  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).
