A Closed-Form Approach to Valuing Risk-Neutral Moments from Option Prices
36 Pages Posted: 12 Feb 2016 Last revised: 12 Jul 2018
Date Written: April 1, 2018
This paper develops closed-form solutions for the finite integrals in the volatility, cubic and quartic contracts in Bakshi, Kapadia and Madan (2003) which avoid discretization errors and do not involve interpolation and extrapolation. It compares the accuracy of the closed-form approach with the popular interpolation-extrapolation approach in the literature. Our results show that the closed-form approach provides more accurate estimates for skewness. This holds across different option pricing models and parameterization which have been shown to be favourable for the interpolation-extrapolation approach. Finally, our results show that the closed-form approach always extracts expectations consistent with the term structure of the volatility smirk whereas the interpolation-extrapolation approach fails several times.
Keywords: Model-free Moment; Option Valuation; Jump Diffusion Model; Stochastic Volatility model.
JEL Classification: G12, G13
Suggested Citation: Suggested Citation