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UBC Theses and Dissertations

Discrete hedging in insurance risk management Sator, Imre Emil

Abstract

Based upon the Black-Scholes option pricing model, Schwartz developed an equilibrium pricing definition of the equity-linked life insurance contract with an asset value guarantee. Under the conditions of this contract, the beneficiary may elect to receive the value of a reference portfolio of securities or a minimum guaranteed amount, whichever is greater. In this sense, the contract is synonymous to investment in a mutual fund and a term insurance policy, The guarantee provision, however, gives rise to non-diversifiable risk. In the event of a general market collapse, the company becomes simultaneously liable for the guarantee on all mature contracts. Such an eventuality could prove to be disasterous. The equilibrium model proposes a hedging strategy which eliminates the probability of this type of a loss. At any point in time, the benefits of the contract may be viewed as the present value of the guarantee plus the value of a call option on the reference portfolio. Conversely, it can also be stated as the present value of the reference portfolio plus the value of the put option. Since the call option is sold short, a fully hedged position may be established by the appropriate investment in the reference portfolio. Maintenance of this position implies that no gains or losses will occur. In practise, however, continuous hedging is impossible because of transaction costs. Adoption of a policy of periodic revision to re-establish the hedged position will result in gains and losses. Exposure to risk, therefore, is not eliminated. This dissertation deals with the problem of risk exposure resulting from a discrete revision strategy. Through the employment of simulation techniques, the impact of various revision strategies and transaction cost levels on the losses is examined. As a basis of comparison, a naive strategy was also developed. That is, under the naive strategy, the company buys the market portfolio with the premium and holds it until maturity. The case under consideration is that of the single premium contract with a known maturity date, The results of the analysis establish the dominance of the periodic revision strategy over the naive. Furthermore, for lower transaction cost levels, the dispersion of losses is reduced as the number of revisions is increased. Although the simulation model does not provide an optimal solution, it does provide the framework for the establishment of a management strategy which is consistent with the firm's perception of acceptable risk. It is hoped that the proposed strategy will find acceptance not only by the insurance industry but also in the areas of mutual and pension fund management.

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