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

Gianluca Frasso; Paul H.C. Eilers

doi:10.1080/07350015.2021.1906686

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

Gianluca Frasso^*
, Paul H.C. Eilers

^*Corresponding author for this work

Epidemiology

University of Liege

Research output: Contribution to journal › Article › Academic › peer-review

Abstract

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.

Original language	English
Pages (from-to)	1179-1190
Number of pages	12
Journal	Journal of Business and Economic Statistics
Volume	40
Issue number	3
Early online date	4 May 2021
DOIs	https://doi.org/10.1080/07350015.2021.1906686
Publication status	Published - 2022

Bibliographical note

Funding Information:
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.

Publisher Copyright:
© 2021 American Statistical Association.

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10.1080/07350015.2021.1906686

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title = "Direct Semi-Parametric Estimation of the State Price Density Implied in Option Prices",

abstract = "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.",

author = "Gianluca Frasso and Eilers, \{Paul H.C.\}",

note = "Funding Information: 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. Publisher Copyright: {\textcopyright} 2021 American Statistical Association.",

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AU - Eilers, Paul H.C.

N1 - Funding Information: 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. Publisher Copyright: © 2021 American Statistical Association.

PY - 2022

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N2 - 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.

AB - 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.

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JO - Journal of Business and Economic Statistics

JF - Journal of Business and Economic Statistics

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ER -

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

Abstract

Bibliographical note

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