Exact Simulation for a Class of Tempered Stable and Related Distributions

In this paper, we develop a new scheme of exact simulation for a class of tempered stable (TS) and other related distributions with similar Laplace transforms. We discover some interesting integral representations for the underlying density functions that imply a unique simulation framework based on a backward recursive procedure. Therefore, the foundation of this simulation design is very different from existing schemes in the literature. It works pretty efficiently for some subclasses of TS distributions, where even the conventional acceptance-rejection mechanism can be avoided. It can also generate some other distributions beyond the TS family. For applications, this scheme could be easily adopted to generate a variety of TS-constructed random variables and TS-driven stochastic processes for modelling observational series in practice. Numerical experiments and tests are performed to demonstrate the accuracy and effectiveness of our scheme