Valuing basket-spread options with default risk under Hawkes jump-diffusion processes

Abstract

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.