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We study the problem of option replication under constant proportionaltransaction costs in models where stochastic volatility and jumps are combinedto capture the market's important features. Assuming some mild condition on thejump size distribution we show that transaction costs can be approximatelycompensated by applying the Leland adjusting volatility principle and theasymptotic property of the hedging error due to discrete readjustments ischaracterized. In particular, the jump risk can be approximately eliminated andthe results established in continuous diffusion models are recovered. The studyalso confirms that for the case of constant trading cost rate, the approximateresults established by Kabanov and Safarian (1997)and by Pergamenschikov (2003)are still valid in jump-diffusion models with deterministic volatility usingthe classical Leland parameter in Leland (1986).

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