In this essay, we empirically test the Constant–Elasticity-of-Variance (CEV) option pricing model by Cox (1975, 1996 ) and Cox and Ross (1976), and compare the performances of the CEV and alternative option pricing models, mainly the stochastic volatility model, in terms of European option pricing and cost-accuracy based analysis of their numerical procedures. In European-style option pricing, we have tested the empirical pricing performance of the CEV model and compared the results with those by Bakshi et al. (1997). The CEV model, introducing only one more parameter compared with Black-Scholes formula, improves the performance notably in all of the tests of in-sample, out-of-sample and the stability of implied volatility. Furthermore, with a much simpler model, the CEV model can still perform better than the stochastic volatility model in short term and out-of-the-money categories. When applied to American option pricing, high-dimensional lattice models are prohibitively expensive. Our numerical experiments clearly show that the CEV model performs much better in terms of the speed of convergence to its closed form solution, while the implementation cost of the stochastic volatility model is too high and practically infeasible for empirical work. In summary, with a much less implementation cost and faster computational speed, the CEV option pricing model could be a better candidate than more complex option pricing models, especially when one wants to apply the CEV process for pricing more complicated path-dependent options or credit risk models.
A Comparison of the Black-Scholes Option Pricing Model and Its Alternatives