Error analysis of the optimal quantization algorithm for obstacle problems
Author
Abstract
Suggested Citation
Download full text from publisher
As the access to this document is restricted, you may want to search for a different version of it.
References listed on IDEAS
- Philip Protter & Emmanuelle Clément & Damien Lamberton, 2002. "An analysis of a least squares regression method for American option pricing," Finance and Stochastics, Springer, vol. 6(4), pages 449-471.
- Cox, John C. & Ross, Stephen A. & Rubinstein, Mark, 1979. "Option pricing: A simplified approach," Journal of Financial Economics, Elsevier, vol. 7(3), pages 229-263, September.
- BALLY Vlad & PAGÈS Gilles & PRINTEMS Jacques, 2001. "A stochastic quantization method for nonlinear problems," Monte Carlo Methods and Applications, De Gruyter, vol. 7(1-2), pages 21-34, December.
- N. El Karoui & S. Peng & M. C. Quenez, 1997. "Backward Stochastic Differential Equations in Finance," Mathematical Finance, Wiley Blackwell, vol. 7(1), pages 1-71, January.
- Pagès Gilles & Printems Jacques, 2003. "Optimal quadratic quantization for numerics: the Gaussian case," Monte Carlo Methods and Applications, De Gruyter, vol. 9(2), pages 135-165, April.
- 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.
Citations
Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
Cited by:
- Jean-Franc{c}ois Chassagneux & Mohan Yang, 2021. "Numerical approximation of singular Forward-Backward SDEs," Papers 2106.15496, arXiv.org.
- Fina, Alessandro & Gnoatto, Alessandro & Picarelli, Athena, 2024. "Quantization of stochastic volatility models: Numerical tests and an open source implementation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 225(C), pages 29-51.
- Olivier Aj Bardou & Sandrine Bouthemy & Gilles Pag`es, 2007. "Optimal quantization for the pricing of swing options," Papers 0705.2110, arXiv.org.
- Jin, Xing & Li, Xun & Tan, Hwee Huat & Wu, Zhenyu, 2013. "A computationally efficient state-space partitioning approach to pricing high-dimensional American options via dimension reduction," European Journal of Operational Research, Elsevier, vol. 231(2), pages 362-370.
- Sebastian Becker & Patrick Cheridito & Arnulf Jentzen & Timo Welti, 2019. "Solving high-dimensional optimal stopping problems using deep learning," Papers 1908.01602, arXiv.org, revised Aug 2021.
- Marie Bernhart & Huyên Pham & Peter Tankov & Xavier Warin, 2011.
"Swing Options Valuation:a BSDE with Constrained Jumps Approach,"
Working Papers
hal-00553356, HAL.
- Marie Bernhart & Huy^en Pham & Peter Tankov & Xavier Warin, 2011. "Swing Options Valuation: a BSDE with Constrained Jumps Approach," Papers 1101.0975, arXiv.org.
- Gobet, Emmanuel & Makhlouf, Azmi, 2010. "-time regularity of BSDEs with irregular terminal functions," Stochastic Processes and their Applications, Elsevier, vol. 120(7), pages 1105-1132, July.
- Gassiat, Paul & Kharroubi, Idris & Pham, Huyên, 2012. "Time discretization and quantization methods for optimal multiple switching problem," Stochastic Processes and their Applications, Elsevier, vol. 122(5), pages 2019-2052.
- Pagès, Gilles & Sagna, Abass, 2018. "Improved error bounds for quantization based numerical schemes for BSDE and nonlinear filtering," Stochastic Processes and their Applications, Elsevier, vol. 128(3), pages 847-883.
- Jean-Franc{c}ois Chassagneux & Junchao Chen & Noufel Frikha & Chao Zhou, 2021. "A learning scheme by sparse grids and Picard approximations for semilinear parabolic PDEs," Papers 2102.12051, arXiv.org.
- Céline Labart & Jérôme Lelong, 2011. "A Parallel Algorithm for solving BSDEs - Application to the pricing and hedging of American options," Working Papers hal-00567729, HAL.
- 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.
- Said Hamadène & Monique Jeanblanc, 2007. "On the Starting and Stopping Problem: Application in Reversible Investments," Mathematics of Operations Research, INFORMS, vol. 32(1), pages 182-192, February.
- Jean-Franc{c}ois Chassagneux & Junchao Chen & Noufel Frikha, 2022. "Deep Runge-Kutta schemes for BSDEs," Papers 2212.14372, arXiv.org.
- Bruno Bouchard & Jean-François Chassagneux & Géraldine Bouveret, 2016. "A backward dual representation for the quantile hedging of Bermudan options," Post-Print hal-01069270, HAL.
- J. Bonnans & Zhihao Cen & Thibault Christel, 2012. "Energy contracts management by stochastic programming techniques," Annals of Operations Research, Springer, vol. 200(1), pages 199-222, November.
