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Pricing equations in jump-to-default models. (English) Zbl 1295.91084

Summary: We study pricing equations in jump-to-default models, and we provide conditions under which the option price is the unique classical solution, with a special focus on boundary conditions. In particular, we find precise conditions ensuring that the option price at the default boundary coincides with the recovery payment. We also study spatial convexity of the option price, and we explore the connection between preservation of convexity and parameter monotonicity.

MSC:

91G20 Derivative securities (option pricing, hedging, etc.)
60G40 Stopping times; optimal stopping problems; gambling theory
60H30 Applications of stochastic analysis (to PDEs, etc.)
91G40 Credit risk
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