Optimal Arbitrage under Limits to Arbitrage: The Case of Convergence Trade
50 Pages Posted: 19 Nov 2019 Last revised: 28 Nov 2019
Date Written: November 8, 2019
As a popular arbitrage strategy, convergence trade aims to exploit relative mispricing between two closely related assets. We examine optimal convergence trade strategies in the presence of three types of limits to arbitrage: short-selling cost, funding cost, and forced liquidation of investment positions. Our results show that the optimal allocation rules are piecewise linear functions of the mispricing level, allowing the trader to better balance the profits and costs incurred when she trades on mispricing. We also find that these limits to arbitrage have a stronger deterrence effect on short-selling than on purchasing, driving the optimal trading strategy significantly away from a delta-neutral one. Moreover, we find that it is optimal to liquidate positions on the convergence assets faster when the fund's termination risk increases.
Keywords: Pairs trading, Funding cost, Short-selling cost, Risky arbitrage
JEL Classification: C32, G11, G12
Suggested Citation: Suggested Citation