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

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  • Gianluca Frasso
  • Paul H.C. Eilers

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.

Suggested Citation

  • Gianluca Frasso & Paul H.C. Eilers, 2022. "Direct Semi-Parametric Estimation of the State Price Density Implied in Option Prices," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 40(3), pages 1179-1190, June.
    • Handle: RePEc:taf:jnlbes:v:40:y:2022:i:3:p:1179-1190
    DOI: 10.1080/07350015.2021.1906686
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