Catastrophe option pricing with auto-correlated and catastrophe-dependent intensity

Abstract A discrete-time pricing model is proposed to investigate catastrophe equity put options with auto-correlated and catastrophe-dependent intensity. Catastrophic events are assumed to occur according to a Poisson process and the intensity is affected by the numbers of catastrophic events that occurred in the past. Stochastic volatility of the underlying asset is captured by a GARCH process. We derive a pricing formula for catastrophe equity put options. Numerical simulations show that the ordinary level of catastrophe intensity and the speed of weakening the impact of catastrophe events have an inverted U-shaped relationship with the catastrophe put option prices.