The Constant Elasticity of Variance Model and Its Implications For Option Pricing

Abstract

where the instantaneous variance of the percentage price change is equal to U2/S2and hence is a direct inverse function of the stock price. In the traditionally used lognormal model, which corresponds to the limiting case a = 2, the variance rate is not a function of the stock price itself. Both casual empiricism and economic rationale tend to support the inverse relationship. If this relationship is borne out by the empirical data, an option pricing formula based on the constant elasticity of variance diffusion could fit the actual market prices better than the Black-Scholes model. In this article we empirically investigate the relationship between the stock price level and its variance of return and perform a comparative statics analysis of the Black-Scholes prices and those based on two special cases of the constant elasticity of variance class (a = 1 and a = 0).