SFB 303 Discussion Paper No. B - 422
Author:
Dudenhausen, Antje, Erik
Schloegl and Lutz Schloegl
Title: Robustness of Gaussian Hedges and the Hedging of Fixed Income Derivatives
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 that 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 that are available.
Keywords:
Interest rates, misspecification, Gaussian hedges, market models
JEL-Classification-Number:
E43 G12 G13
Creation-Date:
April 1999 ( revised version )
URL: ../1999/b/bonnsfb422.pdf
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