Properties of the Variance-Gamma Process With Drift Switching Component With Financial Applications

Abstract

We consider an extension of the variance-gamma process implying that the linear drift rate of the process can switch suddenly by a jump. The value of jump is modeled by the multidimensional distribution, the jump time is simulated by the exponential distribution. Together with the simplest properties of the new process, its distribution function is derived explicitly. Applications to the credit risk measurement are supplied. Obtained results exploit values of some special mathematical functions including the generalized hypergeometric ones.

Keywords: variance-gamma process; exponential distribution; multidimensional distribution; credit risk; drift jump; risk measure; generalized hypergeometric function

JEL Classification: C02; C51; C52; C63; G01