Implicit Probability Distribution for WTI Options : The Black Scholes vs. The Semi-Nonparametric Approach

This paper contributes to the literature on the estimation of the Risk Neutral Density (RND) function by modeling the prices of options for West Texas Intermediate (WTI) crude oil that were traded in the period between January 2016 and January 2017. For these series we extract the implicit RND in the option prices by applying the traditional Black & Scholes (1973) model and the semi-nonparametric (SNP) model proposed by Backus, Foresi, Li, & Wu (1997). The results obtained show that when the average market price is compared to the average theoretical price, the lognormal specification tends to systematically undervalue the estimation. On the contrary, the SNP option pricing model, which explicitly adjust for negative skewness and excess kurtosis, results in markedly improved accuracy