We develop a variance reduction technique, based on importance sampling in conjunction with the stochastic Robbins–Monro algorithm, for option prices of jump–diffusion models with stochastic volatility. This is done by combining the work developed by Arouna for pricing diffusion models, and extended by Kawai for Lévy processes without a Brownian component. We apply this technique to improve the numerical computation of derivative price sensitivities for general Lévy processes, allowing both Brownian and jump parts. Numerical examples are performed for both the Black–Scholes and Heston models with jumps and for the Barndorff–Nielsen–Shephard model to illustrate the efficiency of this numerical technique. The numerical results support that the proposed methodology improves the efficiency of the usual Monte Carlo procedures.

中文翻译：

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应用于具有随机波动率的跳跃扩散模型的希腊人的重要性采样

我们开发了一种方差减少技术，基于重要性采样结合随机 Robbins-Monro 算法，用于具有随机波动率的跳跃扩散模型的期权价格。这是通过结合 Arouna 为定价扩散模型开发的工作以及 Kawai 为没有布朗组件的 Lévy 过程扩展的工作来完成的。我们应用这种技术来改进一般 Lévy 过程的衍生价格敏感性的数值计算，允许布朗和跳跃部分。对具有跳跃的 Black-Scholes 和 Heston 模型以及 Barndorff-Nielsen-Shephard 模型进行了数值示例，以说明这种数值技术的效率。数值结果支持所提出的方法提高了通常的蒙特卡罗程序的效率。