Box Spread Strategies and Arbitrage Opportunities

Abstract

Arbitrage, or more precisely, absence of arbitrage opportunities, is at the heart of derivatives theory, and the literature abounds with empirical studies of arbitrage strategies. Some model-based arbitrage trades are straightforward, like the cash-and-carry trade in futures; others are harder, like option replication through dynamic hedging; and some represent a kind of “notional” arbitrage that may not be possible at all in practice, like most of those covered by the “absence of arbitrage opportunities” assumption in an option model with unobservable latent factors. In empirical tests of arbitrage strategies, as in so many other things, “the devil is in the details.” There are many ways in which a seemingly reasonable test methodology can fail to reflect important aspects of the actual trades that would have to be executed in real world arbitrage. Was all of the necessary information available at the time of the trade? Were price quotes on all of the instruments simultaneous? After price quotes are observed, does the methodology allow an adequate reaction time interval before trades are assumed to be executed? What quantity could have been traded at the specified prices? Would the profit have been eliminated by normal transactions costs? And so on. Handling these issues properly places severe demands on the data-gathering process. In the end, very, very few empirical tests of arbitrage strategies can fully capture the reality of the actual trade. But this article by Benzion, Danan, and Yagil does. The authors have done everything right, from their choice of the box spread arbitrage strategy, which is both very low risk and internally hedged without any need for rebalancing, to installing a specialized computer program on a broker's computer to look for trades in real time, to taking care that the same mispriced option is not assumed to be simultaneously part of multiple “arbitrage opportunities.” The bottom line: there are quite a few profitable arbitrage opportunities on the Tel Aviv stock exchange—so long as one can detect them and execute the necessary trades within one second