Option Pricing with Polynomial Chaos Expansion Stochastic Bridge Interpolators and Signed Path Dependence

45 Pages Posted: 28 May 2020

See all articles by Fabio Dias

Fabio Dias

University College London - Department of Statistical Science

Gareth Peters

Department of Actuarial Mathematics and Statistics, Heriot-Watt University; University College London - Department of Statistical Science; University of Oxford - Oxford-Man Institute of Quantitative Finance; London School of Economics & Political Science (LSE) - Systemic Risk Centre; University of New South Wales (UNSW) - Faculty of Science

Date Written: April 29, 2020

Abstract

Recent empirical studies in Equity markets show evidence that, while asset log-returns are largely uncorrelated, it is possible to predict with some accuracy their future sign. Such prediction is made over a given forecast horizon based solely on the observed sign of the cumulative log-return over a lookback horizon. This manuscript proposes a methodology to study the impact of such findings on option pricing by embedding into the risk premium the effects of signed path dependence. This is achieved by devising 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. Under the real-world measure we propose a price dynamics model that is compatible with an asset price process that is largely uncorrelated but still exhibits signed path dependence. The risk premium behaviour is subsequently inferred non-parametrically via a stochastic bridge interpolation that couples the risk neutral Polynomial Chaos Expansion result with the signed path dependence mixture binomial tree dynamic model to obtain a dynamic stochastic model for the implied risk premium process.

Keywords: option pricing, time series momentum, mixture models, polynomial chaos expansion, signed path dependence

Suggested Citation

Dias, Fabio and Peters, Gareth, Option Pricing with Polynomial Chaos Expansion Stochastic Bridge Interpolators and Signed Path Dependence (April 29, 2020). Available at SSRN: https://ssrn.com/abstract=3588871 or http://dx.doi.org/10.2139/ssrn.3588871

Fabio Dias

University College London - Department of Statistical Science ( email )

1-19 Torrington Place
London, WC1 7HB
United Kingdom

Gareth Peters (Contact Author)

Department of Actuarial Mathematics and Statistics, Heriot-Watt University ( email )

Edinburgh Campus
Edinburgh, EH14 4AS
United Kingdom

HOME PAGE: http://garethpeters78.wixsite.com/garethwpeters

University College London - Department of Statistical Science ( email )

1-19 Torrington Place
London, WC1 7HB
United Kingdom

University of Oxford - Oxford-Man Institute of Quantitative Finance ( email )

University of Oxford Eagle House
Walton Well Road
Oxford, OX2 6ED
United Kingdom

London School of Economics & Political Science (LSE) - Systemic Risk Centre ( email )

Houghton St
London
United Kingdom

University of New South Wales (UNSW) - Faculty of Science ( email )

Australia

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