Linear-Time Accurate Lattice Algorithms for Tail Conditional Expectation

55 Pages Posted: 27 May 2014  

Bryant Chen

University of California, Los Angeles (UCLA)

William W.Y. Hsu

National Taiwan Ocean University (NTOU); Academia Sinica, Institute of Information Science

Jan-Ming Ho

Academia Sinica, Institute of Information Science

Ming-Yang Kao

Northwestern University - Department of Electrical Engineering and Computer Science

Date Written: May 26, 2014

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.

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Suggested Citation

Chen, Bryant and Hsu, William W.Y. and Ho, Jan-Ming and Kao, Ming-Yang, Linear-Time Accurate Lattice Algorithms for Tail Conditional Expectation (May 26, 2014). Algorithmic Finance 2014, 3:1-2, 87-140. Available at SSRN: https://ssrn.com/abstract=2441817

Bryant Chen

University of California, Los Angeles (UCLA) ( email )

405 Hilgard Avenue
Box 951361
Los Angeles, CA 90095
United States

William W.Y. Hsu (Contact Author)

National Taiwan Ocean University (NTOU) ( email )

2 Pei-Ning Road
Keelung, 20224
Taiwan

HOME PAGE: http://140.121.196.121/wwyhsu

Academia Sinica, Institute of Information Science ( email )

Nankang
Taipei, 11529
Taiwan

Jan-Ming Ho

Academia Sinica, Institute of Information Science ( email )

Nankang
Taipei, 11529
Taiwan

Ming-Yang Kao

Northwestern University - Department of Electrical Engineering and Computer Science ( email )

Evanston, IL
United States

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