Numerical method of pricing discretely monitored Barrier option

Yicheng Hong, Sung chul Lee, Tianguo Li

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

A Barrier option is an option whose payoff depends on the underlying asset prices during the life of the option. Most Barrier option pricing usually assumes the continuous monitoring of the barrier. However, Barrier options traded in markets are discretely monitored and in this discretely monitoring case there are no closed form solutions available. In this paper we use four different recombining quadrature methods, which are a kind of recombining multinomial tree, to price a discretely monitored Single Barrier option. We compare these recombining multinomial tree methods with the existing trapezoidal, Simpson and Milev-Tagliani (2010) methods. We find that all four recombining methods outperform the classical trapezoidal and Simpson methods, while Clenshaw-Curtis (CC), Gauss-Legendre-Lobatto (GLL) and Milev-Tagliani methods are comparable in convergence speed. More interestingly, among the four recombining methods, Fejér and Gauss-Legendre methods, which do not use the barrier as an end point, outperform Clenshaw-Curtis and Gauss-Legendre-Lobatto methods, which do use the barrier as an end point.

Original languageEnglish
Pages (from-to)149-161
Number of pages13
JournalJournal of Computational and Applied Mathematics
Volume278
DOIs
Publication statusPublished - 2015 Apr 15

Fingerprint

Barrier Options
Pricing
Numerical methods
Numerical Methods
Monitoring
Costs
Legendre
Gauss
End point
Quadrature Method
Option Pricing
Convergence Speed
Closed-form Solution

All Science Journal Classification (ASJC) codes

  • Computational Mathematics
  • Applied Mathematics

Cite this

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abstract = "A Barrier option is an option whose payoff depends on the underlying asset prices during the life of the option. Most Barrier option pricing usually assumes the continuous monitoring of the barrier. However, Barrier options traded in markets are discretely monitored and in this discretely monitoring case there are no closed form solutions available. In this paper we use four different recombining quadrature methods, which are a kind of recombining multinomial tree, to price a discretely monitored Single Barrier option. We compare these recombining multinomial tree methods with the existing trapezoidal, Simpson and Milev-Tagliani (2010) methods. We find that all four recombining methods outperform the classical trapezoidal and Simpson methods, while Clenshaw-Curtis (CC), Gauss-Legendre-Lobatto (GLL) and Milev-Tagliani methods are comparable in convergence speed. More interestingly, among the four recombining methods, Fej{\'e}r and Gauss-Legendre methods, which do not use the barrier as an end point, outperform Clenshaw-Curtis and Gauss-Legendre-Lobatto methods, which do use the barrier as an end point.",
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Numerical method of pricing discretely monitored Barrier option. / Hong, Yicheng; Lee, Sung chul; Li, Tianguo.

In: Journal of Computational and Applied Mathematics, Vol. 278, 15.04.2015, p. 149-161.

Research output: Contribution to journalArticle

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