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.