英文标题：
《Approximate hedging with proportional transaction costs in stochastic
volatility models with jumps》
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作者：
Thai Huu Nguyen and Serguei Pergamenschchikov
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最新提交年份：
2019
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英文摘要：
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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中文摘要：
在随机波动和跳跃相结合的模型中，我们研究了在固定比例交易成本下的期权复制问题，以捕捉市场的重要特征。假设跳跃大小分布上的一些温和条件，我们证明了交易成本可以通过应用Leland调整波动率原理来近似补偿，并且刻画了由于离散调整而产生的套期保值误差的渐近性质。特别是，可以近似地消除跳跃风险，并恢复在连续扩散模型中建立的结果。该研究还证实，在交易成本率不变的情况下，卡巴诺夫和萨法里安（1997年）以及佩尔加门奇科夫（2003年）建立的近似结果仍然适用于使用利兰（1986年）中经典的利兰参数的具有确定性波动性的跳跃扩散模型。
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分类信息：

一级分类：Quantitative Finance 数量金融学
二级分类：Mathematical Finance 数学金融学
分类描述：Mathematical and analytical methods of finance, including stochastic, probabilistic and functional analysis, algebraic, geometric and other methods
金融的数学和分析方法，包括随机、概率和泛函分析、代数、几何和其他方法
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