Spectral binomial tree: New algorithms for pricing barrier options

Yoshifumi Muroi, Takashi Yamada

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

Abstract

This paper introduces new and significantly fast algorithms to evaluate the price of double barrier options using binomial trees. To compute the price of double barrier options accurately, trees with large numbers of steps must be used, which is time consuming. In order to overcome this weakness, we develop new computational algorithms based on the spectral expansion method. The original idea of this method is coming from the eigenexpansion approach in PDEs. We show that this method enables us to compute double barrier options within 0.07 s, even if we use binomial trees with one billion steps. Moreover, this algorithm is easy to implement. In addition, the prices obtained by the proposed approach are always the same as those obtained by conventional binomial trees and show a good approximation to those by earlier studies.

Original languageEnglish
Pages (from-to)107-119
Number of pages13
JournalJournal of Computational and Applied Mathematics
Volume249
DOIs
Publication statusPublished - 2013 Apr 2

Keywords

  • Spectral methods Tridiagonal matrix Eigenvalue problems Double barrier options Rebates

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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