Assessing the Least Squares Monte-Carlo Approach to American Option Valuation
AbstractA detailed analysis of the Least Squares Monte-Carlo (LSM) approach to American option valuation suggested in Longstaff and Schwartz (2001) is performed. We compare the specification of the cross-sectional regressions with Laguerre polynomials used in Longstaff and Schwartz (2001) with alternative specifications and show that some of these have numerically better properties. Furthermore, each of these specifications leads to a trade-off between the time used to calculate a price and the precision of that price. Comparing the method-specific trade-offs reveals that a modified specification using ordinary monomials is preferred over the specification based on Laguerre polynomials. Next, we generalize the pricing problem by considering options on multiple assets and we show that the LSM method can be implemented easily for dimensions as high as ten or more. Furthermore, we show that the LSM method is computationally more efficient than existing numerical methods. In particular, when the number of assets is high, say five, Finite Difference methods are infeasible, and we show that our modified LSM method is superior to the Binomial Model.
Download InfoIf 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.
Bibliographic InfoArticle provided by Springer in its journal Review of Derivatives Research.
Volume (Year): 7 (2004)
Issue (Month): 2 (08)
Contact details of provider:
Web page: http://www.springerlink.com/link.asp?id=102989
You can help add them by filling out this form.
CitEc Project, subscribe to its RSS feed for this item.
- Berridge, S.J. & Schumacher, J.M., 2004.
"An Irregular Grid Approach for Pricing High-Dimensional American Options,"
2004-18, Tilburg University, Center for Economic Research.
- Berridge, S.J. & Schumacher, J.M., 2002. "An Irregular Grid Approach for Pricing High Dimensional American Options," Discussion Paper 2002-99, Tilburg University, Center for Economic Research.
- Mario Cerrato & Kan Kwok Cheung, 2007. "Valuing American Style Options by Least Squares Methods," Money Macro and Finance (MMF) Research Group Conference 2006 49, Money Macro and Finance Research Group.
- Boyer, M. Martin & Stentoft, Lars, 2013.
"If we can simulate it, we can insure it: An application to longevity risk management,"
Insurance: Mathematics and Economics,
Elsevier, vol. 52(1), pages 35-45.
- M. Martin Boyer & Lars Peter Stentoft, 2012. "If we can simulate it, we can insure it: An application to longevity risk management," CIRANO Working Papers 2012s-08, CIRANO.
- Carmona, Julio & León, Angel & Vaello-Sebastiá, Antoni, 2011.
"Does Stock Return Predictability Affect ESO Fair Value?,"
QM&ET Working Papers
11-2, Universidad de Alicante, Departamento de Métodos Cuantitativos y Teoría Económica, revised 16 Jan 2012.
- Carmona, Julio & León, Angel & Vaello-Sebastià, Antoni, 2012. "Does stock return predictability affect ESO fair value?," European Journal of Operational Research, Elsevier, vol. 223(1), pages 188-202.
- Jeroen V.K. Rombouts & Lars Stentoft & Francesco Violante, 2012.
"The Value of Multivariate Model Sophistication: An Application to pricing Dow Jones Industrial Average options,"
CREATES Research Papers
2012-04, School of Economics and Management, University of Aarhus.
- Rombouts, Jeroen & Stentoft, Lars & Violante, Franceso, 2014. "The value of multivariate model sophistication: An application to pricing Dow Jones Industrial Average options," International Journal of Forecasting, Elsevier, vol. 30(1), pages 78-98.
- Jeroen Rombouts & Lars Peter Stentoft & Francesco Violente, 2012. "The Value of Multivariate Model Sophistication: An Application to pricing Dow Jones Industrial Average Options," CIRANO Working Papers 2012s-05, CIRANO.
- ROMBOUTS, Jeroen V. K. & STENTOFT, Lars & VIOLANTE, Francesco, 2012. "The value of multivariate model sophistication: an application to pricing Dow Jones Industrial Average options," CORE Discussion Papers 2012003, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Mario Cerrato, 2008.
"Valuing American Derivatives by Least Squares Methods,"
2008_12, Business School - Economics, University of Glasgow, revised Sep 2008.
- Cerrato, Mario, 2008. "Valuing American Derivatives by Least Squares Methods," SIRE Discussion Papers 2008-44, Scottish Institute for Research in Economics (SIRE).
- Engesaeth, E.J.P., 2011. "Managerial compensation contracting," Open Access publications from Tilburg University urn:nbn:nl:ui:12-4807459, Tilburg University.
- Nelson Areal & Artur Rodrigues & Manuel Armada, 2008. "On improving the least squares Monte Carlo option valuation method," Review of Derivatives Research, Springer, vol. 11(1), pages 119-151, March.
- Alexander Boogert & Cyriel de Jong, 2007. "Gas Storage Valuation Using a Monte Carlo Method," Birkbeck Working Papers in Economics and Finance 0704, Birkbeck, Department of Economics, Mathematics & Statistics.
- Minqiang Li, 2010.
"A quasi-analytical interpolation method for pricing American options under general multi-dimensional diffusion processes,"
Review of Derivatives Research,
Springer, vol. 13(2), pages 177-217, July.
- Li, Minqiang, 2009. "A Quasi-analytical Interpolation Method for Pricing American Options under General Multi-dimensional Diffusion Processes," MPRA Paper 17348, University Library of Munich, Germany.
- Guglielmo Maria Caporale & Mario Cerrato, 2008. "Chebyshev polynomial approximation to approximate partial differential equations," Working Papers 2008_16, Business School - Economics, University of Glasgow.
- Katarzyna Toporek, 2012. "Simple is better. Empirical comparison of American option valuation methods," Ekonomia journal, Faculty of Economic Sciences, University of Warsaw, vol. 29.
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.