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 |
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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 | |
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.