Robustness of Gaussian Hedges and the Hedging of Fixed Income Derivatives

April 1999

24 Pages Posted: 4 May 1999

See all articles by Antje Brigitte Mahayni

Antje Brigitte Mahayni

Mercator School of Management

Erik Schlögl

University of Technology Sydney (UTS), Quantitative Finance Research Centre; University of Cape Town (UCT) - The African Institute of Financial Markets and Risk Management; Faculty of Science, Department of Statistics, University of Johannesburg; Financial Research Network (FIRN)

Lutz Schlögl

University of Bonn - Institute of Statistics

Date Written: SFB B-422

Abstract

The effect of model and parameter misspecification on the effectiveness of Gaussian hedging strategies for derivative financial instruments is analyzed, showing that Gaussian hedges in the "natural" hedging instruments are particularly robust. This is true for all models the imply Black/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 result by El Karoui, Jeanblanc-Picque and Shreve 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 available.

JEL Classification: E43, G12, G13

Suggested Citation

Mahayni, Antje B. and Schloegl, Erik and Schlögl, Lutz, Robustness of Gaussian Hedges and the Hedging of Fixed Income Derivatives (SFB B-422). April 1999, Available at SSRN: https://ssrn.com/abstract=159668 or http://dx.doi.org/10.2139/ssrn.159668

Antje B. Mahayni

Mercator School of Management ( email )

Lotharstraße 65
Duisburg, Nordrhein-Westfalen 47057
Germany

Erik Schloegl

University of Technology Sydney (UTS), Quantitative Finance Research Centre ( email )

Ultimo
PO Box 123
Sydney, NSW 2007
Australia
+61 2 9514 2535 (Phone)

HOME PAGE: http://www.schlogl.com

University of Cape Town (UCT) - The African Institute of Financial Markets and Risk Management ( email )

Leslie Commerce Building
Rondebosch
Cape Town, Western Cape 7700
South Africa

Faculty of Science, Department of Statistics, University of Johannesburg ( email )

Auckland Park, 2006
South Africa

Financial Research Network (FIRN)

C/- University of Queensland Business School
St Lucia, 4071 Brisbane
Queensland
Australia

HOME PAGE: http://www.firn.org.au

Lutz Schlögl (Contact Author)

University of Bonn - Institute of Statistics ( email )

Adenauerallee 24-26, 53113 Bonn
Bonn, 53113
Germany
+49 228 739271 (Phone)
+49 228 735050 (Fax)

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