Valuation of Standard Options under the Constant Elasticity of Variance Model
A binomial model is developed to value options when the underlying process follows the constant elasticity of variance (CEV) model. This model is proposed by Cox and Ross (1976) as an alternative to the Black and Scholes (1973) model. In the CEV model, the stock price change (dS) has volatility £mS £]/2 instead of £mS in the Black-Scholes model. The rationale behind the CEV model is that the model can explain the empirical bias exhibited by the Black-Scholes model, such as the volatility smile. The option pricing formula when the underlying process follows the CEV model is derived by Cox and Ross (1976), and the formula is further simplified by Schroder (1989). However, the closed-form formula is useful in some limited cases. In this paper, a binomial process for the CEV model is constructed to yield a simple and efficient computation procedure for practical valuation of standard options. The binomial option pricing model can be employed under general conditions. Also, on average, the numerical results show the binomial option pricing model approximates better than other analytic approximations.
Volume (Year): 4 (2005)
Issue (Month): 2 (August)
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- Merton, Robert C., 1975.
"Option pricing when underlying stock returns are discontinuous,"
787-75., Massachusetts Institute of Technology (MIT), Sloan School of Management.
- Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
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- Emanuel, David C. & MacBeth, James D., 1982. "Further Results on the Constant Elasticity of Variance Call Option Pricing Model," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 17(04), pages 533-554, November.
- Cox, John C. & Ross, Stephen A. & Rubinstein, Mark, 1979. "Option pricing: A simplified approach," Journal of Financial Economics, Elsevier, vol. 7(3), pages 229-263, September.
- Cox, John C. & Ross, Stephen A., 1976. "The valuation of options for alternative stochastic processes," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 145-166.
- Beckers, Stan, 1980. " The Constant Elasticity of Variance Model and Its Implications for Option Pricing," Journal of Finance, American Finance Association, vol. 35(3), pages 661-673, June.
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