This paper continues elements of the research direction of the work of Madan et al. [(1998) The variance gamma process and option pricing, European Finance Review 2, 79–105] and gives analytical expressions for the prices of digital and European call options in the variance-gamma model under the assumption that the linear drift rate of stock log-returns can suddenly jump downwards. The time of the jump is taken to be exponentially distributed. The formulas obtained require the computation of some generalized hyperbolic functions.