Risk Managing Bermudan Swaptions in the Libor BGM Model
AbstractThis 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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Bibliographic InfoPaper provided by EconWPA in its series Finance with number 0502004.
Length: 22 pages
Date of creation: 11 Feb 2005
Date of revision:
Note: Type of Document - pdf; pages: 22
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central interest rate model; Libor BGM model; swaption vega; risk management; swap market model; Bermudan swaption;
Other versions of this item:
- Pietersz, R. & Pelsser, A.A.J., 2003. "Risk managing bermudan swaptions in the libor BGM model," Econometric Institute Report EI 2003-33, Erasmus University Rotterdam, Econometric Institute.
- 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-FIN-2005-04-16 (Finance)
- NEP-RMG-2005-04-16 (Risk Management)
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.:
- 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.
- 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.
- 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.
- 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.
- 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.
- Farshid Jamshidian, 1997. "LIBOR and swap market models and measures (*)," Finance and Stochastics, Springer, vol. 1(4), pages 293-330.
- Mark Joshi & Jochen Theis, 2002. "Bounding Bermudan swaptions in a swap-rate market model," Quantitative Finance, Taylor and Francis Journals, vol. 2(5), pages 370-377.
- Pietersz, R. & Regenmortel, M. van, 2005.
"Generic Market Models,"
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, 2005.
"A Comparison of Single Factor Markov-functional and Multi Factor Market Models,"
- 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.
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