A semiparametric estimation of liquidity effects on option pricing

Abstract

This paper proposes a semiparametric option pricing model with liquidity, as proxied by the relative bid-ask spread. A nonparametric volatility function with liquidity costs as an explanatory variable is estimated using the Symmetrized Nearest Neighbors (SNN) estimator rather than the traditional kernel estimator. The SNN estimator is particularly suitable for the characteristics of option data in financial markets. Moreover, we propose a natural extension of the univariate bandwidth parameter optimal estimation to the multivariate case. A statistical design to test competing option pricing models which takes into account the lack of independence between them is also presented. The in-sample performance of the model turns out to be statistically favorable relative to the competing model without liquidity. Also, an additional experiment is performed within sample, but with just a subsample of options not employed in the nonparametric estimation of the implied volatility function being priced. The results are also favorable to our semiparametic theoretical option pricing model with liquidity. However, the out-of-sample performance is quite disappointing regardless of what option pricing model is employed in the estimation.