English

Direct semi-parametric estimation of the state price density implied in option prices

Applications 2021-03-29 v3

Abstract

We present a model for direct semi-parametric estimation of the State Price Density (SPD) implied in 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 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 application to real data.

Keywords

Cite

@article{arxiv.1610.08665,
  title  = {Direct semi-parametric estimation of the state price density implied in option prices},
  author = {Gianluca Frasso and Paul H. C. Eilers},
  journal= {arXiv preprint arXiv:1610.08665},
  year   = {2021}
}