Pricing lookback and barrier options under the CEV process

This paper examines the pricing of lookback and barrier options when the underlying asset follows the constant elasticity of variance (CEV) process. We construct a trinomial method to approximate the CEV process and use it to price lookback and barrier options. For lookback options, we find that the technique proposed by Babbs for the lognormal case can be modified to value lookbacks when the asset price follows the CEV process. We demonstrate the accuracy of our approach for different parameter values of the CEV process. We find that the prices of barrier and lookback options for the CEV process deviate significantly from those for the lognormal process. For standard options, the corresponding differences between the CEV and Black-Scholes models are relatively small. Our results show that it is much more important to have the correct model specification for options that depend on extrema than for standard options.