STANDARD DEVIATIONS OF STOCK PRICE RATIOS IMPLIED IN OPTION PRICES

Abstract

THE OPTION PRICING MODEL derived by Black and Scholes (B-S) is a path breaking work in the area of contingent claim pricing. Of the five variables which are necessary to specify the model, all are directly observable except the standard deviation of returns from the underlying stock.' Due to its rigorous theoretical underpinnings and minimum reliance on subjectively determined inputs, the model has gained a great deal of popularity in both the academic and investment communities. In an empirical test, B-S demonstrated that the model can be used effectively to determine whether call options are properly priced if one uses an estimate of the standard deviation which is based upon an ex post series of returns from the underlying stock. However, they showed that the actual standard deviation which would result over the life of an option would be a better input into the model if it were known in advance. Accordingly, they suggested that the usefulness of the model depends to a great extent upon investors' abilities to make good forecasts of this parameter.2 In this paper we derive standard deviations of continuous price relative returns which are implied in actual call option prices on the assumption that investors behave as if they price options according to the Black and Scholes model. A weighted average of these implied standard deviations (ISDs) is employed as a measure of market forecasts of return variability. These weighted implied standard