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Linear-time accurate lattice algorithms for tail conditional expectation

Author

Listed:
  • Chen, Bryant

    (Department of Computer Science, University of California at Los Angeles)

  • Hsu, William W.Y.

    (Department of Computer Science and Engineering, National Taiwan Ocean University)

  • Ho, Jan-Ming

    (Research Center for Information Technology Innovation)

  • Kao, Ming-Yang

    (Department of Electrical Engineering & Computer Science, Northwestern University)

Abstract

This paper proposes novel lattice algorithms to compute tail conditional expectation of European calls and puts in linear time. We incorporate the technique of prefix-sum into tilting, trinomial, and extrapolation algorithms as well as some syntheses of these algorithms. Furthermore, we introduce fractional-step lattices to help reduce interpolation error in the extrapolation algorithms. We demonstrate the efficiency and accuracy of these algorithms with numerical results. A key finding is that combining the techniques of tilting lattice, extrapolation, and fractional steps substantially increases speed and accuracy.

Suggested Citation

  • Chen, Bryant & Hsu, William W.Y. & Ho, Jan-Ming & Kao, Ming-Yang, 2014. "Linear-time accurate lattice algorithms for tail conditional expectation," Algorithmic Finance, IOS Press, vol. 3(1-2), pages 87-140.
    • Handle: RePEc:ris:iosalg:0010
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    Citations

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    Cited by:

    1. Landsman, Zinoviy & Makov, Udi & Shushi, Tomer, 2016. "Multivariate tail conditional expectation for elliptical distributions," Insurance: Mathematics and Economics, Elsevier, vol. 70(C), pages 216-223.
    2. Landsman, Zinoviy & Makov, Udi & Shushi, Tomer, 2016. "Tail conditional moments for elliptical and log-elliptical distributions," Insurance: Mathematics and Economics, Elsevier, vol. 71(C), pages 179-188.

    More about this item

    Keywords

    Value-at-Risk; tail conditional expectation; lattice; prefix sum; extrapolation; fractional steps;
    All these keywords.

    JEL classification:

    • C00 - Mathematical and Quantitative Methods - - General - - - General
    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics

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