  The Constant Elasticity of Variance (CEV) model significantly outperforms the
Black-Scholes (BS) model in forecasting both prices and options. Furthermore,
the CEV model has a marked advantage in capturing basic empirical regularities
such as: heteroscedasticity, the leverage effect, and the volatility smile. In
fact, the performance of the CEV model is comparable to most stochastic
volatility models, but it is considerable easier to implement and calibrate.
Nevertheless, the standard CEV model solution, using the non-central chi-square
approach, still presents high computational times, specially when: i) the
maturity is small, ii) the volatility is low, or iii) the elasticity of the
variance tends to zero. In this paper, a new numerical method for computing the
CEV model is developed. This new approach is based on the semiclassical
approximation of Feynman's path integral. Our simulations show that the method
is efficient and accurate compared to the standard CEV solution considering the
pricing of European call options.
