Accelerated Share Repurchase: Pricing and Execution Strategy

Abstract

In this paper, we consider the optimal execution problem associated to accelerated share repurchase (ASR) contracts. When firms want to repurchase their own shares, they often enter such a contract with a bank. The bank buys the shares for the firm and is paid the average market price over the execution period, the length of the period being decided upon by the bank during the buying process. Mathematically, the problem is new and related to both option pricing (Asian and Bermudan options) and optimal execution. We provide a model, along with associated numerical methods, to determine the optimal stopping time and the optimal buying strategy of the bank.

Portfolio choice, portfolio liquidation, and portfolio transition under drift uncertainty

“…Following the results of Section 3, solving the optimal portfolio choice of the agent in the CARA case boils down to solving the linear parabolic PDE (22) with terminal condition (23).…”

“…Proof. Let us consider φ ∈ C 1,2 ([0, T ] × R d ) solution of (22) with terminal condition (23). For u defined by (21) and by considering M = M e r(T −t) , we have…”

“…From the previous proposition, we see that solving the HJB equation (19) with terminal condition (20) boils down to solving (22) with terminal condition (23). Because (22) is a simple parabolic PDE, we can easily build a strong solution.…”

Accelerated share repurchase and other buyback programs: what neural networks can bring

“…In particular, they show that the exercise boundary only depends on the time to maturity and the ratio between the stock price and its average value since inception. The case of ASR contracts with fixed number of shares is also dealt with in the paper [18] by Guéant, Pu and Royer who proposed a discrete-time model with general execution cost function, and an expected utility objective function. As in [21], they show that the problem boils down to a set of equations with 3 variables; here time to maturity, the number of shares to be bought, and the difference between the current stock price and the average price since inception.…”

“…In Section 2, we describe the three different types of buyback contracts addressed in the paper: two types of ASR contracts and one VWAP-minus profit-sharing contract. In Section 3, we propose a discrete-time model similar to that of [16,17,18] and define the objective functions. In Section 3, we also describe our deep recurrent neural network method to approximate the optimal strategy for managing the different contracts.…”