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Simulation of Tempered Stable Lévy Bridges and Its Applications

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  • Kyoung-Kuk Kim

    (Department of Industrial and Systems Engineering, Korea Advanced Institute of Science and Technology, Daejeon 34141, South Korea)

  • Sojung Kim

    (Department of Mathematical Sciences, Korea Advanced Institute of Science and Technology, Daejeon 34141, South Korea)

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.

Suggested Citation

  • Kyoung-Kuk Kim & Sojung Kim, 2016. "Simulation of Tempered Stable Lévy Bridges and Its Applications," Operations Research, INFORMS, vol. 64(2), pages 495-509, April.
    • Handle: RePEc:inm:oropre:v:64:y:2016:i:2:p:495-509
    DOI: 10.1287/opre.2016.1477
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    References listed on IDEAS

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    Cited by:

    1. Calzolari, Giorgio & Halbleib, Roxana, 2018. "Estimating stable latent factor models by indirect inference," Journal of Econometrics, Elsevier, vol. 205(1), pages 280-301.
    2. Chengwei Zhang & Zhiyuan Zhang, 2018. "Sequential sampling for CGMY processes via decomposition of their time changes," Naval Research Logistics (NRL), John Wiley & Sons, vol. 65(6-7), pages 522-534, September.
    3. Dassios, Angelos & Qu, Yan & Zhao, Hongbiao, 2018. "Exact simulation for a class of tempered stable," LSE Research Online Documents on Economics 86981, London School of Economics and Political Science, LSE Library.

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