Skip to main content

Main menu

  • Home
  • Current Issue
  • Past Issues
  • Videos
  • Submit an article
  • More
    • About JOD
    • Editorial Board
    • Published Ahead of Print (PAP)
  • IPR Logo
  • About Us
  • Journals
  • Publish
  • Advertise
  • Videos
  • Webinars
  • More
    • Awards
    • Article Licensing
    • Academic Use
  • Follow IIJ on LinkedIn
  • Follow IIJ on Twitter

User menu

  • Sample our Content
  • Request a Demo
  • Log in

Search

  • ADVANCED SEARCH: Discover more content by journal, author or time frame
The Journal of Derivatives
  • IPR Logo
  • About Us
  • Journals
  • Publish
  • Advertise
  • Videos
  • Webinars
  • More
    • Awards
    • Article Licensing
    • Academic Use
  • Sample our Content
  • Request a Demo
  • Log in
The Journal of Derivatives

The Journal of Derivatives

ADVANCED SEARCH: Discover more content by journal, author or time frame

  • Home
  • Current Issue
  • Past Issues
  • Videos
  • Submit an article
  • More
    • About JOD
    • Editorial Board
    • Published Ahead of Print (PAP)
  • Follow IIJ on LinkedIn
  • Follow IIJ on Twitter
Article

A Fully Coupled Solution Algorithm for Pricing Options with Complex Barrier Structures

Zili Zhu and Frank de Hoog
The Journal of Derivatives Fall 2010, 18 (1) 9-17; DOI: https://doi.org/10.3905/jod.2010.18.1.009
Zili Zhu
is the manager of the Exotic Options Reditus Project for the Algorithms and Models for Risk Analysis Group at the Commonwealth Scientific and Industrial Research Organization in Victoria, Australia.
  • Find this author on Google Scholar
  • Find this author on PubMed
  • Search for this author on this site
  • For correspondence: zili.zhu@csiro.au
Frank de Hoog
is the chief scientist in the Division of Mathematics, Informatics and Statistics at the Commonwealth Scientific and Industrial Research Organization in Acton, Australia.
  • Find this author on Google Scholar
  • Find this author on PubMed
  • Search for this author on this site
  • For correspondence: frank.dehoog@csiro.au
  • Article
  • Info & Metrics
  • PDF (Subscribers Only)
Loading

Click to login and read the full article.

Don’t have access? Click here to request a demo 

Alternatively, Call a member of the team to discuss membership options
US and Overseas: +1 646-931-9045
UK: 0207 139 1600

Abstract

The Black–Scholes option pricing equation was a major intellectual achievement, both for academics and for practitioners, but it rests upon a variety of restrictive conditions on the option’s payoff. More complicated structures are priced with numerical methods based on discretizing the state space in either a lattice framework or a discrete approximation to the fundamental partial differential equation (PDE). Both approaches use a fixed step size in the time dimension and converge asymptotically to the continuous-time solution as the step size goes to zero. But for many payoff structures, “asymptotically” entails an enormous number of calculations to achieve acceptable accuracy. Many techniques have been advanced over the years to speed up convergence for particular cases. The main problems with the standard numerical methods arise because of discontinuities in the option’s payoff structure, such as the abrupt change in value when a knock-out option hits its barrier, that interact with the discreteness of the state space approximation.

This article presents a powerful new approach that allows much greater flexibility in constructing the approximating lattice in time and price space, and therefore a potentially huge improvement in computational efficiency. The trick is to abandon the fixed time step and to treat the PDE as a fully coupled system that is solved simultaneously in both the price and time dimensions. As Zhu and de Hoog show, even with fixed time and price steps, this allows the approximation to retain much greater accuracy with larger step sizes than current methods. But the new approach allows the lattice to be structured much more flexibly so that more points can be placed in the regions that are critical for valuation, while leaving less dense coverage where it doesn’t matter. In illustrative examples, the same degree of accuracy is achieved more than 10 times faster with the fully coupled system than with a normal Crank–Nicolson approach.

