On an automatic and optimal importance sampling approach with applications in finance

Calculating high-dimensional integrals efficiently is essential and challenging in many scientific disciplines, such as pricing financial derivatives. This paper proposes an exponentially tilted importance sampling based on the criterion of minimizing the variance of the importance sampling estimato...

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Bibliographic Details
Published in:Quantitative finance 2016-08, Vol.16 (8), p.1259-1271
Main Authors: Teng, Huei-Wen, Fuh, Cheng-Der, Chen, Chun-Chieh
Format: Article
Language:English
Subjects:
Basket default swaps
C150
Caps
Conjugate measures
Credit default swaps
Derivatives
Estimating techniques
Exotic options
Exponential tilting
Gaussian copula
Importance sampling
Integrals
Mathematical problems
Newton's method
Sampling techniques
Studies
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Summary:Calculating high-dimensional integrals efficiently is essential and challenging in many scientific disciplines, such as pricing financial derivatives. This paper proposes an exponentially tilted importance sampling based on the criterion of minimizing the variance of the importance sampling estimators, and its contribution is threefold: (1) A theoretical foundation to guarantee the existence, uniqueness, and characterization of the optimal tilting parameter is built. (2) The optimal tilting parameter can be searched via an automatic Newton's method. (3) Simplified yet competitive tilting formulas are further proposed to reduce heavy computational cost and numerical instability in high-dimensional cases. Numerical examples in pricing path-dependent derivatives and basket default swaps are provided.
ISSN:1469-7688
1469-7696
DOI:10.1080/14697688.2015.1136077