R functions for ‘Exact simulation of tempered stable Ornstein-Uhlenbeck processes’

1 Introduction
Type: R functions for ‘Exact simulation of tempered stable Ornstein-Uhlenbeck processes’
Version: 1.1.0
Date: 2009-12-18
Author: Shibin Zhang
Maintainer: Shibin Zhang <sbzhang@shmtu.edu.cn>
Description: Companion functions to the paper ‘Exact simulation of tempered
stable Ornstein-Uhlenbeck processes’, submitted. These functions are
a preliminary draft. Dont count too much on it until the paper has been published.
This document provides R functions for the exact simulation method
of tempered stable Ornstein-Uhlenbeck processes using the parametrisation
described by Zhang (2009).
Usage: To use the software, you will need to download the file
exact_simu_TSOU.R (in R_exact_simu_TSOU) into a suitable directory on your computer. This contains
the functions listed below and various supporting functions. You should
not need to look at the R code in this file unless you want to see the details of
what’s going on.
2 The functions
rTS(n,kappa,delta,gamma)
rIG(n,delta,gamma)
rPS(n,kappa,delta)
TSOU(x=2*kappa*delta*gamma^ (1-1/kappa), lambda=1, kappa=1/2, delta=1, gamma=1, T=1, N=100, n=100)
IGOU(x=delta/gamma, lambda=1, delta=1, gamma=1, T=1, N=100, n=100)
PSOU(x=1, lambda=1, kappa=1/2, delta=1, T=1, N=100)

The functions rTS, rIG and rPS are used to sample n points from the TS (κ,δ,γ),
IG(δ,γ) and S (κ,δ) distributions, respectively. And the function rTS employs the
double rejection method in Devroye (2009); rIG employs the method in Michael et
al. (1976); and rPS employs the method in Zhang (2008).
The functions TSOU, IGOU and PSOU are the simulations of the O-U process with
marginals TS (κ,δ,γ), IG(δ,γ) and S (κ,δ), respectively. lambda is the intensity parameter
of the O-U process. x is the initial value of the process at time t0. T is the
final time. N is the number of intervals in which to split [t0,T]. n is the number
to improve the acceptance probability in sampling from the DTS law (see Zhang
(2009)). These three functions employ the methods in Zhang and Zhang (2008),
Zhang and Zhang (2009) and Zhang (2009).
References
Devroye, L., 2009. Random variate generation for exponentially and polynomially
tilted stable distributions. ACM Transactions on Modeling and Computer Simulation
(TOMACS) 19(4), Article No. 18.
Michael J. R., Schucany W. R., Haas, R.W., 1976. Generating random variates using
transformations with multiple roots. American Statistician 30, 88C90.
R Development Core Team, 2009. R: A language and environment for statistical
computing. R Foundation for Statistical Computing, Vienna, Austria. ISBN 3-
900051-07-0, URL http://www.R-project.org.
Zhang, S., 2008. Simulation of non-Gaussian OU-based stochastic volatility models.
In: Ai, C.,Wu, D. (Eds.), Proceedings of International Symposium on Financial
Engineering and Risk Management 2008: 234-238.
Zhang, S., Zhang, X., 2008a. Exact simulation of IG-OU processes. Methodol.
Comput. Appl. Probab. 10(3), 337-355.
Zhang, S., Zhang, X., 2009. On the transition law of tempered stable Ornstein-
Uhlenbeck processes. J. Appl. Prob. 46, 721-731.
Zhang S., 2009. Exact simulation of tempered stable Ornstein-Uhlenbeck
processes. submitted.

Attachment: R_exact_simu_TSOU