It is known that the prices of many commodities exhibit mean reversion and are subject to jumps. Particularly, there is mounting empirical evidence that suggests the existence of clustered jumps. In this paper, we consider the valuation problem of arithmetic Asian options under a Hawkes jump diffusion model which captures both the mean reversion and jump clustering phenomena. We compute option prices by means of characteristic functions and Fourier-cosine series expansion. Numerical studies justify the validity and efficiency of our pricing method, and demonstrate the nonnegligible effects of mean reversion and jump clustering on Asian option prices.

中文翻译：

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均值回归和跳跃聚类算术亚洲期权的估值

众所周知，许多商品的价格都会出现均值回归并可能出现跳跃。特别是，越来越多的经验证据表明存在聚集跳跃。在本文中，我们考虑霍克斯跳跃扩散模型下算术亚洲期权的估值问题，该模型捕获了均值回归和跳跃聚类现象。我们通过特征函数和傅里叶余弦级数展开来计算期权价格。数值研究证明了我们定价方法的有效性和效率，并证明了均值回归和跳跃聚类对亚洲期权价格的不可忽视的影响。