Optimal Liquidation Policies of Redeemable Shares

Abstract

In this paper we explore optimal issuance and liquidation of redeemable shares. Redeemable shares are those that the issuer can repurchase, or redeem, at a predetermined price, known as the call price, as soon as a given barrier event is triggered. We first determine the optimal call price for the issuer stating and solving a stylized earning per share maximization problem from the point of view of a company. Once the call price is determined, we focus on the valuation of both perpetual and finite-maturity redeemable shares and we examine the problem of their optimal liquidation from the point of view of a shareholder holding them. Along with the few closed-form results that can be obtained in a lognormal continuous- time framework, we propose an intuitive and flexible method to retrieve the optimal liquidation policy in the form of a liquidation boundary, thanks to a parsimonious Markovianization of the evaluation problem in a binomial framework.

Keywords: Redeemable shares, Call price, American option, Optimal stopping, Variational inequality, Optimal liquidation