Pricing catastrophe risk bonds: A mixed approximation method

This paper presents a contingent claim model similar to the one described by Lee and Yu (2002) for pricing catastrophe risk bonds. First, we derive a bond pricing formula in a stochastic interest rates environment with the losses following a compound nonhomogeneous Poisson process. Furthermore, we estimate and calibrate the parameters of the pricing model using the catastrophe loss data provided by Property Claim Services (PCS) from 1985 to 2010. As no closed-form solution can be obtained, we propose a mixed approximation method to find the numerical solution for the price of catastrophe risk bonds. Finally, numerical experiments demonstrate how financial risks and catastrophic risks affect the prices of catastrophe bonds.

► We present a contingent claim model for pricing catastrophe risk bonds. ► We adopt a mixed approximation method to evaluate aggregate claims distribution. ► Using catastrophe data provided by PCS, we find the GEV distribution is the best fit. ► We construct a new intensity to describe the arrival rate of catastrophic events.