Advanced Search
MyIDEAS: Login

Using Chebyshev Polynomials to Approximate Partial Differential Equations

Contents:

Author Info

  • Guglielmo Caporale

    ()

  • Mario Cerrato

Abstract

This paper suggests a simple method based on a Chebyshev approximation at Chebyshev nodes to approximate partial differential equations. It consists in determining the value function by using a set of nodes and basis functions. We provide two examples: pricing a European option and determining the best policy for shutting down a machine. The suggested method is flexible, easy to programme and efficient. It is also applicable in other fields, providing efficient solutions to complex systems of partial differential equations.

(This abstract was borrowed from another version of this item.)

Download Info

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
File URL: http://hdl.handle.net/10.1007/s10614-009-9172-8
Download Restriction: Access to full text is restricted to subscribers.

As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.

Bibliographic Info

Article provided by Society for Computational Economics in its journal Computational Economics.

Volume (Year): 35 (2010)
Issue (Month): 3 (March)
Pages: 235-244

as in new window
Handle: RePEc:kap:compec:v:35:y:2010:i:3:p:235-244

Contact details of provider:
Web page: http://www.springerlink.com/link.asp?id=100248
More information through EDIRC

Related research

Keywords: European options; Chebyshev polynomial approximation; Chebyshev nodes; C63; G12;

Other versions of this item:

Find related papers by JEL classification:

References

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
as in new window
  1. Abadir, Karim M. & Rockinger, Michael, 2003. "Density Functionals, With An Option-Pricing Application," Econometric Theory, Cambridge University Press, vol. 19(05), pages 778-811, October.
  2. Kenneth L. Judd, 1998. "Numerical Methods in Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262100711, December.
  3. Dangl, Thomas & Wirl, Franz, 2004. "Investment under uncertainty: calculating the value function when the Bellman equation cannot be solved analytically," Journal of Economic Dynamics and Control, Elsevier, vol. 28(7), pages 1437-1460, April.
  4. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," University of California at Los Angeles, Anderson Graduate School of Management qt43n1k4jb, Anderson Graduate School of Management, UCLA.
  5. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-54, May-June.
  6. Avinash Dixit, 1992. "Investment and Hysteresis," Journal of Economic Perspectives, American Economic Association, vol. 6(1), pages 107-132, Winter.
  7. Elias Tzavalis & Shijun Wang, 2003. "Pricing American Options under Stochastic Volatility: A New Method Using Chebyshev Polynomials to Approximate the Early Exercise Boundary," Working Papers 488, Queen Mary, University of London, School of Economics and Finance.
Full references (including those not matched with items on IDEAS)

Citations

Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
as in new window

Cited by:
  1. Niko Jaakkola, 2013. "Green Technologies and the Protracted End to the Age of Oil: A strategic analysis," OxCarre Working Papers 099, Oxford Centre for the Analysis of Resource Rich Economies, University of Oxford.
  2. Alejandro MosiƱo, 2012. "Using Chebyshev Polynomials to Approximate Partial Differential Equations: A Reply," Computational Economics, Society for Computational Economics, vol. 39(1), pages 13-27, January.

Lists

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

Statistics

Access and download statistics

Corrections

When requesting a correction, please mention this item's handle: RePEc:kap:compec:v:35:y:2010:i:3:p:235-244. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Guenther Eichhorn) or (Christopher F. Baum).

If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

If references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.