  • © 2010 Pageant Media Ltd
View Full Text

Don’t have access? Click here to request a demo

Alternatively, Call a member of the team to discuss membership options

US and Overseas: +1 646-931-9045

UK: 0207 139 1600

Log in using your username and password

Forgot your user name or password?
PreviousNext
Back to top

Explore our content to discover more relevant research

  • By topic
  • Across journals
  • From the experts
  • Monthly highlights
  • Special collections

In this issue

The Journal of Derivatives: 18 (1)
The Journal of Derivatives
Vol. 18, Issue 1
Fall 2010
  • Table of Contents
  • Index by author
Print
Download PDF
Article Alerts
Sign In to Email Alerts with your Email Address
Email Article

Thank you for your interest in spreading the word on The Journal of Derivatives.

NOTE: We only request your email address so that the person you are recommending the page to knows that you wanted them to see it, and that it is not junk mail. We do not capture any email address.

Enter multiple addresses on separate lines or separate them with commas.
A Fully Coupled Solution Algorithm for Pricing Options with Complex Barrier Structures
(Your Name) has sent you a message from The Journal of Derivatives
(Your Name) thought you would like to see the The Journal of Derivatives web site.
CAPTCHA
This question is for testing whether or not you are a human visitor and to prevent automated spam submissions.
Citation Tools
A Fully Coupled Solution Algorithm for Pricing Options with Complex Barrier Structures
Zili Zhu, Frank de Hoog
The Journal of Derivatives Aug 2010, 18 (1) 9-17; DOI: 10.3905/jod.2010.18.1.009

Citation Manager Formats

  • BibTeX
  • Bookends
  • EasyBib
  • EndNote (tagged)
  • EndNote 8 (xml)
  • Medlars
  • Mendeley
  • Papers
  • RefWorks Tagged
  • Ref Manager
  • RIS
  • Zotero
Save To My Folders
Share
A Fully Coupled Solution Algorithm for Pricing Options with Complex Barrier Structures
Zili Zhu, Frank de Hoog
The Journal of Derivatives Aug 2010, 18 (1) 9-17; DOI: 10.3905/jod.2010.18.1.009
del.icio.us logo Digg logo Reddit logo Twitter logo CiteULike logo Facebook logo Google logo LinkedIn logo Mendeley logo
Tweet Widget Facebook Like LinkedIn logo

Jump to section

  • Article
    • Abstract
    • FULLY COUPLED SCHEME FOR OPTION PRICING
    • TEST CASES
    • CONCLUSION
    • REFERENCES
  • Info & Metrics
  • PDF (Subscribers Only)
  • PDF (Subscribers Only)

Similar Articles

Cited By...

  • Analytical Valuation of Exotic Double Barrier Options
  • Google Scholar

More in this TOC Section

  • Editor’s Letter
  • Editor’s Letter
  • Interviews with Researchers Who Started Their Career in Physics but Moved to Finance
Show more Article
LONDON
One London Wall, London, EC2Y 5EA
United Kingdom
+44 207 139 1600
 
NEW YORK
41 Madison Avenue, New York, NY 10010
USA
+1 646 931 9045
pm-research@pageantmedia.com
 

Stay Connected

  • Follow IIJ on LinkedIn
  • Follow IIJ on Twitter

MORE FROM PMR

  • Home
  • Awards
  • Investment Guides
  • Videos
  • About PMR

INFORMATION FOR

  • Academics
  • Agents
  • Authors
  • Content Usage Terms

GET INVOLVED

  • Advertise
  • Publish
  • Article Licensing
  • Contact Us
  • Subscribe Now
  • Log In
  • Update your profile
  • Give us your feedback

© 2021 Pageant Media Ltd | All Rights Reserved | ISSN: 1074-1240 | E-ISSN: 2168-8524

  • Site Map
  • Terms & Conditions
  • Privacy Policy
  • Cookies