Pricing The Zero-coupon Bond And Its Fair Premium Under Markov-modulated Jump-diffusion Models

The paper makes a quantitative analysis of default risk under the jump-diffusion models.Different from the common used model,we introduce an economic state variable in this model,which is described by a Markov chain.Thus we propose a default intensity processes with regime switching.Under the two-sided jump-diffusion models,where the macroeconomic environment is taken into account,using the Markov property,we give the integro-differential equations for the Laplace transform of default time and the firm's expected present market value at default.Specially,closed form expressions for them are obtained when the jumps have a symmetry-exponential distribution.Hence,we could obtain the numerical solutions of different economic states for the default probability,the price and the premium of the defaultable zero-coupon bond by inverting those closed form expressions.In the end,by comparing with the no-regime-switching case,we analyze the impact of economic environment on the pricing.