Exact Simulation for a Class of Tempered Stable and Related Distributions

ACM Transactions on Modeling and Computer Simulation

27 Pages Posted: 30 Jan 2018 Last revised: 20 May 2020

See all articles by Angelos Dassios

Angelos Dassios

London School of Economics & Political Science (LSE) - Department of Statistics

Yan Qu

University of Warwick - Department of Statistics

Hongbiao Zhao

Shanghai University of Finance and Economics; London School of Economics & Political Science (LSE)

Date Written: January 22, 2018

Abstract

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.

Keywords: Monte Carlo Simulation, Exact Simulation, Backward Recursive Scheme, Stable Distribution, Tempered Stable Distribution; Exponentially Tilted Stable Distribution, L'evy Process, L'evy Subordinator, Leptokurtosis

Suggested Citation

Dassios, Angelos and Qu, Yan and Zhao, Hongbiao, Exact Simulation for a Class of Tempered Stable and Related Distributions (January 22, 2018). ACM Transactions on Modeling and Computer Simulation, Available at SSRN: https://ssrn.com/abstract=3106579

Angelos Dassios

London School of Economics & Political Science (LSE) - Department of Statistics ( email )

Houghton Street
London, England WC2A 2AE
United Kingdom

Yan Qu

University of Warwick - Department of Statistics ( email )

Coventry, CV47AL
United Kingdom

Hongbiao Zhao (Contact Author)

Shanghai University of Finance and Economics ( email )

No. 777 Guoding Road
Yangpu District
Shanghai, Shanghai 200433
China

HOME PAGE: http://hongbiaozhao.weebly.com/

London School of Economics & Political Science (LSE)

Houghton Street
London, WC2A 2AE
United Kingdom

Do you have a job opening that you would like to promote on SSRN?

Paper statistics

Downloads
21
Abstract Views
230
PlumX Metrics