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

Tests of the Black‐Scholes and Cox Call Option Valuation Models Tests of the Black-Scholes and Cox Call Option Valuation Models JAMES D. MACBETH and LARRY J. MERVILLE* I. Introduction 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 [161 and Fama http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png The Journal of Finance Wiley

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

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References (14)

Publisher
Wiley
Copyright
1980 The American Finance Association
ISSN
0022-1082
eISSN
1540-6261
DOI
10.1111/j.1540-6261.1980.tb02157.x
Publisher site
See Article on Publisher Site

Abstract

Tests of the Black-Scholes and Cox Call Option Valuation Models JAMES D. MACBETH and LARRY J. MERVILLE* I. Introduction 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 [161 and Fama

Journal

The Journal of FinanceWiley

Published: May 1, 1980

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