Eric Briys

Life Insurance in a Contingent Claim Framework: Pricing and Regulatory Implications

In this paper we develop a contingent claim model to evaluate the equity and liabilities of a life insurance company. The limited liability of shareholders is explicitly modelled. We focus on a specific type of life insurance policy–namely, the profit-sharing policy. In this policy, the policyholder is entitled to a guaranteed interest rate and a percentage of the companys yearly financial revenues. The implicit equilibrium interest rate and profit-sharing ratio are derived and analyzed. We finally discuss regulatory measures frequently encountered in the life insurance business such as rate ceilings, capital ratios, and asset restrictions.

Optimal hedging in a futures market with background noise and basis risk

Abstract This paper examines hedging behavior in an incomplete market in which there exists an unhedgeable and uninsurable independent background risk. In the case of a basis risk that satisfies the regressibility property, the background risk might be partly endogenous. Background risk generally has an ambiguous effect on the optimal hedge ratio. However, if preferences exhibit standard risk aversion and the background risk is fully exogenous, the qualitative effect of the added background risk is determinate and depends on the direction of any bias in the futures market. In all cases, the speculative component of the hedge ratio is reduced in the presence of background risk. When the background risk is a basis risk and futures prices exhibit normal backwardation, this qualitative effect need not hold and it depends in part on the direction of regressability for spot and futures prices.

The pricing of forward-starting asian options

Abstract Asian options are path-dependent options whose payoff is based on an average. In some cases, the underlying asset of the option is an average; in others, the strike price itself is computed as an average of the underlying asset recent prices. Asian currency options, as an example, allow corporate users to cover seasonal and so-called strategic foreign exchange positions. Averages are also found in some recent warrant issues, where they are mostly used as poison pills to preclude hostile takeovers. This paper derives a closed-form solution for the valuation of European asian options whose strike price is an average. Both “plain vanilla” average options—i.e. those for which the time interval taken into account for the strike average calculation is the life of the option—and forward-starting average options are considered. The valuation formula is obtained by relying upon a slight linear approximation. Although some previous contributions in the literature already use approximation techniques, our approach contrary to others allows the derivation of a formal upper bound to the approximation error. The numerical values given by this formula are then compared to those generated by an antithetic variate Monte-Carlo method. Based on this comparison and the computation of an upper bound to the approximation error, it is shown that the closed-form solution performs quite well and is obviously computationally efficient.

Reliability of Risk Management: Market Insurance, Self-Insurance and Self-Protection Reconsidered

This paper examines the three main tools of risk management in a setting where reliability cannot be guaranteed. Thus, for example, insurers might be insolvent, sprinkler systems might be inoperative and alarm systems might be faulty. These types of nonreliability are shown to have significant consequences for risk management. In particular, the relationships between increased risk aversion and the use of the various risk management tools do not carry over from models with full reliability. Moreover, the well-known result of Ehrlich and Becker, that market insurance and self-insurance are substitutes, is shown to fail in the presence of nonreliability risk.

Optimal currency hedge ratios and interest rate risk

Abstract The objective of this article is to provide a framework for the interpretation of the optimal currency hedge ratios on foreign investments, taking into account interest rate risk. This is made possible by using a continuous-time setting in the spirit of Merton (1969). We focus on the importance of the interest rate differential (forward basis) in setting the optimal currency hedge because of the influence of interest rates on exchange rates. More specifically, we consider two discount bonds, a domestic and a foreign one, which follow stochastic processes possibly correlated with the other state variables of the model. It is shown that the optimal hedge ratio can be split into five components: (a) a ‘macro-economic’ component which is a function of the volatility of the interest rate differential and its covariance with currency movements; this term depends on the currency considered but not on the asset being hedged; (b) an ‘asset-specific’ term which is directly related to the covariance of the foreign currency asset return with exchange and interest rate movements; (c) a ‘speculative’ term function of the investors risk preference and of the conditional risk premium on the exchange rate, and (d) two stochastic opportunity set hedging terms. The analysis of the optimal hedge ratio is illustrated on the period December 1970–1989 for stock and bond investments in seven countries. (JEL G15, F31)

Endogenous risks and the risk premium

This note tries to correct a deficiency of the microeconomic literature on decision making under uncertainty. Indeed, when considering meaningful comparative statics results in situations where risks are at least partially controllable (endogenous), this literature has mostly relied upon the traditional Arrow-Pratt risk aversion functions and has paid very little attention to the definition of the risk premium. However when they defined the risk premium and the risk aversion functions, Arrow and Pratt considered only roulette gambles, i.e. risks totally exogenous to the individual. This note highlights the fact that several definitions of the risk premium may be proposed for endogenous risks. Two of them, already used in the literature, do not preserve the intuitively-appealing properties of the Arrow-Pratt risk premium. An alternative definition is then proposed. It is shown that this new definition of the risk premium applied to endogenous risks exhibits the properties generally admitted for roulette gambles.