Hostname: page-component-cd9895bd7-8ctnn Total loading time: 0 Render date: 2024-12-23T08:04:11.467Z Has data issue: false hasContentIssue false
  • English
  • Français

Estimation in the Constant Elasticity of Variance Model

Published online by Cambridge University Press:  10 June 2011

K.C. Yuen ,
H. Yang  and
K.L. Chu
K.C. Yuen
Affiliation:
Department of Statistics and Actuarial Science, University of Hong Kong, Pokfulam Road, Hong Kong. Tel: +852-2859-1915; Fax: +852-2858-9041
K.L. Chu
Affiliation:
Department of Statistics and Actuarial Science, University of Hong Kong, Pokfulam Road, Hong Kong. Tel: +852-2859-1915; Fax: +852-2858-9041
Get access Rights & Permissions [Opens in a new window]

Abstract

The constant elasticity of variance (CEV) diffusion process can be used to model heteroscedasticity in returns of common stocks. In this diffusion process, the volatility is a function of the stock price and involves two parameters. Similar to the Black-Scholes analysis, the equilibrium price of a call option can be obtained for the CEV model. The purpose of this paper is to propose a new estimation procedure for the CEV model. A merit of our method is that no constraints are imposed on the elasticity parameter of the model. In addition, frequent adjustments of the parameter estimates are not required. Simulation studies indicate that the proposed method is suitable for practical use. As an illustration, real examples on the Hong Kong stock option market are carried out. Various aspects of the method are also discussed.

Keywords

Constant Elasticity of VarianceDiffusion ProcessLeast SquaresOption PricingVolatility
Type
Sessional meetings: papers and abstracts of discussions
Information
British Actuarial Journal , Volume 7 , Issue 2 , 01 June 2001 , pp. 275 - 292
Copyright
Copyright © Institute and Faculty of Actuaries 2001

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

Aït-Sahalia, Y. (1999). Maximum likelihood estimation of discretely sampled diffusions: a closed-form approximation approach. Working paper, Princeton University.Google Scholar
Black, F. & Scholes, M. (1973). The pricing of options and corporate liabilities. Journal of Political Economy, 81, 637–654.Google Scholar
Black, F. (1976). Studies of stock price volatility changes. Proceedings of the meetings of the American Statistical Association, Business and Economics Statistics Section, Chicago.Google Scholar
Blattberg, R.C. & Gonedes, N.J. (1974). A comparison of the stable and student distributions as stochastic models for stock prices. Journal of Business, 47, 244–280.CrossRefGoogle Scholar
Boyle, P.P. & Tian, Y. (1999). Pricing lookback and barrier options under CEV process. Journal of Financial and Quantitative Analysis, 34, 241–264.CrossRefGoogle Scholar
Chesney, M., Elliott, R.J., Madan, D. & Yang, H. (1993). Diffusion coefficient estimation and asset pricing when risk premia and sensitivities are time varying. Mathematical Finance, 3, 85–99.CrossRefGoogle Scholar
Cox, J. (1975). Notes on option pricing I: constant elasticity of diffusions. Unpublished draft. Stanford University.Google Scholar
Cox, J. & Ross, S. (1976). The valuation of options for alternative stochastic processes. Journal of Financial Economics, 3, 145–166.CrossRefGoogle Scholar
Davydov, D. & Linetsky, V. (2000a). The valuation and hedging of barrier and lookback options for alternative stochastic processes. Management Science (to appear).Google Scholar
Davydov, D. & Linetsky, V. (2000b). Pricing options on scalar diffusions: an eigenfunction expansion approach. Working paper, Northwestern University.Google Scholar
Emanuel, D.C. & MacBeth, J.D. (1982). Further results on the constant elasticity of variance call option pricing model. Journal of Financial and Quantitative Analysis, 17, 533–554.CrossRefGoogle Scholar
MacBeth, J.D. & Merville, L.J. (1979). An empirical examination of the Black-Scholes call option pricing model. Journal of Finance, 34, 1173–1186.Google Scholar
MacBeth, J.D. & Merville, L.J. (1980). Tests of the Black-Scholes and Cox call option valuation models. Journal of Finance, 35, 285–301.Google Scholar
Manaster, S. (1980). Discussion of MacBeth J.D. & Merville L.J. ‘Tests of the Black-Scholes and Cox call option valuation models’. Journal of Finance, 35, 301–303.Google Scholar
Mihlstein, G.N. (1974). Approximate integration of stochastic differential equations. Theory of Probability and Its Applications, 19, 557–562.Google Scholar
Singleton, K.J. (2001). Estimation of affine asset pricing models using the empirical characteristic function. Journal of Econometrics (to appear).CrossRefGoogle Scholar