Knowledge that Transforms

This paper considers the equilibrium pricing of equity-linked life insurance policies with an asset value guarantee; such policies provide for benefits which depend upon the performance of a reference portfolio subject to a minimum guaranteed benefit. The benefit is decomposed into a sure amount and an immediately exercisable call option on the reference portfolio. A numerical procedure for determining the value of the call option is presented and the risk minimizing investment strategy to be followed by the issuer of the policy is derived.

This paper examines the structure of option valuation problems and develops a new technique for their solution. It also introduces several jump and diffusion processes which have not been used in previous models. The technique is applied to these processes to find explicit option valuation formulas, and solutions to some previously unsolved problems involving the pricing of securities with payouts and potential bankruptcy.

In this paper we present evidence on the existence of seasonality in monthly rates of return on the New York Stock Exchange from 1904–1974. With the exception of the 1929–1940 period, there are statistically significant differences in mean returns among months due primarily to large January returns. Dispersion measures reveal no consistent seasonal patterns and the characteristic exponent seems invariant among months. We also explore possible implications of the observed seasonality for the capital asset pricing model and other research.

Numerical approximations are presented for the expected utility of wealth over a single time period for a small investor who proportions her or his available capital between a risk-free asset and a risky stock. The stock price is assumed to be a log-stable random variable. The utility functional is logarithmic or isoeleastic (yaq, q extless 0). Analytic results are presented for special choices of model parameters, and for large and small time periods.

The contract price on a forward contract stays fixed for the life of the contract, while a futures contract is rewritten every day. The value of a futures contract is zero at the start of each day. The expected change in the futures price satisfies a formula like the capital asset pricing model. If changes in the futures price are independent of the return on the market, the futures price is the expected spot price. The futures market is not unique in its ability to shift risk, since corporations can do that too. The futures market is unique in the guidance it provides for producers, distributors, and users of commodities. Using assumptions like those used in deriving the original option formula, we find formulas for the values of forward contracts and commodity options in terms of the futures price and other variables.

It is assumed that a collection of market agents can be treated as a statistical ensemble. Their market activities are depicted as the stochastic generation of market orders according to a Poisson process. The objective is to effectively describe the ‘temporal microstructure’, or moment-to-moment trading activities in asset markets. Two basic models, ‘dealership’ vs. ‘auction’ markets (and their variants) are put forth. Implications are drawn from each model. The implications include several testable hypotheses regarding the aggregate behavior of markets and market-makers as well as some qualitative insight into the transaction-to-transaction nature of realistic exchange processes.

International capital market equilibrium is characterized for a world economy in which consumption preferences are defined multiplicatively over many commodities. It is shown that the set of relative asset prices under pure exchange in international capital markets depends on the real purchasing power of nominal payoffs under uncertainty and does not depend on the currency in which the nominal payoffs are denominated. A Sharpe-Lintner type international capital asset pricing model is derived as a special case. Proportional ad valorem commodity taxes and transportation costs are incorporated in the valuation model, interest rate parity and purchasing power parity are reinterpreted under uncertainty, and international differences in borrowing and lending are shown to reflect, in part, differences in risk aversion across countries.

This paper determines the effect of estimation risk on optimal portfolio choice under uncertainty. In most realistic problems, the parameters of return distributions are unknown and are estimated using available economic data. Traditional analysis neglects estimation risk by treating the estimated parameters as if they were the true parameters to determine the optimal choice under uncertainty. We show that for normally distributed returns and ‘non-informative’ or ‘invariant’ priors, the admissible set of portfolios taking the estimation uncertainty into account is identical to that given by traditional analysis. However, as a result of estimation risk, the optimal portfolio choice differs from that obtained by traditional analysis. For other plausible priors, the admissible set, and consequently the optimal choice, is shown to differ from that in traditional analysis.