Accelerated Share Repurchases Under Stochastic Volatility

Accelerated share repurchases (ASRs) are a type of stock buyback wherein the repurchasing firm contracts a financial intermediary to acquire the shares on its behalf. The intermediary purchases the shares from the open market and is compensated by the firm according to the average of the stock price over the repurchasing interval, whose end can be chosen by the intermediary. Hence, the intermediary needs to decide both how to minimize the cost of acquiring the shares, and when to exercise its contract to maximize its payment. Studies of ASRs typically assume a constant volatility, but the longer time horizon of ASRs, on the order of months, indicates that the variation of the volatility should be considered. We analyze the optimal strategy of the intermediary within the continuous-time framework of the Heston model for the evolution of the stock price and volatility, which is described by a free-boundary problem which we derive here. To solve this system numerically, we make use of deep learning. Through simulations, we find that the intermediary can acquire shares at lower cost and lower risk if it takes into account the stochasticity of the volatility.