Valuing basket-spread options with default risk under Hawkes jump-diffusion processes
研究了在霍克斯跳跃扩散过程下，篮子价差期权考虑违约风险的定价问题，通过匹配二阶矩的几何平均近似算术平均得到期权价格，数值实验显示精度较高。
In this paper, we investigate the pricing of basket-spread options with default risk under Hawkes jump-diffusion processes. A self-exciting Hawkes process is employed to describe jump clustering, and jump amplitudes of different assets in baskets are all correlated. In addition, the diffusive components of assets are also assumed to be correlated with each other. We obtain option prices by approximating the arithmetic average of the underlying assets in the basket with their second moment-matched geometric average values, and numerical experiments show that our approximated prices are quite accurate, spanning different underlying asset numbers and alternative strike prices. Finally, we illustrate the effects of default risk and clustered jump risk on the prices of basket-spread options.