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