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BLACK AND SCHOLES [3] derived their seminal option pricing formula under the assumption that underlying stock price returns follow a lognormal diffusion process: S= 1 dt + a dZ dS This implies that the percentage price change, ?-, over the interval dt is normally distributed with instantaneous mean , and instantaneous variance a2. While it is well known that the lognormality assumption does not hold exactly, the pricing of European call options has been studied recently for alternative diffusion models. Specifically, Cox [4] and Cox and Ross [5] focused their attention on the constant elasticity of variance diffusion class: dS = IS dt + uSa12 dZ (the elasticity factor 0 c a < 2)where the instantaneous variance of the percentage price change is equal to U2/S2-and 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). I. The Relationship Between the Variance of Stock Price Returns and the Level of the Stock PriceIt is sometimes argued that a simple economic mechanism might cause an inverse relationship between the level of the stock price and its variance of return. If a * Vlaamse Ekonomische Hogeschool and European Institute for Advanced Studies in Management, Brussels. The author gratefully acknowledges the helpful suggestions of Mark Rubinstein, Barr Rosenbeig and Larry J. Merville. John Cox kindly provided us with a simplified formula for the square root option price. All remaining errors are of course ours. 661 662The Journal of Finance firm's stock price falls, the market value of its equity tends to fall more rapidly than the market value of its debt, causing the debt-equity ratio to rise; hence the riskiness of the stock increases. A similar effect could be observed even if a firm has almost no debt. Since every firm faces fixed costs, which have to be met irrespective of its income, a decrease in income will decrease the value of the firm and at the same time increase its riskiness. Both operating and financial leverage arguments can be used to explain the inverse relationship between variance and stock price observed in the literature (Black [1], Schmalensee and Trippi [11]). Black [2] states that cause and effect also may be inverted so that a downturn in the general business climate might lead to an increase in the stock price volatility and hence to a drop in stock prices.The C...

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