Fast Accurate Algorithms for Tail Conditional Expectation

This paper proposes novel lattice algorithms to compute tail conditional expectation. To improve the naive approach, we develop tilting, trinomial, and extrapolation algorithms together with some syntheses of these algorithms. Furthermore, we introduce fractional‐step lattices to prevent interpolation error in the extrapolation algorithms. A key finding is that combining the techniques of tilting lattice, extrapolation and fractional steps substantially increases speed and accuracy. We demostrate the efficiency and accuracy of these algorithms with numerical results.