Simulation of Tempered Stable Lévy Bridges and Its Applications

Research output: Contribution to journalArticleResearch

Authors

  • Sojung Kim
  • Kyoung-Kuk Kim

External Research Organisations

  • Korea Advanced Institute of Science and Technology (KAIST)
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Details

Original languageEnglish
Pages (from-to)495-509
Number of pages15
JournalOperations Research
Volume64
Issue number2
Publication statusPublished - 2016
Externally publishedYes

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

Cite this

Simulation of Tempered Stable Lévy Bridges and Its Applications. / Kim, Sojung; Kim, Kyoung-Kuk.
In: Operations Research, Vol. 64, No. 2, 2016, p. 495-509.

Research output: Contribution to journalArticleResearch

Kim S, Kim KK. Simulation of Tempered Stable Lévy Bridges and Its Applications. Operations Research. 2016;64(2):495-509. doi: 10.1287/opre.2016.1477
Kim, Sojung ; Kim, Kyoung-Kuk. / Simulation of Tempered Stable Lévy Bridges and Its Applications. In: Operations Research. 2016 ; Vol. 64, No. 2. pp. 495-509.
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