Pricing and simulating catastrophe risk bonds in a Markov-dependent environment

At present, insurance companies are seeking more adequate liquidity funds to cover the insured property losses related to natural and manmade disasters. Past experience shows that the losses caused by catastrophic events, such as earthquakes, tsunamis, floods, or hurricanes, are extremely high. An alternative method for covering these extreme losses is to transfer part of the risk to the financial markets by issuing catastrophe-linked bonds. In this paper, we propose a contingent claim model for pricing catastrophe risk bonds (CAT bonds). First, using a two-dimensional semi-Markov process, we derive analytical bond pricing formulae in a stochastic interest rate environment with aggregate claims that follow compound forms, where the claim inter-arrival times are dependent on the claim sizes. Furthermore, we obtain explicit CAT bond prices formulae in terms of four different payoff functions. Next, we estimate and calibrate the parameters of the pricing models using catastrophe loss data provided by Property Claim Services from 1985 to 2013. Finally, we use Monte Carlo simulations to analyse the numerical results obtained with the CAT bond pricing formulae.