Abstract
In this paper, we consider a structural model where two firms following jump diffusion processes have the same Poisson process (i.e. the moment of jumps is the same) and the jump sizes are correlated. In the market, we also observe this kind of phenomenon whereby firms experience the same jumps. We first establish the characteristics of the pair of default stopping times and their joint distribution, as well as the associated martingales. Second, we consider the question of the copula which gives the correlation of the two default stopping times and determine the copula that appears in our model. Our model can be used for the pricing of credit derivatives such as the first to default, discount bond, and CDS. Our objective is to give a general model for pricing credit derivatives on two firms presented in this framework, in the presence of the special anticipated default stopping time. The technical tool we mostly use in this paper is the intensity approach in a framework of structural model.
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