Knowledge that Transforms

Don B. Panton, V. Parker Lessig, O. Maurice Joy, Comovement of International Equity Markets: A Taxonomic Approach, The Journal of Financial and Quantitative Analysis, Vol. 11, No. 3 (Sep., 1976), pp. 415-432

The validity of the classic Black-Scholes option pricing formula depends on the capability of investors to follow a dynamic portfolio strategy in the stock that replicates the payoff structure to the option. The critical assumption required for such a strategy to be feasible, is that the underlying stock return dynamics can be described by a stochastic process with a continuous sample path. In this paper, an option pricing formula is derived for the more-general case when the underlying stock returns are generated by a mixture of both continuous and jump processes. The derived formula has most of the attractive features of the original Black-Scholes formula in that it does not depend on investor preferences or knowledge of the expected return on the underlying stock. Moreover, the same analysis applied to the options can be extended to the pricing of corporate liabilities.

status: Published

In this paper we derive and present optimal critical points for pre-tests in regression using a minimum average relative risk criterion. We use the same type risk functions as Sawa and Hiromatsu [8] who, in a recent paper in this journal, derived pre-test critical values using a minimax regret criterion. Since James-Stein type estimators can be shown to dominate any pre-test estimator for the risk functions used here and in [8], no normative claims are made for the critical values we give. However, the use of pre-testing procedures continues in practice and the results given here, contrasted with other results, add to information about the character of costs and returns to such practices.

This paper considers the effect of aggregation on the variance of parameter estimates for a linear regression model with random coefficients and an additive error term. Aggregate and microvariances are compared and measures of relative efficiency are introduced. Necessary conditions for efficient aggregation procedures are obtained from the Theil aggregation weights and from measures of synchronization related to the work of Grunfeld and Griliches.