Simulation of Tempered Stable Levy Bridges and Its Applications

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We consider tempered stable Levy 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 Levy 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.
Publisher
INFORMS
Issue Date
2016-03
Language
English
Article Type
Article
Keywords

SADDLEPOINT APPROXIMATIONS; DIFFUSION-PROCESSES; RANDOM-VARIABLES; MONTE-CARLO; SMALL-TIME; DISTRIBUTIONS; INFERENCE; VARIANCE; MODELS

Citation

OPERATIONS RESEARCH, v.64, no.2, pp.495 - 509

ISSN
0030-364X
DOI
10.1287/opre.2016.1477
URI
http://hdl.handle.net/10203/209231
Appears in Collection
IE-Journal Papers(저널논문)
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