Pairs Trading Under Drift Uncertainty and Risk Penalization

26 Pages Posted: 20 Apr 2017  

Sühan Altay

Vienna University of Technology - Financial and Actuarial Mathematics Research Group

Katia Colaneri

University of Perugia, Department of Economics

Zehra Eksi

Vienna University of Economics and Business, Institute for Statistics and Mathematics

Date Written: April 18, 2017

Abstract

In this work, we study the dynamic portfolio optimization problem related to the pairs trading, which is an investment strategy that matches a long position in one security with a short position in an another security with similar characteristics. The relation between pairs, called spread, is modeled by a Gaussian mean-reverting process whose drift rate is modulated by an unobservable continuous-time finite state Markov chain. Using the classical stochastic filtering theory, we reduce this problem with partial information to the one with complete information and solve it for the logarithmic utility function, where the terminal wealth is penalized by the riskiness of the portfolio according to the realized volatility of the wealth process. We characterize optimal dollar-neutral strategies as well as optimal value functions under both full and partial information and show that the certainty principle holds for the optimal portfolio strategy. Finally, we provide a numerical analysis for a simple example with a two-state Markov chain.

Keywords: pairs trading, regime-switching, utility maximization, risk penalization and partial information

JEL Classification: C02, C61, G11

Suggested Citation

Altay, Sühan and Colaneri, Katia and Eksi, Zehra, Pairs Trading Under Drift Uncertainty and Risk Penalization (April 18, 2017). Available at SSRN: https://ssrn.com/abstract=2954762 or http://dx.doi.org/10.2139/ssrn.2954762

Sühan Altay

Vienna University of Technology - Financial and Actuarial Mathematics Research Group ( email )

Karlsplatz 13
A-1040 Vienna
Austria

Katia Colaneri

University of Perugia, Department of Economics ( email )

Via Pascoli 22
Perigoa, 06121
Italy

Zehra Eksi (Contact Author)

Vienna University of Economics and Business, Institute for Statistics and Mathematics ( email )

Welthandelsplatz 1
Building D4, 4th floor
Vienna, 1020
Austria

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