First-to-default and second-to-default options in models with various information flows

We continue to study a credit risk model of a financial market introduced recently by the authors, in which the dynamics of intensity rates of two default times are described by linear combinations of three independent geometric Brownian motions. The dynamics of two default-free risky asset prices are modeled by two geometric Brownian motions that are not independent of the ones describing the default intensity rates. We obtain closed form expressions for the no-arbitrage prices of some first-to-default and second-to-default European style contingent claims given the reference filtration initially and progressively enlarged by the two successive default times. The accessible default-free reference filtration is generated by the standard Brownian motions driving the model.