On the optimal exercise boundaries of swing put options

We use probabilistic methods to characterise the optimal exercise region of a swing option with put payoff, $n\ge 2$ exercise rights and finite maturity, when the underlying asset's dynamics is specified according to the Black & Scholes model. The optimal exercise region of each right (except the last) is described in terms of two boundaries which are continuous functions of time and uniquely solve a system of coupled integral equations of Volterra-type. The swing option's price is then obtained as the sum of a European part and an early exercise premium which depends on the optimal boundaries.