Before revision:  Under a structural credit risk model based on spectrally negative Levy processes, we analyze the existence of the Nash equilibrium and derive the associated saddle point. Using the principles of smooth and continuous fit , we determine the buyer's and seller's equilibrium exercise strategies , which are of threshold type . Numerical examples are provided to illustrate the impacts of default risk and  contractual features on the fair premium and exercise strategies .
After revision:  Under a structural credit risk model based on spectrally negative Levy processes, we apply the principles of smooth and continuous fit , we determine the buyer's and seller's equilibrium exercise strategies , which are of threshold type . Numerical examples are provided to illustrate the impacts of default risk and contractual features on the fair premium and exercise strategies .