Testing volatility autocorrelation in the constant elasticity of variance model

Since its …rst introduction many suggestions have been proposed for the generalization of Black and Scholes option pricing model (Black and Scholes, 1973). One of the most widely spread approaches is allowing for random volatility of the underlying stock price process as in the seminal papers by Hull and White (1987), Scott (1987), Wiggins (1987), Stein and Stein (1991) and Heston (1993). A complete list of references on stochastic volatility is beyond the scope of this paper. Stochastic volatility models (SV models hereafter) account for many empirical facts in the stock and in the derivative markets, such as the leptokurtosis of …nancial log-returns and the so called smile curve of options’implied volatility when plotted against the options strike price (see, among others, Cont, 2001). The estimation of stochastic volatility (SV) models is still a challenging issue; recently, Ben-Hamida and Cont (2001), Ewald and Zhang (2004) and others have suggested di¤erent techniques in order to estimate model parameters in SV models by …tting theoretical option prices to market ones (model calibration). This approach has brought a renewed interest for the Heston and the GARCH di¤usion models; in fact, a quasi-closed formula is available for European option prices in the former case (see Heston, 1993) and Barone Adesi et al. (2005) derive an approximated analytical option pricing formula for the latter. The calibration to market option prices is, thus, rather straightforward in both settings. However, from a model risk minimization perspective (see Cont, 2006), before estimating a model, one should perform a preliminary analysis to test whether the model re‡ects some properties of observed data (e.g. moments, serial dependence etc.). This paper focuses on the Constant Elasticity of Variance stochastic volatility (CEV SV) model which includes both the Heston model (Heston, 1993) and the GARCH di¤usion introduced in Nelson (1990). By taking advantage of the results in Genon-Catalot et al. (2000) , it is proved that, if the data generating process (DGP hereafter) of a stock price is a CEV