Pricing index-based catastrophe bonds: Part 2: Object-oriented design issues and sensitivity analysis

Abstract

This work is the second installment in a two-part series, and focuses on object-oriented programming methods to implement an augmented-state variable approach to aggregate the PCS index and introduce the Bermudan-style call feature into the proposed CAT bond model. The PCS index is aggregated quarterly using a discrete Asian running-sum formulation. The resulting aggregate PCS index augmented-state variable is used to specify the payoff (principle) on the CAT bond based on reinsurance layers. The purpose of the Bermudan-style call option is to allow the reinsurer to minimize their interest rate risk exposure on making fixed coupon payments under prevailing interest rates. A sensitivity analysis is performed to determine the impact of uncertainty in the frequency and magnitude of hurricanes on the price of the CAT bond. Results indicate that while the CAT bond is highly sensitive to the natural variability in the frequency of landfalling hurricanes between El Ninõ and non-El Ninõ years, it remains relatively insensitive to uncertainty in the magnitude of damages. In addition, results indicate that the maximum price of the CAT bond is insensitive to whether it is engineered to cover low frequency high magnitude events in a ‘high’ reinsurance layer relative to high frequency low magnitude events in a ‘low’ reinsurance layer. Also, while it is possible for the reinsurer to minimize their interest rate risk exposure on the fixed coupon payments, the impact of this risk on the price of the CAT bond appears small relative to the natural variability in the CAT bond price, and consequently catastrophic risk, due to uncertainty in the frequency and magnitude of landfalling hurricanes.