Quantile Diffusions

35 Pages Posted: 13 Jan 2020

See all articles by Holly Brannelly

Holly Brannelly

University College London

Andrea Macrina

University College London; University of Cape Town (UCT)

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: December 23, 2019

Abstract

This paper focuses on the development of a new class of diffusion processes that allows for direct and dynamic modelling of quantile diffusions. We constructed quantile diffusion processes by transforming each marginal of a given univariate diffusion process under a composite map consisting of a distribution function and quantile function, which in turn produces the marginals of the resulting quantile process. The transformation allows for the moments of the underlying process to be directly interpreted with regard to parameters of the transformation. For instance, skewness or kurtosis may be introduced to enable more realistic modelling of data such as financial asset returns, as well as the recycling of samples of the underlying process to make simulation of the transformed quantile process easier. We derive the stochastic differential equation satisfied by the quantile diffusion, and characterise the conditions under which strong and weak solutions exist, both in the general case and for the more specific Tukey g-h, g-transform and h-transform families of quantile diffusions.

Keywords: Continuous-time diffusion processes, quantiles, rank transmutation map, Tukey g-h transforms, skew, kurtosis, SDE, weak/strong solutions

Suggested Citation

Brannelly, Holly and Macrina, Andrea and Peters, Gareth, Quantile Diffusions (December 23, 2019). Available at SSRN: https://ssrn.com/abstract=3508702 or http://dx.doi.org/10.2139/ssrn.3508702

Holly Brannelly

University College London ( email )

Gower Street
London, WC1E 6BT
United Kingdom

Andrea Macrina (Contact Author)

University College London ( email )

Gower Street
London, WC1E 6BT
United Kingdom

University of Cape Town (UCT) ( email )

Private Bag X3
Rondebosch, Western Cape 7701
South Africa

Gareth Peters

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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