Pricing Default‐Risky CAT Bonds With Moral Hazard and Basis Risk

Abstract

ABSTRACT This article develops a contingent claim model to price a default-risky, catastrophe-linked bond. This model incorporates stochastic interest rates and more generic loss processes and allows for practical considerations of moral hazard, basis risk, and default risk. The authors compute default-free and default-risky CAT prices by using the Monte Carlo method. The results show that both moral hazard and basis risk drive down the prices substantially; these effects should not be ignored in pricing the CAT bonds. The authors also show how the prices are related to catastrophe occurrence intensity, loss volatility, trigger level, the issuing firm's capital position, debt structure, and interest rate uncertainty. INTRODUCTION Property-liability insurance companies traditionally hedge their low-loss frequency, high-loss-severity catastrophe risks by buying catastrophe reinsurance contracts. The traditional reinsurance and catastrophe insurance options, which trade in the Chicago Board of Trade (CBOT), are asset hedge instruments for insurers' or reinsurers' catastrophe risk management. A recent innovation in catastrophe risk management is the catastrophe (CAT hereafter). The CAT which is also named as an Act of God bond or insurance-linked bond, is a liability hedge instrument for insurance companies, for which there have been many successful CAT issues recently. (1) CAT provisions have debt-forgiveness triggers whose generic design allows for the payment of interest and/or the return of principal forgiveness, and the extent of forgiveness can be total, partial, or scaled to the size of loss. Moreover, the debt forgiveness can be triggered by the insurer's (or reinsurer's) actual losses or on a compos ite index of insurers' losses during a specific period. The advantage of a CAT hedge for (re)insurers (insurers, hereafter) is that the issuer can avoid the credit risk that may arise with traditional reinsurance or catastrophe-linked options. The CAT bondholders provide the hedge to the insurer by forgiving existing debt. Thus, the value of this hedge is independent of the bondholders' assets, and the issuer has no risk of nondelivery on the hedge. However, from the bondholder's perspective, the default risk, the potential moral hazard behavior, and the basis risk of the issuing firm are critical in determining the value of CAT bonds. The moral hazard behavior occurs when the insurer's cost of loss control efforts exceeds the benefits from debt forgiveness. That is, the insurer has an incentive to pay the claims more generously when the loss amount is near the trigger set in the debt-forgiveness provision. Doherty (1997) pointed out that moral hazard results from less loss control efforts by the insurer issuing CAT bonds because these efforts will increase the amount of debt that must be repaid. Bantwal and Kunreuther (1999) also noted the tendency for insurers to write additional policies in a catastrophe-prone area, spending less time and money in their auditing of losses after a disaster. The moral hazard behavior may increase the claim payments at the expense of the bondholders' coupon (or principal) reduction and affect the price. Another important element that needs to be considered in pricing a CAT is the basis risk. The CAT bond's basis risk refers to the gap between the insurer's actual loss and the composite index of losses that prevents the insurer from receiving complete risk hedging. The basis risk may cause insurers to default on their debt in the case of high individual loss but low index of loss, and therefore affects the price. A tradeoff indeed exists between basis risk and moral hazard. If one uses an independently calculated index to define the CAT payments, then the insurer's opportunity to cheat the bondholders is reduced or eliminated, but basis risk is created. Doherty (1997) and Belonsky (1998), among others, have looked into the effect of basis risk and moral hazard, but not from the perspective of pricing. …