Linear-time accurate lattice algorithms for tail conditional expectation

Bryant Chen, William W.Y. Hsu*, Jan Ming Ho, Ming-Yang Kao

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)87-140
Number of pages54
JournalAlgorithmic Finance
Issue number1-2
StatePublished - 2014


  • Value-at-Risk
  • extrapolation
  • fractional steps
  • lattice
  • prefix sum
  • tail conditional expectation

ASJC Scopus subject areas

  • Finance
  • Computer Vision and Pattern Recognition
  • Computer Science Applications
  • Computational Mathematics


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