Optimal Convergence Trading with Unobservable Pricing Errors

TL;DR

This paper develops a dynamic portfolio optimization model for convergence trading that accounts for unobservable Markov-modulated pricing errors, providing strategies under full and partial information.

Contribution

It extends existing models by incorporating unobservable Markovian errors and derives filtering equations for optimal strategies in convergence trading.

Findings

Optimal strategies under full and partial information derived

Filtering equations for unobservable errors established

Model demonstrated with a two-state Markov chain example

Abstract

We study a dynamic portfolio optimization problem related to convergence trading, which is an investment strategy that exploits temporary mispricing by simultaneously buying relatively underpriced assets and selling short relatively overpriced ones with the expectation that their prices converge in the future. We build on the model of Liu and Timmermann (2013) and extend it by incorporating unobservable Markov-modulated pricing errors into the price dynamics of two co-integrated assets. We characterize the optimal portfolio strategies in full and partial information settings both under the assumption of unrestricted and beta-neutral strategies. By using the innovations approach, we provide the filtering equation that is essential for solving the optimization problem under partial information. Finally, in order to illustrate the model capabilities, we provide an example with a two-state Markov chain.