A numerical method to estimate the parameters of the CEV model implied by American option prices: Evidence from NYSE

Abstract

We develop a highly efficient procedure to forecast the parameters of the constant elasticity of variance (CEV) model implied by American options. In particular, first of all, the American option prices predicted by the CEV model are calculated using an accurate and fast finite difference scheme. Then, the parameters of the CEV model are obtained by minimizing the distance between theoretical and empirical option prices, which yields an optimization problem that is solved using an ad-hoc numerical procedure. The proposed approach, which turns out to be very efficient from the computational standpoint, is used to test the goodness-of-fit of the CEV model in predicting the prices of American options traded on the NYSE. The results obtained reveal that the CEV model does not provide a very good agreement with real market data and yields only a marginal improvement over the more popular Black–Scholes model.