Default Swap Games Driven By Spectrally Negative Levy Processes
This paper studies the valuation of game-type Credit Default Swaps (CDSs) that allow the protection buyer and seller to raise or reduce the respective position once prior to default. This leads to the study of a stochastic game with optimal stopping subject to early termination resulting from a default. Under a structural credit risk model based on spectrally negative Levy processes, the authors analyze the existence of the Nash equilibrium and derive the associated saddle point. Using the principles of smooth and continuous fit, they 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.