Option pricing with polynomial chaos expansion stochastic bridge interpolators and signed path dependence

Fabio S. Dias, Gareth W. Peters

Research output: Contribution to journalArticlepeer-review

Abstract

Recent technological advances have made possible the obtention of vast amounts of market data and strong computing power for advanced models which would not have been practicable for use in real market settings before. In this manuscript we devise a model-free empirical risk-neutral distribution based on Polynomial Chaos Expansions coupled with stochastic bridge interpolators that includes information from the entire set of observable European call option prices under all available strikes and maturities for a given underlying asset in a way that is guaranteed by construction to produce a valid state price distribution function at all times. We also obtain a non parametric model for the risk premium behaviour via an optimisation problem that joins the risk-neutral Polynomial Chaos Expansion result with any general model for the real-world distribution. Finally, we show an empirical application on SP500 Options on Futures using a real-world distribution that assumes the presence of signed path dependence in the returns of the underlying asset.

Original languageEnglish
Article number126484
JournalApplied Mathematics and Computation
Volume411
Early online date14 Jul 2021
DOIs
Publication statusE-pub ahead of print - 14 Jul 2021

Keywords

  • Mixture models
  • Option pricing
  • Polynomial chaos expansion
  • Signed path dependence
  • Time series momentum

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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