MINIMUM GUARANTEED PAYMENTS AND COSTLY CANCELLATION RIGHTS: A STOPPING GAME PERSPECTIVE

Abstract

We consider the valuation and optimal exercise policy of a δ-penalty minimum guaranteed payment option in the case where the value of the underlying dividend-paying asset follows a linear diffusion. We characterize both the value and optimal exercise policy of the considered game option explicitly and demonstrate that increased volatility increases the value of the option and postpones exercise by expanding the continuation region where exercising is suboptimal. An interesting and natural implication of this finding is that the value of the embedded cancellation rights of the issuer increase as volatility increases.