Valuation of Indonesian catastrophic earthquake bonds with generalized extreme value (GEV) distribution and Cox-Ingersoll-Ross (CIR) interest rate model

Abstract

Indonesia is a country with high risk of earthquake, because of its position in the border of earth’s tectonic plate. An earthquake could raise very high amount of damage, loss, and other economic impacts. So, Indonesia needs a mechanism for transferring the risk of earthquake from the government or the (reinsurance) company, as it could collect enough money for implementing the rehabilitation and reconstruction program. One of the mechanisms is by issuing catastrophe bond, ‘act-of-God bond’, or simply CAT bond. A catastrophe bond issued by a special-purpose-vehicle (SPV) company, and then sold to the investor. The revenue from this transaction is joined with the money (premium) from the sponsor company and then invested in other product. If a catastrophe happened before the time-of-maturity, cash flow from the SPV to the investor will discounted or stopped, and the cash flow is paid to the sponsor company to compensate their loss because of this catastrophe event. When we consider the earthquake only, the amount of discounted cash flow could determine based on the earthquake’s magnitude. A case study with Indonesian earthquake magnitude data show that the probability of maximum magnitude can model by generalized extreme value (GEV) distribution. In pricing this catastrophe bond, we assumed stochastic interest rate that following the Cox-Ingersoll-Ross (CIR) interest rate model. We develop formulas for pricing three types of catastrophe bond, namely zero coupon bonds, ‘coupon only at risk’ bond, and ‘principal and coupon at risk’ bond. Relationship between price of the catastrophe bond and CIR model’s parameter, GEV’s parameter, percentage of coupon, and discounted cash flow rule then explained via Monte Carlo simulation.