Pricing double barrier options by combinatorial approaches

Tian-Shyr Dai*, Yuh Dauh Lyuu

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Scopus citations

Abstract

Double barrier options are important path-dependent derivatives in the financial market. How to price them efficiently and accurately is thus important. Until now, no simple closed-form pricing formula for double barrier options is reported. Double barrier options can be priced on a lattice that divides a certain time interval (from option initial date to maturity date) into n equal-length time steps. The pricing results obtained by the lattice algorithm converge to the true option value as n ← ∞, and the results oscillate significantly especially when n is not large enough. To obtain an accurate pricing result without suffering from price oscillation, n is required to be a large number. Unfortunately, the lattice pricing algorithm runs in O(n2) time. This paper proposes a linear-time combinatorial algorithm that can generate the same pricing results as the lattice algorithm. Thus our algorithm can handle very large n's efficiently. This algorithm uses a novel technique based on the re ection principle and the inclusion-exclusion principle. Numerical experiments are given to verify the excellent performance of our algorithm.

Original languageEnglish
Title of host publicationSoft Computing as Transdisciplinary Science and Technology - Proceedings of the 4th IEEE International Workshop, WSTST 2005
Pages1131-1140
Number of pages10
EditionAISC
DOIs
StatePublished - 1 Dec 2005
Event4th IEEE International Workshop on Soft Computing as Transdisciplinary Science and Technology, WSTST 2005 - Muroran, Japan
Duration: 25 May 200527 May 2005

Publication series

NameAdvances in Soft Computing
NumberAISC
ISSN (Print)1615-3871
ISSN (Electronic)1860-0794

Conference

Conference4th IEEE International Workshop on Soft Computing as Transdisciplinary Science and Technology, WSTST 2005
CountryJapan
CityMuroran
Period25/05/0527/05/05

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