Academic journal article Journal of Risk and Insurance

Accuracy of Premium Calculation Models for Cat Bonds-An Empirical Analysis

Academic journal article Journal of Risk and Insurance

Accuracy of Premium Calculation Models for Cat Bonds-An Empirical Analysis

Article excerpt

ABSTRACT

CAT bonds are of significant importance in the field of alternative risk transfer. Because the market of CAT bonds is not complete, the application of an appropriate pricing model is of high relevance. We apply different premium calculation models to compare them with regard to their predictive power. Without taking the financial crisis into account, a version of the Wang transformation model and the linear model are the most accurate ones. In contrast, under consideration of the financial crisis, all analyzed models are approximately equivalent. Furthermore, we find that CAT bond specific information does not improve out-of-sample results.

INTRODUCTION

Because both the trend of insured losses and the trend of numbers of catastrophes are positive, (re-)insurance companies have to consider new ways of coping with the risk.1 One possibility is to transfer the risk from reinsurance markets to financial markets. Important financial instruments that are used for the transfer are (CAT-) astrophe bonds.2 The volume of CAT bond principal outstanding rose to US$ 13.8 billion in 2007.3 After a collapsing market was observed in 2008, the market regained strength in 2009. The main idea of catastrophe securitization by a CAT bond transaction is that a sponsor-usually a (re-)insurer-enters into an alternative reinsurance contract with a Special Purpose Vehicle (SPV). Thus, the sponsor is protected against high losses due to a specified catastrophe up to a certain limit. To guarantee insurance coverage up to the limit, the SPV issues CAT bonds to investors. Investors buy the bonds to diversify their portfolios and to receive high yields resulting from the covered peril.4 A challenging question for the trading of CAT bonds is how CAT bond transactions can be priced best. The objective of this article is the identification of the most accurate pricing model. Therefore, we compare different selected premium calculation models and include pricing determining factors. To describe these models, Figure 1 presents the basic structure of a CAT bond transaction.

Within the framework of the basic structure, the sponsor pays premiums Ï to the SPV to receive insurance coverage up to the limit h. The premium Ï consists of the expected value of loss EL plus a load for risk margin and expenses Î. To guarantee insurance coverage for the sponsor, the SPV, in turn, issues CAT bonds to an investor5 who pays the par amount h at issue date. If no triggering event occurs, the investor receives at maturity the par amount h and a coupon c consisting of the risk-free interest rate r and the premium p. In case of a triggering event, the coupon to the investor is reduced by d, 0 ≤ d ≤ 1. Furthermore, the par amount at maturity h might be reduced by f, 0 ≤ f ≤ 1. However, the sponsor receives insurance coverage according to the reinsurance contract between the sponsor and the SPV up to the limit h.

Obviously, the key parameter of a CAT bond transaction, and thus of the CAT bond price, is the premium p. The premiums are usually determined on the basis of premium calculation models that use the relationship between Ï and EL. For instance, Lane (2000) takes the relationship of Figure 1 as a basis and models Î by applying a Cobb-Douglas production function on the probability of first loss PFL and the conditional expected loss CEL. Instead, Lane and Beckwith (2008) and Lane and Mahul (2008) suggest a multiple linear relationship between p, EL, and an additional factor that covers cycle effects. Other multiple linear approaches have been established by Berge (2005) and Dieckmann (2008). Both analyses identify further premium determining factors to characterize the risk load A. In contrast, Major and Kreps (2003) use a loglinear relationship between ? and EL to describe catastrophe risk premiums. However, they do not consider catastrophe risk premiums of CAT bonds, but of traditional treaties.6 Finally, Wang (2000) develops a distortion operator, which transforms a probability of loss into an empirical one. …

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