Analytically Deriving Risk-Neutral Densities from Volatility Smiles

18 Pages Posted: 27 Jul 2019

See all articles by Fumio Hayashi

Fumio Hayashi

National Graduate Institute for Policy Studies

Date Written: July 25, 2019

Abstract

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

Hayashi, Fumio, Analytically Deriving Risk-Neutral Densities from Volatility Smiles (July 25, 2019). Available at SSRN: https://ssrn.com/abstract=3426488 or http://dx.doi.org/10.2139/ssrn.3426488

Fumio Hayashi (Contact Author)

National Graduate Institute for Policy Studies ( email )

Roppongi 7-22-1
Minato-ku
Tokyo, 106-0032
Japan

HOME PAGE: http://https://sites.google.com/site/fumiohayashi/home

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