Direct Semi-Parametric Estimation of the State Price Density Implied in Option Prices. Issue 3 (16th June 2022)

• Record Type: Journal Article
• Authors: Frasso, Gianluca; Eilers, Paul H.C.
• Is Part Of: Journal of business & economic statistics. Volume 40:Issue 3(2022)
• Page Start: 1179
• Page End: 1190
• Publication Date: 2022-06-16
• Subjects: Arbitrage-free estimates -- Inverse problem -- Penalized composite link model -- State price density; Economics -- Statistical methods -- Periodicals; Commercial statistics -- Periodicals; Économie politique -- Méthodes statistiques -- Périodiques; Statistique commerciale -- Périodiques; 330.015195
• DOI: 10.1080/07350015.2021.1906686
• Languages: English
• ISSNs: 0735-0015

Abstract

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.