Pairs Trading of Two Assets with Uncertainty in Co-Integration's Level of Mean Reversion

31 Pages Posted: 18 Apr 2016 Last revised: 27 Jun 2017

See all articles by Sangmin Lee

Sangmin Lee

NYU Polytechnic School of Engineering - Department of Finance and Risk Engineering

Andrew Papanicolaou

NYU Tandon School of Engineering, Department of Finance and Risk Engineering

Date Written: April 11, 2016

Abstract

This paper considers a stochastic control problem derived from a model for pairs trading under incomplete information. We decompose an individual asset’s drift into two parts: an industry drift plus some additional stochasticity. The extra stochasticity may be unobserved, which means the investor has only partial information. We solve the control problem under both full and partial information for utility function U(x) = x^{1−γ}/(1−γ), and we make comparisons. We show the existence of stable solution to the associated matrix Riccati equations in both cases for γ > 1, but for 0 < γ < 1 there remains potential for infinite value functions in finite time. Also, we quantify the expected loss in utility due to partial information, and present a numerical study to illustrate the contribution of this paper.

Keywords: Pairs trading, Co-integration, Kalman filter, Partial Information, Stochastic Control

Suggested Citation

Lee, Sangmin and Papanicolaou, Andrew, Pairs Trading of Two Assets with Uncertainty in Co-Integration's Level of Mean Reversion (April 11, 2016). International Journal of Theoretical and Applied Finance, Forthcoming; NYU Tandon Research Paper No. 2762512. Available at SSRN: https://ssrn.com/abstract=2762512 or http://dx.doi.org/10.2139/ssrn.2762512

Sangmin Lee (Contact Author)

NYU Polytechnic School of Engineering - Department of Finance and Risk Engineering ( email )

NY
United States

Andrew Papanicolaou

NYU Tandon School of Engineering, Department of Finance and Risk Engineering ( email )

6 Metrotech Center
Brooklyn, NY 11201
United States

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