- Labart Céline & Lelong Jérôme, 2013. "A parallel algorithm for solving BSDEs," Monte Carlo Methods and Applications, De Gruyter, vol. 19(1), pages 11-39, March.
- Crisan, D. & Manolarakis, K. & Touzi, N., 2010. "On the Monte Carlo simulation of BSDEs: An improvement on the Malliavin weights," Stochastic Processes and their Applications, Elsevier, vol. 120(7), pages 1133-1158, July.
Most related items
These are the items that most often cite the same works as this one and are cited by the same works as this one.- Chen Liu & Henry Schellhorn & Qidi Peng, 2019. "American Option Pricing With Regression: Convergence Analysis," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(08), pages 1-31, December.
- Zineb El Filali Ech-Chafiq & Pierre Henry-Labordere & Jérôme Lelong, 2021. "Pricing Bermudan options using regression trees/random forests," Working Papers hal-03436046, HAL.
- Doan, Viet_Dung & Gaikwad, Abhijeet & Bossy, Mireille & Baude, Françoise & Stokes-Rees, Ian, 2010. "Parallel pricing algorithms for multi-dimensional Bermudan/American options using Monte Carlo methods," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(3), pages 568-577.
- Zhongkai Liu & Tao Pang, 2016. "An efficient grid lattice algorithm for pricing American-style options," International Journal of Financial Markets and Derivatives, Inderscience Enterprises Ltd, vol. 5(1), pages 36-55.
- 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.
- 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.
- Mario Cerrato, 2008.
"Valuing American Derivatives by Least Squares Methods,"
Working Papers
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).
- Jeechul Woo & Chenru Liu & Jaehyuk Choi, 2024. "Leave‐one‐out least squares Monte Carlo algorithm for pricing Bermudan options," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 44(8), pages 1404-1428, August.
- 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.
- Katarzyna Toporek, 2012. "Simple is better. Empirical comparison of American option valuation methods," Ekonomia journal, Faculty of Economic Sciences, University of Warsaw, vol. 29.
- Francesco Rotondi, 2019. "American Options on High Dividend Securities: A Numerical Investigation," Risks, MDPI, vol. 7(2), pages 1-20, May.
- Nordahl, Helge A., 2008. "Valuation of life insurance surrender and exchange options," Insurance: Mathematics and Economics, Elsevier, vol. 42(3), pages 909-919, June.
- Weihan Li & Jin E. Zhang & Xinfeng Ruan & Pakorn Aschakulporn, 2024. "An empirical study on the early exercise premium of American options: Evidence from OEX and XEO options," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 44(7), pages 1117-1153, July.
- Pringles, Rolando & Olsina, Fernando & Penizzotto, Franco, 2020. "Valuation of defer and relocation options in photovoltaic generation investments by a stochastic simulation-based method," Renewable Energy, Elsevier, vol. 151(C), pages 846-864.
- Marta Biancardi & Giovanni Villani, 2017. "Robust Monte Carlo Method for R&D Real Options Valuation," Computational Economics, Springer;Society for Computational Economics, vol. 49(3), pages 481-498, March.
- Vladislav Kargin, 2005.
"Lattice Option Pricing By Multidimensional Interpolation,"
Mathematical Finance, Wiley Blackwell, vol. 15(4), pages 635-647, October.
- Vladislav Kargin, 2003. "Lattice Option Pricing By Multidimensional Interpolation," Finance 0309003, University Library of Munich, Germany, revised 29 Oct 2004.
- Axel Kind, 2005. "Pricing American-Style Options By Simulation," Financial Markets and Portfolio Management, Springer;Swiss Society for Financial Market Research, vol. 19(1), pages 109-116, June.
- Song-Ping Zhu & Xin-Jiang He, 2018. "A hybrid computational approach for option pricing," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 5(03), pages 1-16, September.
- Hatem Ben-Ameur & Michèle Breton & Pierre L'Ecuyer, 2002. "A Dynamic Programming Procedure for Pricing American-Style Asian Options," Management Science, INFORMS, vol. 48(5), pages 625-643, May.
- Roger J. A. Laeven & John G. M. Schoenmakers & Nikolaus F. F. Schweizer & Mitja Stadje, 2020. "Robust Multiple Stopping -- A Pathwise Duality Approach," Papers 2006.01802, arXiv.org, revised Sep 2021.
More about this item
Keywords
Numerical probability Optimal stopping Snell envelope Optimal quantization of random variables Reflected backward stochastic differential equation American option pricing;Statistics
Access and download statisticsCorrections
All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:spapps:v:106:y:2003:i:1:p:1-40. See general information about how to correct material in RePEc.
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 CitEc recognized a bibliographic reference but did not link an item in RePEc 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 RePEc Author Service profile, as there may be some citations waiting for confirmation.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description .
Please note that corrections may take a couple of weeks to filter through the various RePEc services.