In this article, we propose a jump diffusion framework to price the power exchange options. We model the price dynamics of assets using a Hawkes jump diffusion model with common factors to describe the correlated jump risk and clustering of asset price jumps. In the proposed model, the jumps, reflecting common systematic risk and idiosyncratic risk, are modeled by self-exciting Hawkes process with exponential decay. A pricing formula for valuation of power exchange option is obtained following the measure-change technique. Existing models in the literature are shown to be special cases of the proposed model. Finally, sensitivity analysis is given to illustrate the effect of jump risk and jump clustering on option prices. We observe that jump clustering significantly effects the option prices.

中文翻译：

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霍克斯跳扩散过程对功率交换选项的定价

在本文中，我们提出了一个跳跃扩散框架来为电源交换选项定价。我们使用具有共同因素的霍克斯跳数扩散模型对资产的价格动态进行建模，以描述相关的跳变风险和资产价格跳变的聚类。在提出的模型中，反映了共同的系统风险和特质风险的跳跃是通过具有指数衰减的自激霍克斯过程建模的。遵循度量变更技术，获得了用于电力交换期权评估的定价公式。文献中的现有模型显示为所提出模型的特例。最后，通过敏感性分析来说明跳跃风险和跳跃聚类对期权价格的影响。我们观察到跳跃聚类显着影响期权价格。