Details
Original language | English |
---|---|
Pages (from-to) | 495-509 |
Number of pages | 15 |
Journal | Operations Research |
Volume | 64 |
Issue number | 2 |
Publication status | Published - 2016 |
Externally published | Yes |
Abstract
We consider tempered stable Lévy subordinators and develop a bridge sampling method. An approximate conditional probability density function (PDF) given the terminal values is derived with stable index less than one, using the double saddlepoint approximation. We then propose an acceptance-rejection algorithm based on the existing gamma bridge and the inverse Gaussian bridge as proposal densities. Its performance is comparable to existing sequential sampling methods such as Devroye (2009) [Devroye L (2009) Random variate generation for exponentially and ploynomially tilted stable distributions. ACM Trans. Modeling Comput. Simulation 19(4):18:1-20.] and Hofert (2011) [Hofert M (2011) Sampling exponentially tilted stable distributions. ACM Trans. Modeling Comput. Simulation 22(1):3:1-11.] when generating a fixed number of observations. As applications, we consider option pricing problems in Lévy models. First, we demonstrate the effectiveness of bridge sampling when combined with adaptive sampling under finite-variance CGMY processes. Second, further efficiency gain is achieved in terms of variance reduction via stratified sampling.
Keywords
- Bridge sampling, Lévy process, Saddlepoint approximation, Tempered stable subordinator
ASJC Scopus subject areas
- Computer Science(all)
- Computer Science Applications
- Decision Sciences(all)
- Management Science and Operations Research
Cite this
- Standard
- Harvard
- Apa
- Vancouver
- BibTeX
- RIS
In: Operations Research, Vol. 64, No. 2, 2016, p. 495-509.
Research output: Contribution to journal › Article › Research
}
TY - JOUR
T1 - Simulation of Tempered Stable Lévy Bridges and Its Applications
AU - Kim, Sojung
AU - Kim, Kyoung-Kuk
N1 - Publisher Copyright: © 2016 INFORMS.
PY - 2016
Y1 - 2016
N2 - We consider tempered stable Lévy subordinators and develop a bridge sampling method. An approximate conditional probability density function (PDF) given the terminal values is derived with stable index less than one, using the double saddlepoint approximation. We then propose an acceptance-rejection algorithm based on the existing gamma bridge and the inverse Gaussian bridge as proposal densities. Its performance is comparable to existing sequential sampling methods such as Devroye (2009) [Devroye L (2009) Random variate generation for exponentially and ploynomially tilted stable distributions. ACM Trans. Modeling Comput. Simulation 19(4):18:1-20.] and Hofert (2011) [Hofert M (2011) Sampling exponentially tilted stable distributions. ACM Trans. Modeling Comput. Simulation 22(1):3:1-11.] when generating a fixed number of observations. As applications, we consider option pricing problems in Lévy models. First, we demonstrate the effectiveness of bridge sampling when combined with adaptive sampling under finite-variance CGMY processes. Second, further efficiency gain is achieved in terms of variance reduction via stratified sampling.
AB - We consider tempered stable Lévy subordinators and develop a bridge sampling method. An approximate conditional probability density function (PDF) given the terminal values is derived with stable index less than one, using the double saddlepoint approximation. We then propose an acceptance-rejection algorithm based on the existing gamma bridge and the inverse Gaussian bridge as proposal densities. Its performance is comparable to existing sequential sampling methods such as Devroye (2009) [Devroye L (2009) Random variate generation for exponentially and ploynomially tilted stable distributions. ACM Trans. Modeling Comput. Simulation 19(4):18:1-20.] and Hofert (2011) [Hofert M (2011) Sampling exponentially tilted stable distributions. ACM Trans. Modeling Comput. Simulation 22(1):3:1-11.] when generating a fixed number of observations. As applications, we consider option pricing problems in Lévy models. First, we demonstrate the effectiveness of bridge sampling when combined with adaptive sampling under finite-variance CGMY processes. Second, further efficiency gain is achieved in terms of variance reduction via stratified sampling.
KW - Bridge sampling
KW - Lévy process
KW - Saddlepoint approximation
KW - Tempered stable subordinator
UR - http://www.scopus.com/inward/record.url?scp=84964614575&partnerID=8YFLogxK
U2 - 10.1287/opre.2016.1477
DO - 10.1287/opre.2016.1477
M3 - Article
VL - 64
SP - 495
EP - 509
JO - Operations Research
JF - Operations Research
SN - 0030-364X
IS - 2
ER -