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

Physics and Derivatives: On Three Important Problems in Mathematical Finance

Alexander Lipton and Vadim Kaushansky
The Journal of Derivatives Special Issue 2020, jod.2020.1.098; DOI: https://doi.org/10.3905/jod.2020.1.098
Alexander Lipton
is chief technical officer at SilaMoney in Portland, OR, visiting professor and Dean’s Fellow in The Jerusalem School of Business Administration at The Hebrew University of Jerusalem, Israel, and a Fellow in Connection Science and Engineering at Massachusetts Institute of Technology in Cambridge MA
  • Find this author on Google Scholar
  • Find this author on PubMed
  • Search for this author on this site
Vadim Kaushansky
is an assistant adjunct professor in the Department of Mathematics at the University of California in Los Angeles, CA
  • Find this author on Google Scholar
  • Find this author on PubMed
  • Search for this author on this site
  • 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

In this article, we use recently developed extension of the classical heat potential method in order to solve three important but seemingly unrelated problems of financial engineering: (A) American put pricing; (B) default boundary determination for the structural default problem; and (C) evaluation of the hitting time probability distribution for the general time-dependent Ornstein–Uhlenbeck process. We show that all three problems boil down to analyzing behavior of a standard Wiener process in a semi-infinite domain with a quasi-square-root boundary.

TOPICS: Derivatives, options, credit default swaps

Key Findings

  • • We introduce a powerful extension of the classical method of heat potentials designed for solving initial boundary value problems for the heat equation with moving boundaries.

  • • We demonstrate the versatility of our method by solving several classical problems of financial engineering in a unified fashion.

  • • In particular, we find the boundary corresponding to the constant default intensity in the structural default model, thus solving in the affirmative a long outstanding problem.

  • © 2020 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?
Next
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: 29 (3)
The Journal of Derivatives
Vol. 29, Issue 3
Spring 2022
  • Table of Contents
  • Index by author
  • Complete Issue (PDF)
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.
Physics and Derivatives: On Three Important Problems in Mathematical Finance
(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
Physics and Derivatives: On Three Important Problems in Mathematical Finance
Alexander Lipton, Vadim Kaushansky
The Journal of Derivatives Feb 2020, jod.2020.1.098; DOI: 10.3905/jod.2020.1.098

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
Physics and Derivatives: On Three Important Problems in Mathematical Finance
Alexander Lipton, Vadim Kaushansky
The Journal of Derivatives Feb 2020, jod.2020.1.098; DOI: 10.3905/jod.2020.1.098
del.icio.us logo Digg logo Reddit logo Twitter logo Facebook logo Google logo LinkedIn logo Mendeley logo
Tweet Widget Facebook Like LinkedIn logo

Jump to section

  • Article
    • Abstract
    • The American Put Option
    • The Structural Default Problem
    • First Time Hitting of an Ornstein–Uhlenbeck Process
    • Article Structure
    • THE METHOD OF HEAT POTENTIALS
    • THE AMERICAN PUT OPTION
    • THE STRUCTURAL DEFAULT PROBLEM
    • FIRST HITTING TIME DENSITY FOR AN ORNSTEIN–UHLENBECK PROCESS
    • CONCLUSION
    • ADDITIONAL READING
    • ACKNOWLEDGMENT
    • APPENDIX A
    • ENDNOTES
    • REFERENCES
  • Info & Metrics
  • PDF (Subscribers Only)
  • PDF (Subscribers Only)

Similar Articles

Cited By...

  • Semi-Analytical Solutions for Barrier and American Options Written on a Time-Dependent Ornstein-Uhlenbeck Process
  • Google Scholar
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

© 2022 Pageant Media Ltd | All Rights Reserved | ISSN: 1074-1240 | E-ISSN: 2168-8524

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