This paper analyzes the efficiency of hedging strategies for stock options in the presence of jump clustering. In the proposed model, the asset is ruled by a jump-diffusion process, wherein the arrival of jumps is correlated to the amplitude of past shocks. This feature adds feedback effects and time heterogeneity to the initial jump diffusion. After a presentation of the main properties of the process, a numerical method for options pricing is proposed. Next, we develop four hedging policies, minimizing the variance of the final wealth. These strategies are based on first- and second-order approximations of option prices. The hedging instrument is either the underlying asset or another option. The performance of these hedges is measured by simulations for put and call options, with a model fitted to the Standard & Poor’s 500.

中文翻译：

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存在跳跃聚类时的期权套期保值

本文分析了存在跳跃聚类的股票期权套期保值策略的效率。在所提出的模型中，资产由跳跃扩散过程控制，其中跳跃的到达与过去冲击的幅度相关。此功能为初始跳跃扩散增加了反馈效果和时间异质性。在介绍了该过程的主要特性之后，提出了一种期权定价的数值方法。接下来，我们制定四种对冲策略，最小化最终财富的方差。这些策略基于期权价格的一阶和二阶近似值。对冲工具是标的资产或另一种选择。这些对冲的表现是通过模拟看跌期权和看涨期权来衡量的，模型适合标准普尔 500 指数。