Regression methods in pricing American and Bermudan options using consumption processes
AbstractHere we develop methods for e±cient pricing multidimensional discrete-time American and Bermudan options by using regression based algorithms together with a new approach towards constructing upper bounds for the price of the option. Applying the sample space with payoffs at the optimal stopping times, we propose sequential estimates for continuation values, values of the consumption process, and stopping times on the sample paths. The approach admits constructing both low and upper bounds for the price by Monte Carlo simulations. The methods are illustrated by pricing Bermudan swaptions and snowballs in the Libor market 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 InfoPaper provided by Sonderforschungsbereich 649, Humboldt University, Berlin, Germany in its series SFB 649 Discussion Papers with number SFB649DP2006-051.
Length: 30 pages
Date of creation: Jul 2006
Date of revision:
American and Bermudan options; Low and Upper bounds; Monte Carlo simulations; Consumption process; Regression methods; Optimal stopping times;
Other versions of this item:
- Denis Belomestny & Grigori Milstein & Vladimir Spokoiny, 2009. "Regression methods in pricing American and Bermudan options using consumption processes," Quantitative Finance, Taylor and Francis Journals, vol. 9(3), pages 315-327.
- C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
- G12 - Financial Economics - - General Financial Markets - - - Asset Pricing
This paper has been announced in the following NEP Reports:
- NEP-ALL-2006-07-15 (All new papers)
- NEP-FIN-2006-07-15 (Finance)
- NEP-FMK-2006-07-15 (Financial Markets)
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.:
- Broadie, Mark & Glasserman, Paul, 1997. "Pricing American-style securities using simulation," Journal of Economic Dynamics and Control, Elsevier, vol. 21(8-9), pages 1323-1352, June.
- Vladislav Kargin, 2003.
"Lattice Option Pricing By Multidimensional Interpolation,"
0309003, EconWPA, revised 29 Oct 2004.
- Vladislav Kargin, 2005. "Lattice Option Pricing By Multidimensional Interpolation," Mathematical Finance, Wiley Blackwell, vol. 15(4), pages 635-647.
- Denis Belomestny & Grigori Milstein, 2006. "Adaptive Simulation Algorithms for Pricing American and Bermudian Options by Local Analysis of Financial Market," SFB 649 Discussion Papers SFB649DP2006-038, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
- Denis Belomestny & Grigori N. Milstein, 2006. "Monte Carlo Evaluation Of American Options Using Consumption Processes," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 9(04), pages 455-481.
- 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.
- Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," Review of Financial Studies, Society for Financial Studies, vol. 14(1), pages 113-47.
- Anastasia Kolodko & John Schoenmakers, 2006. "Iterative construction of the optimal Bermudan stopping time," Finance and Stochastics, Springer, vol. 10(1), pages 27-49, 01.
- Boyle, Phelim & Broadie, Mark & Glasserman, Paul, 1997. "Monte Carlo methods for security pricing," Journal of Economic Dynamics and Control, Elsevier, vol. 21(8-9), pages 1267-1321, June.
- Vlad Bally & Gilles Pagès & Jacques Printems, 2005. "A Quantization Tree Method For Pricing And Hedging Multidimensional American Options," Mathematical Finance, Wiley Blackwell, vol. 15(1), pages 119-168.
- L. C. G. Rogers, 2002. "Monte Carlo valuation of American options," Mathematical Finance, Wiley Blackwell, vol. 12(3), pages 271-286.
- John Schoenmakers, 2012. "A pure martingale dual for multiple stopping," Finance and Stochastics, Springer, vol. 16(2), pages 319-334, April.
- Denis Belomestny, 2011. "Pricing Bermudan options by nonparametric regression: optimal rates of convergence for lower estimates," Finance and Stochastics, Springer, vol. 15(4), pages 655-683, December.
- Denis Belomestny & G. Milstein & John Schoenmakers, 2010. "Sensitivities for Bermudan options by regression methods," Decisions in Economics and Finance, Springer, vol. 33(2), pages 117-138, November.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (RDC-Team).
If references are entirely missing, you can add them using this form.