Simulated Swaption Delta-Hedging in the Lognormal Forward Libor Model

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Simulated Swaption Delta-Hedging in the Lognormal Forward Libor Model

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Tim Dunn
Erik Schlögl () (School of Finance and Economics, University of Technology, Sydney)
Geoff Barton

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Erik Schlogl

Abstract

Alternative approaches to hedging swaptions are explored and tested by simulation. Hedging methods implied by the Balck swaption formula are compared with a lognormal forward LIBOR model approach encompassing all the relevant forward rates. The simulation is undertaken within the LIBOR model framework for a range of swaptions and volatility structures. Despite incompatibilities with the model assumptions, the Black method performs equally well as the LIBOR method, yielding very similar distributions for the hedging profit and loss - even at high rehedging frequencies. This result demonstrates the robustness of the Black hedging technique and implies that - being simpler and generally better understood by financial practitioners - it would be the preferred method in practice.

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Paper provided by Quantitative Finance Research Centre, University of Technology, Sydney in its series Research Paper Series with number 40.

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Date of creation: 01 Mar 2000
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Handle: RePEc:uts:rpaper:40

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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.:

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!]
A. Dudenhausen & Erik Schlögl & L. Schlögl, 1999. "Robustness of Gaussian Hedges and the Hedging of Fixed Income Derivatives," Research Paper Series 19, Quantitative Finance Research Centre, University of Technology, Sydney. [Downloadable!]
Other versions:
- Dudenhausen, Antje & Erik Schloegl & Lutz Schloegl, 1999. "Robustness of Gaussian Hedges and the Hedging of Fixed Income Derivatives," Discussion Paper Serie B 422, University of Bonn, Germany, revised Apr 1999. [Downloadable!]
Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-54, May-June. [Downloadable!] (restricted)
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)

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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.)

Antonis Papapantoleon & Maria Siopacha, 2009. "Strong Taylor approximation of Stochastic Differential Equations and application to the L\'evy LIBOR model," Quantitative Finance Papers 0906.5581, arXiv.org. [Downloadable!]
Erik Schlögl, 2002. "Extracting the Joint Volatility Structure of Foreign Exchange and Interest Rates from Option Prices," Research Paper Series 79, Quantitative Finance Research Centre, University of Technology, Sydney. [Downloadable!]

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