Pairs-Trading: An Optimal Selling Rule

This paper I worked on as part of a VIGRE research class during Spring 2013, along with my coauthors Kuo, Luu, Nguyen, Thompson, and Zhang. The abstract is as follows:

Pairs trading involves two cointegrated securities. When divergence is underway, i.e., one stock moves up while the other moves down, a pairs trade is entered consisting of a short position in the outperforming stock and a long position in the underperforming one. Such a strategy bets the spread between the two would eventually converge. This paper is concerned with an optimal pairs-trade selling rule. In this paper, a difference of the pair is governed by a mean-reverting model. The trade will be closed whenever the difference reaches a target level or a cut-loss limit. Given a fixed cutloss level, the objective is to determine the optimal target so as to maximize an overall return. This optimization problem is related to an optimal stopping problem as the cutloss level vanishes. Expected holding time and profit probability are also obtained. Numerical examples are reported to demonstrate the results.

Separate Calvo Price-Stickiness Parameters in an Aggregate Supply and Demand Model

My Masters Thesis in Economics. The abstract is as follows:

This paper tests whether or not the degree of price-stickiness between supply and demand shocks differs. An aggregate supply and demand model is used to derive theoretical impulse response functions for both supply and demand shocks. Then the Blanchard-Quah long-run identifying restrictions are used to identify supply and demand shocks in monthly time series data of industrial production and the consumer price index from January 1975 to January 2000, which are then used to derive empirical impulse response functions for supply and demand shocks. Then the Calvo price-stickiness parameter is separately calibrated for supply and demand shocks by fitting the theoretical impulse response functions to the empirical ones. This paper finds that there is no significant improvement in the fit of the theoretical impulse response functions to the empirical impulse response functions by calibrating the Calvo parameter separately for supply and demand shocks, and hence suggests that firms take approximately the same amount of time to adjust prices in response to demand shocks as they do to supply shocks.