A Semiparametric Estimation of Liquidity Effects on Option Pricing

Biltoki Working Paper No. 08, 1999

48 Pages Posted: 10 Oct 2000

See all articles by Eva Ferreira

Eva Ferreira

University of the Basque Country - Department of Applied Economics III (Econometrics and Statistics)

Mónica Gago

Mondragon University - Ciencias Empresariales

Gonzalo Rubio

University of the Basque Country - Department of Foundations of Economic Analysis I

Abstract

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.

Keywords: Multivariate Kernel and SNN Regressions, Volatility Smile, Option Pricing

JEL Classification: G12, G13

Suggested Citation

Ferreira Garcia, Eva and Gago, Mónica and Rubio, Gonzalo A., A Semiparametric Estimation of Liquidity Effects on Option Pricing. Biltoki Working Paper No. 08, 1999, Available at SSRN: https://ssrn.com/abstract=234574 or http://dx.doi.org/10.2139/ssrn.234574

Eva Ferreira Garcia

University of the Basque Country - Department of Applied Economics III (Econometrics and Statistics) ( email )

Avda. Lehendakari Aguirre 83
Bilbao, Vizcaya 48015
Spain
+34 94 601 3739 (Phone)
+34 94 601 3754 (Fax)

Mónica Gago

Mondragon University - Ciencias Empresariales ( email )

Gonzalo A. Rubio (Contact Author)

University of the Basque Country - Department of Foundations of Economic Analysis I ( email )

Avda. Lehendakari Aguirre 83
Bilbao, Vizcaya 48015 48015
Spain
+34 94 601 3770 (Phone)
+34 94 601 3774 (Fax)

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