Professor Song invites you to attend the PhD Dissertation Defense of Emmanuel Tamakloe.

WHEN: Thursday, July 29th, at 2:00pm

"Optimal Pair-Trading Decision Rules for a Class of Non-linear Boundary Crossings by Ornstein-Uhlenbeck Processes"

ABSTRACT:

The Ornstein-Uhlenbeck (OU) stochastic process originated from physics is a stationary Gauss-Markov process that has found widespread use in many areas such as finance, economics, life and physical sciences. Among its various attractive properties, the most useful feature widely used in finance is its mean-reverting property: the OU process tends to drift towards its longterm mean (its equilibrium state) over time. This important feature makes the OU process arguably the most popular statistical model for developing best pair-trading strategies. However, optimal strategies depend crucially on the first passage time (FPT) of the OU process to a suitably chosen boundary and its probability density is not analytically available in general. Even for crossing a simple constant boundary, the FPT of the OU process would lead to crossing a square root boundary by a Brownian motion process whose FPT density involves the complicated parabolic cylinder function. To overcome the limitations of the existing methods, we propose a novel class of non-linear boundaries for obtaining optimal decision thresholds. We prove the existence and uniqueness of the maximizer of our decision rules. We also derive simple formulas for some FPT moments without analytical expressions of its density functions. We conduct some Monte Carlo simulations and analyze several pairs of stocks including Coca-Cola and Pepsi, Target and Walmart, Chevron and Exxon Mobil. The results demonstrate that our method outperforms the existing procedures