Analytically Deriving Risk-Neutral Densities from Volatility Smiles
The Journal of Derivatives, Summer 2020; DOI: https://doi.org/10.3905/jod.2020.1.099
Posted: 27 Jul 2019
Date Written: July 25, 2019
This paper develops a method to analytically derive RNDs (risk-neutral distributions) from volatility smiles. The strike price measure in the volatility smile does not have to be the strike price itself. It can be moneyness, the delta, or other popular strike price measures. The method utilizes analytical derivatives of the volatility smile that come with parametric interpolations of observed data on options. This makes numerical second derivatives of the call price function unnecessary. A worked-out example shows that the analytically derived RNDs are free of distortions associated with numerical second derivatives. The proposed method should be useful to practitioners.
Keywords: options, risk-neutral densities, volatility smiles, the delta
JEL Classification: G13
Suggested Citation: Suggested Citation