Exact Simulation for a Class of Tempered Stable Distributions ∗ Angelos Dassios † London School of Economics Yan Qu ‡ London School of Economics Hongbiao Zhao § Shanghai University of Finance and Economics 22nd January 2018 Abstract In this paper, we develop a new scheme of exact simulation for a class of tempered sta- ble (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. Keywords: Monte Carlo simulation; Exact simulation; Backward recursive scheme; Stable distribution; Tempered stable distribution; Exponentially tilted stable distribution; Lévy process; Lévy subordinator; Leptokurtosis Mathematics Subject Classification (2010): Primary: 60E07 · 65C10; Secondary: 65C05 · 60G51 · 60G52 * An edited version to be published by ACM Transactions on Modeling and Computer Simulation † Department of Statistics, London School of Economics, Houghton Street, London WC2A 2AE, United Kingdom. Email: a.dassios@lse.ac.uk ‡ Department of Statistics, London School of Economics, Houghton Street, London WC2A 2AE, United Kingdom. Email: y.qu3@lse.ac.uk § Corresponding author, School of Statistics and Management, Shanghai University of Finance and Economics, No. 777 Guoding Road, Shanghai 200433, China. Email: h.zhao1@lse.ac.uk 1