RT Journal Article
SR Electronic
T1 Analytically Deriving Risk-Neutral Densities from Volatility Smiles in Delta
JF The Journal of Derivatives
FD Institutional Investor Journals
SP 6
OP 12
DO 10.3905/jod.2020.1.099
VO 27
IS 4
A1 Hayashi, Fumio
YR 2020
UL http://jod.pm-research.com/content/27/4/6.abstract
AB This article develops a method for analytically deriving RNDs (risk-neutral densities) of future asset prices from volatility smiles. It extends an existing analytical method, which is for volatility smiles with respect to the strike price, to cover smiles with respect to option delta. A worked-out example on currency options shows that the analytically derived RNDs are free of approximation errors that would arise with numerical methods. The proposed method should be useful to practitioners.TOPICS: Options, futures and forward contractsKey Findings• This article develops an analytical method for deriving RNDs (risk-neutral probability densities) of future asset prices from volatility smiles with respect to option delta.• A worked-out example shows that exact RNDs computed by the method are free of approximation errors associated with numerical derivatives.• The proposed method should be useful to practitioners.