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Mathematical Sciences - Colloquium-Qing Zhang (University of Georgia) "Pairs Trading under Geometric Brownian Motions" (via Zoom)

Friday, December 04, 2020
11:00 am to 11:50 am
Floor/Room #: 
via Zoom

Speaker: Qing Zhang (University of Georgia)
Title: "Pairs Trading under Geometric Brownian Motions"
This talk will be held via Zoom. Please contact Qingshuo Song at qsong@wpi.edu for Zoom meeting information 

ABSTRACT: 

This talk is about an optimal strategy for simultaneously trading a pair of stocks. The idea of pairs-trading is to monitor theirprice movements and compare their relative strength over time. A pairs trade is triggered by their prices divergence and consists of a pair of positions to short the strong stock and to long the weak one. Such strategy bets on the reversal of their price strengths.

From the viewpoint of technical tractability, typical pairs trading models assume a difference in the stock prices follows a mean reversion equation. In this talk, we consider the optimal pairs-trading problem by allowing the stock prices to

follow general geometric Brownian motions. The objective is to trade the pairs over time to maximize an overall return with a fixed commission cost for each transaction. The optimal policy is characterized by threshold curves obtained by solving the associated HJB equations. Numerical examples are included to demonstrate the dependence of our trading rules on various parameters and to illustrate how to implement the results in practice.