An analysis of a least squares regression method for American option pricing
AbstractRecently, various authors proposed Monte-Carlo methods for the computation of American option prices, based on least squares regression. The purpose of this paper is to analyze an algorithm due to Longstaff and Schwartz. This algorithm involves two types of approximation. Approximation one: replace the conditional expectations in the dynamic programming principle by projections on a finite set of functions. Approximation two: use Monte-Carlo simulations and least squares regression to compute the value function of approximation one. Under fairly general conditions, we prove the almost sure convergence of the complete algorithm. We also determine the rate of convergence of approximation two and prove that its normalized error is asymptotically Gaussian.
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 Finance and Stochastics.
Volume (Year): 6 (2002)
Issue (Month): 4 ()
Note: received: April 2001; final version received: January 2002
Contact details of provider:
Web page: http://www.springerlink.com/content/101164/
Find related papers by JEL classification:
- G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
- G12 - Financial Economics - - General Financial Markets - - - Asset Pricing
- G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
You can help add them by filling out this form.
CitEc Project, subscribe to its RSS feed for this item.
- Hisashi Nakamura & Wataru Nozawa & Akihiko Takahashi, 2009. "Macroeconomic Implications of Term Structures of Interest Rates Under Stochastic Differential Utility with Non-Unitary EIS," Asia-Pacific Financial Markets, Springer, vol. 16(3), pages 231-263, September.
- Tebaldi, Claudio, 2005. "Hedging using simulation: a least squares approach," Journal of Economic Dynamics and Control, Elsevier, vol. 29(8), pages 1287-1312, August.
- Bouchard, Bruno & Chassagneux, Jean-François, 2008. "Discrete-time approximation for continuously and discretely reflected BSDEs," Stochastic Processes and their Applications, Elsevier, vol. 118(12), pages 2269-2293, December.
- 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.
- Mario Cerrato & Abdollah Abbasyan, 2009.
"Optimal martingales and American option pricing,"
2009_27, Business School - Economics, University of Glasgow.
- Cerrato, Mario & Abbasyan, Abdollah, 2008. "Optimal Martingales and American Option Pricing," SIRE Discussion Papers 2008-36, Scottish Institute for Research in Economics (SIRE).
- Cerrato, Mario & Abbasyan, Abdollah, 2009. "Optimal Martingales and American Option Pricing," SIRE Discussion Papers 2009-38, Scottish Institute for Research in Economics (SIRE).
- Lajos Gergely Gyurko & Ben Hambly & Jan Hendrik Witte, 2011. "Monte Carlo methods via a dual approach for some discrete time stochastic control problems," Papers 1112.4351, arXiv.org.
- 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).
- Berridge, S.J. & Schumacher, J.M., 2002.
"An Irregular Grid Approach for Pricing High Dimensional American Options,"
2002-99, Tilburg University, Center for Economic Research.
- Berridge, S.J. & Schumacher, J.M., 2004. "An Irregular Grid Approach for Pricing High-Dimensional American Options," Discussion Paper 2004-18, Tilburg University, Center for Economic Research.
- 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.
- Christian Fries, 2005. "The Foresight Bias in Monte-Carlo Pricing of Options with Early," Finance 0511002, EconWPA, revised 08 Nov 2005.
- Ammann, Manuel & Kind, Axel & Wilde, Christian, 2008.
"Simulation-based pricing of convertible bonds,"
Journal of Empirical Finance,
Elsevier, vol. 15(2), pages 310-331, March.
- Detemple, Jérôme & Garcia, René & Rindisbacher, Marcel, 2005. "Intertemporal asset allocation: A comparison of methods," Journal of Banking & Finance, Elsevier, vol. 29(11), pages 2821-2848, November.
- Garcia, Diego, 2003. "Convergence and Biases of Monte Carlo estimates of American option prices using a parametric exercise rule," Journal of Economic Dynamics and Control, Elsevier, vol. 27(10), pages 1855-1879, August.
- Farid AitSahlia & Manisha Goswami & Suchandan Guha, 2010. "American option pricing under stochastic volatility: an efficient numerical approach," Computational Management Science, Springer, vol. 7(2), pages 171-187, April.
- Bally, Vlad & Pagès, Gilles, 2003. "Error analysis of the optimal quantization algorithm for obstacle problems," Stochastic Processes and their Applications, Elsevier, vol. 106(1), pages 1-40, July.
- Nordahl, Helge A., 2008. "Valuation of life insurance surrender and exchange options," Insurance: Mathematics and Economics, Elsevier, vol. 42(3), pages 909-919, June.
- Bouchard, Bruno & Touzi, Nizar, 2004. "Discrete-time approximation and Monte-Carlo simulation of backward stochastic differential equations," Stochastic Processes and their Applications, Elsevier, vol. 111(2), pages 175-206, June.
- Axel Kind, 2005. "Pricing American-Style Options By Simulation," Financial Markets and Portfolio Management, Springer, vol. 19(1), pages 109-116, June.
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 references are entirely missing, you can add them using this form.