Theory of Probability &Its Applications, Volume 65, Issue 2, Page 224-248, January 2020.
We study a 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. 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 [Finance Stoch., 1 (1997), pp. 239--250] and by Pergamenschikov [Ann. Appl. Probab., 13 (2003), pp. 1099--1118] are still valid in jump-diffusion models with deterministic volatility.

中文翻译：

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具有跳跃性的金融市场中具有恒定比例交易成本的近似对冲

概率论及其应用，第65卷，第2期，第224-248页，2020年1月。
我们在模型中研究了在比例交易成本不变的情况下的期权复制问题，在该模型中，随机波动和跳跃组合在一起以捕捉市场的重要特征。假设跳跃规模分布有一些温和的条件，我们表明可以通过应用Leland调整波动率原理和由于离散重新调整而产生的对冲误差的渐近性质来大致补偿交易成本。特别是，可以大致消除跳跃风险，并且可以恢复在连续扩散模型中建立的结果。该研究还证实，对于恒定的交易成本率，由Kabanov和Safarian [Finance Stoch。，1（1997），pp。239--250]和Pergamenschikov [Ann。应用 Probab。，13（2003），第2页。