Fast drift approximated pricing in the BGM model

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Fast drift approximated pricing in the BGM model

Author Info

Raoul Pietersz (Erasmus University Rotterdam)
Antoon Pelsser (Erasmus University Rotterdam)
Marcel van Regenmortel (ABN AMRO Bank)

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Abstract

This 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.

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Paper provided by EconWPA in its series Finance with number 0502005.

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Length: 37 pages
Date of creation: 11 Feb 2005
Date of revision:
Handle: RePEc:wpa:wuwpfi:0502005

Note: Type of Document - pdf; pages: 37
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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)

References listed on IDEAS
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.:

Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," Review of Financial Studies, Oxford University Press for 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. [Downloadable!] (restricted)
Farshid Jamshidian, 1997. "LIBOR and swap market models and measures (*)," Finance and Stochastics, Springer, vol. 1(4), pages 293-330. [Downloadable!] (restricted)
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. [Downloadable!] (restricted)
Other versions:
- 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. [Downloadable!]
Joanne Kennedy & Phil Hunt & Antoon Pelsser, 2000. "Markov-functional interest rate models," Finance and Stochastics, Springer, vol. 4(4), pages 391-408. [Downloadable!] (restricted)
Nicolas Merener & Paul Glasserman, 2003. "Numerical solution of jump-diffusion LIBOR market models," Finance and Stochastics, Springer, vol. 7(1), pages 1-27. [Downloadable!] (restricted)
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. [Downloadable!]
Marek Rutkowski & Marek Musiela, 1997. "Continuous-time term structure models: Forward measure approach (*)," Finance and Stochastics, Springer, vol. 1(4), pages 261-291. [Downloadable!] (restricted)

Full references

Cited by:
(explanations, 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.)

Raoul Pietersz & Marcel van Regenmortel, 2005. "Generic Market Models," Finance 0502009, EconWPA. [Downloadable!]
Other versions:
- Pietersz, R. & Regenmortel, M. van, 2005. "Generic Market Models," Research Paper ERS-2005-010-F&A Revision, 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. [Downloadable!]
Ronald Hochreiter & Georg Pflug, 2006. "Polynomial Algorithms for Pricing Path-Dependent Interest Rate Instruments," Computational Economics, Springer, vol. 28(3), pages 291-309, October. [Downloadable!] (restricted)
Joerg Kampen & Anastasia Kolodko & John Schoenmakers, 2008. "Monte Carlo Greeks for financial products via approximative transition densities," Quantitative Finance Papers 0807.1213, arXiv.org. [Downloadable!]

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