Pricing Of Vulnerable Contingent Claims In Regime-switching Market

Vulnerable claims refers to a kind of claims which contains default risk. In 1987, Johnson and Stulz firstly studied the option pricing with credit risk, and discussed the impact of the credit default risk caused. The emergence of contingent claim for active financial markets and improve the market mechanism is of great significance. In this dissertation, we discussed the vulnerable claims in regime-switching market, and provided the corresponding pricing methods.In this paper, we described some necessary elementary knowledge and theoretical framework at first. Next, assumed a macro-economy with finitely many observable economic regimes, containing state information regarding hazard intensity h, loss given default L and so on, while the transformation among different regime were driven by a finite state continuous time Markov process. On this basis, introduced the model for pricing vulnerable claims in regime-switching market. Designed to compute the pricing function of claims, we used a suitable change of probability measure, and the above-mentioned Markov process became the homogeneous process. Then, it can be expressed as series representation by a homogeneous Poisson process with intensity 1. As a result of this series representation, along with the Laplace transformation and the Taylor approximation, the predefault pricing methods of the vulnerable claim was given.Finally, this paper focused on applying the new method to price the European option in regime-switching market. Regime-switching models requested the market containing finite states, and would transform among different states. Some of literatures have taken into account that the regime switching alone was not sufficient to describe the actual action of price, in the real financial market, there was a jump which always happened in the price process while the transformation happened, so we introduced the jump-diffusion models in regime-switching style, based on it, this paper gave the pricing methods of European option in jump-diffusion model in regime-switching market. At the same time, the risk-neutral pricing of European barrier and digital contracts written on the volatility process was a case study of what given the new pricing methods of a class of path-dependent claims in regime-switching market.