A Semiparametric Estimation of Liquidity Effects on Option Pricing

The central point for the empirical testing of option pricing models is whether the actual distribution of the underlying asset implied by the option market data is consistent with the distribution assumed by the theoretical option pricing model. The well known volatility smile pattern suggests that the Black- Scholes formula tends to misprice deep in-the-money and deep out-of-the-money options.A potentially relevant area of research might be related to endogenously incorporating liquidity costs in option pricing models. An effective approach would be based on the estimation of the implied volatility function with semiparametric methodologies, where the Black-Scholes implied volatility is replaced by a nonparametric function which depend upon a vector of explanatory variables. This is the multivariate kernel regression approach which has been recently followed by Ait-Sahalia and Lo (1998a). However, they ignore the potential effects of market frictions on the nonparametric volatility function. We construct the corresponding call pricing function under liquidity costs, and compare its performance relative to more traditional option pricing models. The nonparametric volatility function with liquidity as an explanatory variable is estimated using the Symmetrized Nearest Neighbors (SNN) estimator rather than the traditional kernel estimator. Special care is taken in obtaining the smoothing parameter.The in-sample performance of the model turns out to be statistically favorable relative to a competing model without liquidity. However, the out-of-sample performance of both models is quite disappointing despite the fact that we are not able to reject the stability of risk-neutral densities estimated over different quarters during our sample period