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

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  • Huei-Wen Teng
  • Cheng-Der Fuh
  • Chun-Chieh Chen

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.

Suggested Citation

  • Huei-Wen Teng & Cheng-Der Fuh & Chun-Chieh Chen, 2016. "On an automatic and optimal importance sampling approach with applications in finance," Quantitative Finance, Taylor & Francis Journals, vol. 16(8), pages 1259-1271, August.
    • Handle: RePEc:taf:quantf:v:16:y:2016:i:8:p:1259-1271
    DOI: 10.1080/14697688.2015.1136077
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    References listed on IDEAS

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    1. Cheng-Der Fuh, 2004. "Efficient importance sampling for events of moderate deviations with applications," Biometrika, Biometrika Trust, vol. 91(2), pages 471-490, June.
    2. Cheng-Der Fuh & Inchi Hu & Ya-Hui Hsu & Ren-Her Wang, 2011. "Efficient Simulation of Value at Risk with Heavy-Tailed Risk Factors," Operations Research, INFORMS, vol. 59(6), pages 1395-1406, December.
    3. Zhiyong Chen & Paul Glasserman, 2008. "Fast Pricing of Basket Default Swaps," Operations Research, INFORMS, vol. 56(2), pages 286-303, April.
    4. Boyle, Phelim & Broadie, Mark & Glasserman, Paul, 1997. "Monte Carlo methods for security pricing," Journal of Economic Dynamics and Control, Elsevier, vol. 21(8-9), pages 1267-1321, June.
    5. Mark Joshi & Dherminder Kainth, 2004. "Rapid and accurate development of prices and Greeks for nth to default credit swaps in the Li model," Quantitative Finance, Taylor & Francis Journals, vol. 4(3), pages 266-275.
    6. Paul Glasserman & Philip Heidelberger & Perwez Shahabuddin, 1999. "Asymptotically Optimal Importance Sampling and Stratification for Pricing Path‐Dependent Options," Mathematical Finance, Wiley Blackwell, vol. 9(2), pages 117-152, April.
    7. Jan Neddermeyer, 2011. "Non-parametric partial importance sampling for financial derivative pricing," Quantitative Finance, Taylor & Francis Journals, vol. 11(8), pages 1193-1206.
    8. Luca Capriotti, 2008. "Least-squares Importance Sampling for Monte Carlo security pricing," Quantitative Finance, Taylor & Francis Journals, vol. 8(5), pages 485-497.
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    Cited by:

    1. dos Reis, Gonçalo & Smith, Greig & Tankov, Peter, 2023. "Importance sampling for McKean-Vlasov SDEs," Applied Mathematics and Computation, Elsevier, vol. 453(C).
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    3. Çela, Eranda & Hafner, Stephan & Mestel, Roland & Pferschy, Ulrich, 2021. "Mean-variance portfolio optimization based on ordinal information," Journal of Banking & Finance, Elsevier, vol. 122(C).
    4. Huei-Wen Teng, 2023. "Importance Sampling for Calculating the Value-at-Risk and Expected Shortfall of the Quadratic Portfolio with t-Distributed Risk Factors," Computational Economics, Springer;Society for Computational Economics, vol. 62(3), pages 1125-1154, October.

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