Up: 3:1-2

Linear-time accurate lattice algorithms for tail conditional expectation

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

Algorithmic Finance (2014), 3:1-2, 87-140
DOI: 10.3233/AF-140034

Published: Abstract, PDF.
Archived: SSRN.

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.

Enhanced Content

Download the code package. Also available here. This package includes the following algorithms:
  • Numerical Integration
  • Naive
  • Tilt
  • Tilt+Extrapolation
  • Trinomial
  • Extrapolation
  • Extrapolation+Fractional Steps
  • Extrapolation+Fractional Steps+Tilt
  • Global Extrapolation

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Stanford University

Herman Chernoff

Harvard University

David S. Johnson

AT&T Labs Research

Leonid Levin

Boston University

Myron Scholes

Stanford University

Michael Sipser

Massachusetts Institute of Technology

Richard Thaler

University of Chicago

Stephen Wolfram

Wolfram Research

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Peter Bossaerts

California Institute of Technology

Emanuel Derman

Columbia University

Ming-Yang Kao

Northwestern University

Pete Kyle

University of Maryland

David Leinweber

Lawrence Berkeley National Laboratory

Richard J. Lipton

Georgia Tech

Avi Silberschatz

Yale University

Robert Webb

University of Virginia

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Giovanni Barone-Adesi

University of Lugano

Bruce Lehmann

University of California, San Diego

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