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Optimal closing of a pair trade with a model containing jumps

Stig Larsson (Institutionen för matematiska vetenskaper, matematik) ; Carl Lindberg (Institutionen för matematiska vetenskaper, matematisk statistik) ; Marcus Warfheimer (Institutionen för matematiska vetenskaper, matematik)
Applications of Mathematics (0862-7940). Vol. 58 (2013), 3, p. 249-268.
[Artikel, refereegranskad vetenskaplig]

A pair trade is a portfolio consisting of a long position in one asset and a short position in another, and it is a widely used investment strategy in the financial industry. Recently, Ekström, Lindberg, and Tysk studied the problem of optimally closing a pair trading strategy when the difference of the two assets is modelled by an Ornstein-Uhlenbeck process. In the present work the model is generalized to also include jumps. More precisely, we assume that the difference between the assets is an Ornstein-Uhlenbeck type process, driven by a Levy process of finite activity. We prove a necessary condition for optimality (a so-called verification theorem), which takes the form of a free boundary problem for an integro-differential equation. We analyze a finite element method for this problem and prove rigorous error estimates, which are used to draw conclusions from numerical simulations. In particular, we present strong evidence for the existence and uniqueness of an optimal solution.

Nyckelord: Pairs trading, optimal stopping, Ornstein-Uhlenbeck type process, finite element method, error estimate



Denna post skapades 2013-06-18. Senast ändrad 2014-09-02.
CPL Pubid: 178784

 

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Institutioner (Chalmers)

Institutionen för matematiska vetenskaper, matematik (2005-2016)
Institutionen för matematiska vetenskaper, matematisk statistik (2005-2016)

Ämnesområden

Matematisk statistik

Chalmers infrastruktur