Pricing Earthquake Catastrophe Options Based on the Mixed-Multinomial Tree Model

Abstract

The discrete time model we propose for option pricing, called the mixed-multinomial tree model (MMTM), extends the conventional multinomial tree model by assuming that both the number of branches of node m and possible values u_i are random variables during each period. The conventional multinomial tree model cannot be used to describe the accumulated loss process in earthquakes because earthquakes occur randomly and different main shocks may have different aftershocks. We therefore apply the MMTM to build an accumulated earthquake loss model in earthquake catastrophe options. We study option pricing for such a model and obtain a call option pricing formula.