Optimal Arbitrage Strategies on Stock Index Futures Under Position Limits
National University of Singapore (NUS) - Department of Mathematics
University of Oxford - Mathematical Institute; University of Oxford - Mathematical Institute
Yue Kuen Kwok
Hong Kong University of Science & Technology - Department of Mathematics
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.
Number of Pages in PDF File: 15
Keywords: index arbitrage, optimal stopping, transaction costs, position limits
JEL Classification: G13working papers series
Date posted: February 8, 2010 ; Last revised: May 7, 2010
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