Sessão Temática 2

Semiparametric Estimation of Liquidity Effects on Option Princing

Eva Ferreira Garcia (Universidad de Bilbao-España)

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.

Given the Black-Scholes (BS) (1973) assumptions, all option prices on the same underlying security with the same expiration date but with different exercise prices should have the same implied volatility. However, the well known volatility smile pattern suggests that the BS formula tends to misprice deep in-the-money and deep out-of-the-money options. There have been several attempts to deal with this apparent failure of the BS valuation model. In principle, the existence of the smile may be attributed to the presence of excess kurtosis in the conditional return distributions of the underlying assets. It is clear that excess kurtosis makes extreme observations more likely than in the BS case. This increases the value of out-of-the-money and in-the-money options relative to at-the-money options, creating the smile. However, at least in equity markets, the pattern shown by data tends to contain an asymmetry in the shape of the smile. This may be due to the presence of skewness in the distribution that has the effect of accentuating just one side of the smile.

Given this evidence, extensions to the BS model that exhibit excess kurtosis and skewness have been proposed in recent years along two lines of research: Jump-diffusion models with a Poisson-driven jump process, and the stochastic volatility framework are the two key developments in theoretical option pricing literature. Unfortunately, the complexities needed to price options seem to increase without bounds. Simple nonparametric (semiparametric) methodologies may be able to incorporate the missing (realistic) factors in our option pricing models.

A simpler alternative consists of estimating the implied volatility function with semiparametric methodologies, in which the Black-Scholes implied volatility is replaced by a nonparametric function that depends upon a vector of explanatory variables, that includes a proxy for liquidity, using Symmetrized Nearest Neighbors (SNN) estimation instead of the more traditional kernel approach.