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Further Results on the Constant Elasticity of Variance Call Option Pricing Model


The Black-Scholes [4] call option model is a member of the class of constant elasticity of variance call option models proposed by Cox [6]. While the Black-Scholes model assumes that the volatility or instantaneous variance of return is constant through time, the other members of the class allow the volatility to change with the stock price. This property is of interest because empirical evidence suggests that returns to common stock are heteroscedastic and also that volatilities, implied from the Black-Scholes model and market prices of call options, are not constant.

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[1]Black Fisher. “Fact and Fantasy in the Use of Options.” Financial Analysts Journal, Vol. (0708 1975), pp. 3672.
[2]Black Fisher. “Forecasting Variance of Stock Prices for Option Trading and Other Purposes.” Proceedings of the Center for Research in Security Prices Seminar. Chicago, IL: University of Chicago (11 1975).
[3]Black Fisher. “Studies of Stock Price Volatility Changes.” Proceedings of the meetings of the American Statistical Association, Business and Economics Statistics, Section, Chicago (1976).
[4]Black F., and Scholes M.. “The Pricing of Options and Corporate Liabilities.” Journal of Political Economy, Vol. 81 (1973), pp. 637654.
[5]Blattberg R. C., and Gonedes N. J.. “A Comparison of the Stable and Student Distributions as Stochastic Models for Stock Prices.” Journal of Business, Vol. 47 (1974), pp. 244280.
[6]Cox John. “Notes on Option Pricing I: Constant Elasticity of Diffusions.” Unpublished draft. Palo Alto, CA: Stanford University (09 1975).
[7]Cox John, and Ross Stephen. “The Valuation of Options for Alternative Stochastic Processes.” Journal of Financial Economics, Vol. (01/03 1976), pp.
[8]Feller W. “Two Singular Diffusion Problems.” Annuals of Mathematics, (1951).
[9]Geske R.The Valuation of Compound Options.” Working paper. Berkeley, CA: University of California (1976).
[10]MacBeth J., and Merville L.. “Tests of the Black-Scholes and Cox Call Option Valuation Models.” Journal of Finance, Vol. 35 (1980), pp. 285301.
[11]Roll R.An Analytic Valuation Formula for Unprotected American Call Options on Stocks with Known Dividends.” Journal of Financial Economics, Vol. 5 (1977), pp. 251258.
[12]Rosenberg Barr. “The Behavior of Random Variables with Nonstationary Variance and the Distribution of Security Prices.” Manuscript. Berkeley, CA: University of California (1973).
[13]Rubinstein Mark. “Displaced Diffusion Option Pricing.” Manuscript. Berkeley, CA: University of California (1981).
[14]Rubinstein Mark, and Cox John. Option Pricing. New York: Prentice-Hall (forthcoming).
[15]Schmalensee R., and Trippi R.. “Common Stock Volatility Expectations Implied by Option Premia.” The Journal of Finance, Vol. 33, No. 1 (03 1978), pp. 129147.
[16]Thorpe Edward O.Common Stock Volatilities in Option Formulas.” Proceedings of the Center for Research in Security Prices Seminar. Chicago, IL: University of Chicago (05 1976).
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Journal of Financial and Quantitative Analysis
  • ISSN: 0022-1090
  • EISSN: 1756-6916
  • URL: /core/journals/journal-of-financial-and-quantitative-analysis
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