Analytical Pairs Trading Under Different Assumptions on the Spread and Ratio Dynamics

40 Pages Posted: 25 Aug 2010 Last revised: 5 Apr 2011

See all articles by Ian Gregory

Ian Gregory

The University of Sydney - School of Mathematics and Statistics

Christian-Oliver Ewald

University of Glasgow; Center for Dynamic Macroeconomic Analysis, University of St. Andrews - School of Economics and Finance

Pieter Knox

affiliation not provided to SSRN

Date Written: November 4, 2010

Abstract

We demonstrate how arbitrarily sized long/short baskets whose portfolio value is modelled with spread or ratio of any asset weighting can be treated as a sequential stopping problem. In particular, when the underlying data generating process follows an Ornstein-Uhlenbeck, Cox-Ingersoll-Ross or GARCH diffusion, we derive closed form expressions for mean and variance of trade time and trade return (with transaction costs). From these expressions the risk and return characteristics are examined when the objective functions aim to maximisise expected return and Sharpe ratio. The SDE where possible are estimated using exact maximum likelihood, Euler and Hermite Polynomial Expansion. The estimation parameters and their sensitivity can be used to rank potential trades and understand the risk/return profi le involved with this style of investment.

Keywords: Pair trading, mean hitting time, Cox-Ingersoll-Ross, GARCH Diffusion, Ornstein Uhlenbeck, Ratio, Spread

Suggested Citation

Gregory, Ian and Ewald, Christian-Oliver and Knox, Pieter, Analytical Pairs Trading Under Different Assumptions on the Spread and Ratio Dynamics (November 4, 2010). 23rd Australasian Finance and Banking Conference 2010 Paper. Available at SSRN: https://ssrn.com/abstract=1663703 or http://dx.doi.org/10.2139/ssrn.1663703

Ian Gregory (Contact Author)

The University of Sydney - School of Mathematics and Statistics ( email )

Sydney, New South Wales 2006
Australia

Christian-Oliver Ewald

University of Glasgow ( email )

Adam Smith Building
Glasgow, Scotland G12 8RT
United Kingdom

Center for Dynamic Macroeconomic Analysis, University of St. Andrews - School of Economics and Finance ( email )

Castlecliffe
The Scores
St. Andrews, Fife KY16 9AL
United Kingdom
+44(0)1334 462435 (Phone)

HOME PAGE: http://www.maths.usyd.edu.au/u/ewald/

Pieter Knox

affiliation not provided to SSRN ( email )

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