Tests of the Black-Scholes and Cox Call Option Valuation Models

IN THIS RESEARCH we use Cox's [7] and Cox and Ross' [8] constant elasticity of variance diffusion processes to model heteroscedasticity in returns to common stocks. The major goal of this paper is to test the Cox call option valuation model for constant elasticity of variance diffusion processes against the Black-Scholes [4] call option valuation model. We find that common stock prices do appear to be generated by constant elasticity of variance diffusion processes; moreover, we find that the Cox valuation model fits market prices of call options significantly better than the Black-Scholes model. Thus, our results have important implications for empirical analysis of call option data and may very- well have important implications for empirical analysis of common stock prices and prices of other financial instruments. At the theoretical level there are several plausible explanations for changes in stock return variances over time. First, firms may internally change their common stock return distribution through technological innovations and/or mergers and acquisitions. Another area of possible explanation for dynamic variances is contained in multiperiod consumption-investment theory (Rubinstein [16] and Fama [9]). If in each period aggregate consumer-investors plan their consumption and investment over multiple future periods, then the variances for securities may change over time as new information arises and new individuals (preferences) bid for risky assets in the capital markets. There is considerable evidence in the empirical literature that returns to common stocks are heteroscedastic. Blattberg and Gonedes [5] present evidence that a process in which the variance of returns changes randomly through time fits empirical data better than a stationary Stable Paretian process. Rosenberg [15] finds that the variance of monthly returns to the Standard and Poors 500 Index follows an autoregressive process through time. Using daily returns, Black [3] observes that the variance of returns varies inversely with the stock price. This inverse relationship between variance of returns and the stock price can be modeled by a constant elasticity of variance diffusion process.