003) are valid in jump-diffusion models with deterministic volatility using the classical Leland parameter.