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

Huei-Wen Teng*, Cheng Der Fuh, Chun Chieh Chen

*Corresponding author for this work

Research output: Contribution to journalArticle

1 Scopus citations

Abstract

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.

Original languageEnglish
Pages (from-to)1259-1271
Number of pages13
JournalQuantitative Finance
Volume16
Issue number8
DOIs
StatePublished - 2 Aug 2016

Keywords

  • Basket default swaps
  • Caps
  • Conjugate measures
  • Exotic options
  • Exponential tilting
  • Gaussian copula
  • Importance sampling
  • Newton’s method

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