Computing survival probabilities based on stochastic differential models

•We propose a very efficient method to compute survival probabilities.•We combine polynomial differential quadrature with high-order time-stepping.•We consider a reduced-form model and a structural model that arise from finance and insurance.•The method is model independent and could also be extended to other stochastic processes.•Numerical comparison with other recent approaches is provided.

We develop a new numerical method to compute survival probabilities based on stochastic differential models, a matter of great importance in several areas of science, such as finance, biology, medicine and geophysics. This novel approach is based on polynomial differential quadrature, which is combined with a high-order time discretization scheme. Numerical experiments are presented showing that the proposed method performs extremely well and is more efficient than the approaches recently developed in Costabile et al. (2013) and Guarin et al. (2011).