Optimal Arbitrage Strategies on Stock Index Futures Under Position Limits

15 Pages Posted: 8 Feb 2010 Last revised: 7 May 2010

See all articles by Min Dai

Min Dai

National University of Singapore (NUS) - Department of Mathematics

Yifei Zhong

University of Oxford - Mathematical Institute; University of Oxford - Mathematical Institute

Yue Kuen Kwok

Hong Kong University of Science & Technology - Department of Mathematics

Date Written: May 6, 2010

Abstract

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

Dai, Min and Zhong, Yifei and Kwok, Yue Kuen, Optimal Arbitrage Strategies on Stock Index Futures Under Position Limits (May 6, 2010). Available at SSRN: https://ssrn.com/abstract=1534527 or http://dx.doi.org/10.2139/ssrn.1534527

Min Dai

National University of Singapore (NUS) - Department of Mathematics ( email )

Singapore

Yifei Zhong

University of Oxford - Mathematical Institute ( email )

Mathematical Institute
24-29 St Giles
Oxford, Oxfordshire OX1 3LB
United Kingdom

University of Oxford - Mathematical Institute ( email )

24-29 St Giles'
Oxford, OX1 3LB
United Kingdom

Yue Kuen Kwok (Contact Author)

Hong Kong University of Science & Technology - Department of Mathematics ( email )

Clearwater Bay
Kowloon, 999999
Hong Kong

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