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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
σS
β/2 instead of
σS 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. |