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

Gianluca Frasso and Paul H.C. Eilers

Journal of Business & Economic Statistics, 2022, vol. 40, issue 3, 1179-1190

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.

Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:taf:jnlbes:v:40:y:2022:i:3:p:1179-1190

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DOI: 10.1080/07350015.2021.1906686

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