Forward or Backward Simulation?: A Comparative Study

Abstract

The aim of this study is to present algorithms for the backward simulation of standard processes that are commonly used in financial applications. We extend the works of Ribeiro and Webber and Avramidis and L’Ecuyer on gamma bridge and obtain the backward construction of a Gamma process. Moreover, we are able to write a novel acceptance-rejection algorithm to simulate Inverse Gaussian (IG) processes backward in time. Therefore, using the time-change approach, we can easily get the backward generation of the Compound Poisson with infinitely divisible jumps, the Variance–Gamma the Normal–Inverse–Gaussian processes and then the time-changed version of the OU process (SubOU) introduced by Li and Linetsky. We then compare the computational costs of the sequential and backward path generation of such processes and show the advantages of adopting the latter one, in particular in the context of pricing American options or energy facilities like gas storages.