Risk managing bermudan swaptions in the libor BGM model

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Risk managing bermudan swaptions in the libor BGM model

Author Info

Pietersz, R.
Pelsser, A.A.J. (Erasmus Econometric Institute)

Additional information is available for the following registered author(s):

Antoon A. J. Pelsser

Abstract

This article presents a novel approach for calculating swap vega per bucket in the Libor BGM model. We show that for some forms of the volatility an approach based on re-calibration may lead to a large uncertainty in estimated swap vega, as the instantaneous volatility structure may be distorted by re-calibration. This does not happen in the case of constant swap rate volatility. We then derive an alternative approach, not based on re-calibration, by comparison with the swap market model. The strength of the method is that it accurately estimates vegas for any volatility function and at a low number of simulation paths. The key to the method is that the perturbation in the Libor volatility is distributed in a clear, stable and well understood fashion, whereas in the re-calibration method the change in volatility is hidden and potentially unstable.

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Paper provided by Erasmus University Rotterdam, Econometric Institute in its series Econometric Institute Report with number EI 2003-33 Revision_Date: 2009-07-29.

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Date of creation: 07 Aug 2003
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Handle: RePEc:dgr:eureir:1765000904

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Paper
- Raoul Pietersz & Antoon Pelsser, 2005. "Risk Managing Bermudan Swaptions in the Libor BGM Model," Finance 0502004, EconWPA. [Downloadable!]

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.
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!]
Xiaoliang Zhao & Paul Glasserman, 2000. "Arbitrage-free discretization of lognormal forward Libor and swap rate models," Finance and Stochastics, Springer, vol. 4(1), pages 35-68. [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!]
Raoul Pietersz & Marcel Regenmortel, 2006. "Generic market models," Finance and Stochastics, Springer, vol. 10(4), pages 507-528, December. [Downloadable!] (restricted)

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