Hostname: page-component-78c5997874-8bhkd Total loading time: 0 Render date: 2024-11-15T02:02:45.075Z Has data issue: false hasContentIssue false

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

Published online by Cambridge University Press:  06 April 2009

Extract

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.

Type
Research Article
Copyright
Copyright © School of Business Administration, University of Washington 1982

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1]Black, Fisher. “Fact and Fantasy in the Use of Options.” Financial Analysts Journal, Vol. (0708 1975), pp. 3672.CrossRefGoogle Scholar
[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).Google Scholar
[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).Google Scholar
[4]Black, F., and Scholes, M.. “The Pricing of Options and Corporate Liabilities.” Journal of Political Economy, Vol. 81 (1973), pp. 637654.Google Scholar
[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.CrossRefGoogle Scholar
[6]Cox, John. “Notes on Option Pricing I: Constant Elasticity of Diffusions.” Unpublished draft. Palo Alto, CA: Stanford University (09 1975).Google Scholar
[7]Cox, John, and Ross, Stephen. “The Valuation of Options for Alternative Stochastic Processes.” Journal of Financial Economics, Vol. (01/03 1976), pp.CrossRefGoogle Scholar
[8]Feller, W. “Two Singular Diffusion Problems.” Annuals of Mathematics, (1951).CrossRefGoogle Scholar
[9]Geske, R.The Valuation of Compound Options.” Working paper. Berkeley, CA: University of California (1976).Google Scholar
[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.Google Scholar
[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.Google Scholar
[12]Rosenberg, Barr. “The Behavior of Random Variables with Nonstationary Variance and the Distribution of Security Prices.” Manuscript. Berkeley, CA: University of California (1973).Google Scholar
[13]Rubinstein, Mark. “Displaced Diffusion Option Pricing.” Manuscript. Berkeley, CA: University of California (1981).Google Scholar
[14]Rubinstein, Mark, and Cox, John. Option Pricing. New York: Prentice-Hall (forthcoming).Google Scholar
[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.CrossRefGoogle Scholar
[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).Google Scholar