In this paper we propose a method for pricing Asian options in market models with the risky asset dynamics driven by a Hawkes process with exponential kernel. For these processes the couple $$ (\lambda (t), X(t) ) $$ ( λ ( t ) , X ( t ) ) is affine, this property allows to extend the general methodology introduced by Hubalek et al. (Quant Finance 17:873–888, 2017) for Geometric Asian option pricing to jump-diffusion models with stochastic jump intensity. Although the system of ordinary differential equations providing the characteristic function of the related affine process cannot be solved in closed form, a COS-type algorithm allows to obtain the relevant quantities needed for options valuation. We describe, by means of graphical illustrations, the dependence of Asian options prices by the main parameters of the driving Hawkes process. Finally, by using Geometric Asian options values as control variates, we show that Arithmetic Asian options prices can be computed in a fast and efficient way by a standard Monte Carlo method.

中文翻译：

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Hawkes型跳跃扩散模型的亚洲期权定价

在本文中，我们提出了一种在市场模型中对亚洲期权进行定价的方法，其风险资产动态由具有指数核的霍克斯过程驱动。对于这些过程，夫妇$（\ lambda（t），X（t））$$（λ（t），X（t））是仿射的，此属性可以扩展Hubalek等人引入的一般方法。（Quant Finance 17：873–888，2017），将“亚洲几何”期权定价转换为具有随机跳跃强度的跳跃扩散模型。尽管不能以封闭形式求解提供相关仿射过程的特征函数的常微分方程组，但COS型算法允许获得期权评估所需的相关量。我们通过图形描述的方式来描述亚洲期权价格对推动霍克斯过程的主要参数的依赖性。最后，