Pricing Accelerated Share Repurchases with Lookback Options

Abstract

Due in part to the current United States tax structure and surrounding market sentiment, share repurchases–the act of a company using its excess capital to repurchase some of its own shares from the market–have become incredibly popular of late. Since the financial crisis of 2008, almost $4, 000, 000, 000, 000 has been spent by U.S. companies on share repurchases. [7] While the rationale behind choosing to spend excess capital on a share repurchase varies for each company, many reacquire these shares through an Accelerated Share Repurchase (ASR) contract. For these share repurchases, which last anywhere from weeks to months, an investment bank, with more knowledge of the surrounding market conditions and often proprietary repurchase strategies–developed to minimize both the effect on stock price of purchasing a large number of shares and the inherent risk associated with the stock price changing through time–will repurchase the shares on behalf of the company. In this paper, I examine the literature and the mathematical theory behind these Accelerated Share Repurchases and the resulting optimal trading strategies. This investigation takes us first through the problem of optimal execution, where we seek to minimize the cost of selling or purchasing a large number of shares over a short period of time. We then adapt what we learned from the optimal execution problem to the problem of ASRs specifically. Though optimal execution problems have been exhaustively examined, the mathematical theory behind ASRs is fairly recent; most of the literature appears after 2014. I then expand the current literature on ASRs by adding the ability to price an ASR contract with a lookback option. Over the course of this paper, we will work our way up through an optimal execution model to an ASR specific model. I then modify these theories to allow for the inclusion of a lookback option on top of the ASR contract and test the execution of these new contracts on simulated stock market data.