Optimal Arbitrage Strategies on Stock Index Futures Under Position Limits
15 Pages Posted: 8 Feb 2010 Last revised: 7 May 2010
Date Written: May 6, 2010
Assuming the absence of market frictions, deterministic interest rates, and certainty in dividend payouts from the stocks in the index basket, an arbitrageur can lock in the profit of a positive (negative) arbitrage basis in a stock index futures by adopting a short (long) futures strategy. In addition, the arbitrageur may improve the arbitrage profit by adopting the so-called early unwinding strategy of liquidating the position before maturity, or more aggressively from the long position directly to the short position or vice versa. In this paper, we examine the optimal arbitrage strategies in stock index futures with position limits and transaction costs. In our analysis, the index arbitrage basis is assumed to follow the Brownian Bridge process. The model formulation of the option value functions leads to a coupled system of variational inequalities. We determine the values of the arbitrage opportunities and the optimal threshold values of the arbitrage basis at which the arbitrageur should optimally close an existing position or open a new index arbitrage position. In particular, we examine the impact of transaction costs on the index arbitrage strategies.
Keywords: index arbitrage, optimal stopping, transaction costs, position limits
JEL Classification: G13
Suggested Citation: Suggested Citation