How Financial Theory Applies to Catastrophe-Linked Derivatives-An Empirical Test of Several Pricing Models. [*]

Article excerpt

Julio J. Lucia [*]

ABSTRACT

This paper discusses the PCS Catastrophe Insurance Option Contracts, providing empirical support on the level of correspondence between real quotes and standard financial theory. The highest possible precision is incorporated since the real quotes are perfectly synchronized and the bid-ask spread is always considered. A static setting is assumed and the main topics of arbitrage, hedging, and portfolio choice are involved in the analysis. Three significant conclusions are reached. First, the catastrophe derivatives may often be priced by arbitrage methods, and the paper provides some examples of practical strategies that were available in the market. Second, hedging arguments also yield adequate criteria to price the derivatives, and some real examples are provided as well. Third, in a variance aversion context many agents could be interested in selling derivatives to invest the money in stocks and bonds. These strategies show a suitable level in the variance for any desired expected return. Furthermore, the m ethodology here applied seems to be quite general and may be useful to price other derivative securities. Simple assumptions on the underlying asset behavior are the only required conditions.

INTRODUCTION

New investment and financing opportunities and innovative risk management techniques involving derivatives have been developed to allow individuals and corporations to cost-effectively reallocate funds and transfer risks to other parties. A growing concern about catastrophe losses has particularly brought attention to catastrophe derivatives and their potential financing and risk sharing benefits for the insurance industry.

The PCS (Property Claim Services) Catastrophe Insurance Options Contracts, launched by the Chicago Board of Trade (CBOT) on September 29, 1995, are among the most significant catastrophe derivatives. These are standardized option contracts based on indices that track the insured losses, as estimated by PCS, resulting from catastrophic events that occur in a given area and period. Previously, the CBOT had traded catastrophe futures and options contracts on an index provided by Insurance Services Office (ISO). Moreover, the CBOT planned to list PCS Single-Event Catastrophe options in 1998 to broaden its product offering. In 1997 the Bermuda Commodities Exchange (BCOE) also began trading derivative securities based on the Guy Carpenter Catastrophe Index, an index of losses from climate events in the United States.

This article focuses on the CBOT's PCS options. Previous literature on these particular contracts and other related catastrophe derivatives can be roughly divided into two major categories, according to their main objective. The first group of articles concentrates on pricing issues. They view catastrophe derivatives as financial instruments and, accordingly, they take a financial approach to valuing (see Cummins and Geman (1995), German and Yor (1997), among others; Tomas (1998) suggests an actuarial approach). They theorize on the dynamic stochastic behavior of the relevant underlying variables in order to obtain the desired pricing result. From a theoretical point of view this line of research is extremely important and very promising. From a practical point of view, there are some difficulties due to market imperfections (bidask spread, other transaction costs, short-selling restrictions, illiquidity that makes continuous trading rather difficult, etc.) and some specific properties shown by the underlying indices (their stochastic behavior, the absence of any underlying security available for trading, etc.). This motivates the existence of a second group of articles devoted to describing the contracts and illustrating their most significant applications to both insurance and capital markets (e.g., D'Arcy and France (1992), Canter et al. (1996), Litzenberger et al. (1996), O'Brien (1997) and Jaffee and Russell (1997)). …