Direct Semi-Parametric Estimation of the State Price Density Implied in Option Prices

Arbitrage-free estimates; Inverse problem; Penalized composite link model; State price density; Statistics and Probability; Social Sciences (miscellaneous); Economics and Econometrics; Statistics, Probability and Uncertainty

Abstract :

[en] We present a model for direct semi-parametric estimation of the state price density (SPD) implied by quoted option prices. We treat the observed prices as expected values of possible pay-offs at maturity, weighted by the unknown probability density function. We model the logarithm of the latter as a smooth function, using P-splines, while matching the expected values of the potential pay-offs with the observed prices. This leads to a special case of the penalized composite link model. Our estimates do not rely on any parametric assumption on the underlying asset price dynamics and are consistent with no-arbitrage conditions. The model shows excellent performance in simulations and in applications to real data.

Disciplines :

Quantitative methods in economics & management

Author, co-author :

Frasso, Gianluca ; Université de Liège - ULiège > Département des sciences sociales > Méthodes quantitatives en sciences sociales

Eilers, Paul H.C.; Erasmus University Medical Center, Rotterdam, Netherlands

Language :

English

Title :

Direct Semi-Parametric Estimation of the State Price Density Implied in Option Prices

Publication date :

2022

Journal title :

Journal of Business and Economic Statistics

ISSN :

0735-0015

eISSN :

1537-2707

Publisher :

American Statistical Association

Volume :

Issue :

Pages :

1179 - 1190

Peer reviewed :

Peer Reviewed verified by ORBi

Additional URL :

https://www.tandfonline.com/doi/pdf/10.1080/07350015.2021.1906686

Funding text :

We thank professor Oleg Bondarenko for sharing the code used to estimate risk-neutral densities with the positive convolution approximation. We also thank the two anonymous reviewers and the associated editor for their insightful comments and remarks.

Available on ORBi :

since 29 March 2023

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