Constructing Random Times with Given Survival Processes and Applications to Valuation of Credit Derivatives
We provide an explicit construction of a random time when the associated Azéma semimartingale (also known as the survival process) is given in advance. Our approach hinges on the use of a variant of Girsanov’s theorem combined with a judicious choice of the Radon-Nikodým density process. The proposed solution is also partially motivated by the classic example arising in the filtering theory.
KeywordsProbability Measure Random Time Credit Default Swap Local Martingale Credit Derivative
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