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Robustness of Gaussian Hedges and the Hedging of Fixed Income Derivatives

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Abstract

The effect of model and parameter misspecification on the effectiveness of Gaussian hedging strategies for derivative financial instrumens is analyzed, showing that Gaussian hedges in the "natural" hedging instruments are particularly robust. This is true for all models that imply Balck/Scholes - type formulas for option prices and hedging strategies. In this paper we focus on the hedging of fixed income derivatives and show how to apply these results both within the framework of Gaussian term structure models as well as the increasingly popular market models where the prices for caplets and swaptions are given by the corresponding Black formulas. By explicitly considering the behaviour of the hedging strategy under misspecification we also derive the El Karoui, Jeanblanc-Picque and Shreve (1995, 1998) and Avellaneda, Levy and Paras (1995) results that a superhedge is obtained in the Black/Scholes model if the misspecified volatility dominates the true volatility. Furthermore, we show that the robustness and superhedging result do not hold if the natural hedging instruments are unavailable. In this case, we study criteria for the optimal choice from the instruments that are available.

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  • Antje Dudenhausen & Erik Schlögl & Lutz 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.
    • Handle: RePEc:uts:rpaper:19
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    1. Chen An & Mahayni Antje B., 2008. "Endowment Assurance Products: Effectiveness of Risk-Minimizing Strategies under Model Risk," Asia-Pacific Journal of Risk and Insurance, De Gruyter, vol. 2(2), pages 1-29, March.
    2. Branger, Nicole & Mahayni, Antje, 2006. "Tractable hedging: An implementation of robust hedging strategies," Journal of Economic Dynamics and Control, Elsevier, vol. 30(11), pages 1937-1962, November.
    3. Tim Dun & Geoff Barton & Erik Schlögl, 2001. "Simulated Swaption Delta–Hedging In The Lognormal Forward Libor Model," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 4(04), pages 677-709.
    4. Antje B. Mahayni & Klaus Sandmann, 2008. "Return Guarantees with Delayed Payment," German Economic Review, Verein für Socialpolitik, vol. 9(2), pages 207-231, May.
    5. Rasmussen, Nicki Søndergaard, 2002. "Hedging with a Misspecified Model," Finance Working Papers 02-15, University of Aarhus, Aarhus School of Business, Department of Business Studies.
    6. Nicole Branger & Antje Mahayni, 2011. "Tractable hedging with additional hedge instruments," Review of Derivatives Research, Springer, vol. 14(1), pages 85-114, April.
    7. Antje Mahayni, 2003. "Effectiveness of Hedging Strategies under Model Misspecification and Trading Restrictions," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 6(05), pages 521-552.
    8. Balder, Sven & Brandl, Michael & Mahayni, Antje, 2009. "Effectiveness of CPPI strategies under discrete-time trading," Journal of Economic Dynamics and Control, Elsevier, vol. 33(1), pages 204-220, January.
    9. Simon Ellersgaard & Martin Jönsson & Rolf Poulsen, 2017. "The Fundamental Theorem of Derivative Trading - exposition, extensions and experiments," Quantitative Finance, Taylor & Francis Journals, vol. 17(4), pages 515-529, April.

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