Fast drift approximated pricing in the BGM model
AbstractThis paper shows that the forward rates process discretized by a single time step together with a separability assumption on the volatility function allows for representation by a low-dimensional Markov process. This in turn leads to e±cient pricing by for example finite differences. We then develop a discretization based on the Brownian bridge especially designed to have high accuracy for single time stepping. The scheme is proven to converge weakly with order 1. We compare the single time step method for pricing on a grid with multi step Monte Carlo simulation for a Bermudan swaption, reporting a computational speed increase of a factor 10, yet pricing sufficiently accurate.
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 EconWPA in its series Finance with number 0502005.
Length: 37 pages
Date of creation: 11 Feb 2005
Date of revision:
Note: Type of Document - pdf; pages: 37
Contact details of provider:
Web page: http://184.108.40.206
BGM model; predictor-corrector; Brownian bridge; Markov processes; separability; Feynman-Kac; Bermudan swaption;
Find related papers by JEL classification:
- G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
This paper has been announced in the following NEP Reports:
- NEP-ALL-2005-04-16 (All new papers)
- NEP-CMP-2005-04-16 (Computational Economics)
- NEP-FIN-2005-04-16 (Finance)
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.:
- Marek Rutkowski & Marek Musiela, 1997. "Continuous-time term structure models: Forward measure approach (*)," Finance and Stochastics, Springer, vol. 1(4), pages 261-291.
- Farshid Jamshidian, 1997. "LIBOR and swap market models and measures (*)," Finance and Stochastics, Springer, vol. 1(4), pages 293-330.
- Björk, Tomas & Landén, Camilla & Svensson, Lars, 2002. "Finite dimensional Markovian realizations for stochastic volatility forward rate models," Working Paper Series in Economics and Finance 498, Stockholm School of Economics, revised 06 May 2002.
- Nicolas Merener & Paul Glasserman, 2003. "Numerical solution of jump-diffusion LIBOR market models," Finance and Stochastics, Springer, vol. 7(1), pages 1-27.
- Miltersen, Kristian R & Sandmann, Klaus & Sondermann, Dieter, 1997.
" Closed Form Solutions for Term Structure Derivatives with Log-Normal Interest Rates,"
Journal of Finance,
American Finance Association, vol. 52(1), pages 409-30, March.
- Miltersen, K. & K. Sandmann & D. Sondermann, 1994. "Closed Form Solutions for Term Structure Derivatives with Log-Normal Interest Rates," Discussion Paper Serie B 308, University of Bonn, Germany.
- Joanne Kennedy & Phil Hunt & Antoon Pelsser, 2000. "Markov-functional interest rate models," Finance and Stochastics, Springer, vol. 4(4), pages 391-408.
- Peter Ritchken & L. Sankarasubramanian, 1995. "Volatility Structures Of Forward Rates And The Dynamics Of The Term Structure," Mathematical Finance, Wiley Blackwell, vol. 5(1), pages 55-72.
- 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.
- Heath, David & Jarrow, Robert & Morton, Andrew, 1992. "Bond Pricing and the Term Structure of Interest Rates: A New Methodology for Contingent Claims Valuation," Econometrica, Econometric Society, vol. 60(1), pages 77-105, January.
- Mark Broadie & Paul Glasserman, 1996. "Estimating Security Price Derivatives Using Simulation," Management Science, INFORMS, vol. 42(2), pages 269-285, February.
- 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.
- Raoul Pietersz & Marcel Regenmortel, 2006.
"Generic market models,"
Finance and Stochastics,
Springer, vol. 10(4), pages 507-528, December.
- Raoul Pietersz & Marcel van Regenmortel, 2005. "Generic Market Models," Finance 0502009, EconWPA.
- Pietersz, R. & Regenmortel, M. van, 2005. "Generic Market Models," Research Paper ERS-2005-010-F&A, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus Uni.
- Raoul Pietersz & Antoon Pelsser, 2010.
"A comparison of single factor Markov-functional and multi factor market models,"
Review of Derivatives Research,
Springer, vol. 13(3), pages 245-272, October.
- Pietersz, R. & Pelsser, A.A.J., 2005. "A Comparison of Single Factor Markov-Functional and Multi Factor Market Models," Research Paper ERS-2005-008-F&A, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus Uni.
- Raoul Pietersz & Antoon Pelsser, 2005. "A Comparison of Single Factor Markov-functional and Multi Factor Market Models," Finance 0502008, EconWPA.
- Ronald Hochreiter & Georg Pflug, 2006. "Polynomial Algorithms for Pricing Path-Dependent Interest Rate Instruments," Computational Economics, Society for Computational Economics, vol. 28(3), pages 291-309, October.
- Henrard, Marc, 2007. "CMS swaps in separable one-factor Gaussian LLM and HJM model," MPRA Paper 3228, University Library of Munich, Germany.
- Christian Fries & Joerg Kampen, 2010. "Global existence, regularity and a probabilistic scheme for a class of ultraparabolic Cauchy problems," Papers 1002.5031, arXiv.org, revised Oct 2012.
- Joerg Kampen & Anastasia Kolodko & John Schoenmakers, 2008. "Monte Carlo Greeks for financial products via approximative transition densities," Papers 0807.1213, arXiv.org.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (EconWPA).
If references are entirely missing, you can add them using this form.