Using a suitable change of probability measure, we obtain a novel Poissonseries representation for the arbitrage- free price process of vulnerablecontingent claims in a regime-switching market driven by an underlyingcontinuous- time Markov process. As a result of this representation, along witha short-time asymptotic expansion of the claim's price process, we develop anefficient method for pricing claims whose payoffs may depend on the full pathof the underlying Markov chain. The proposed approach is applied to price notonly simple European claims such as defaultable bonds, but also a new type ofpath-dependent claims that we term self-decomposable, as well as the importantclass of vulnerable call and put options on a stock. We provide a detailederror analysis and illustrate the accuracy and computational complexity of ourmethod on several market traded instruments, such as defaultable bond prices,barrier options, and vulnerable call options. Using again our Poisson seriesrepresentation, we show differentiability in time of the pre-default pricefunction of European vulnerable claims, which enables us to rigorously deduceFeynman-Kac representations for the pre-default pricing function and newsemimartingale representations for the price process of the vulnerable claimunder both risk-neutral and objective probability measures.
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