An Examination of the Effects of Parameter Misspecification

It is well-known that Gaussian hedging strategies are robust in the sense that they always lead to a cost process of bounded variation and that a superhedge is possible if upper bounds on the volatility of the relevant processes are available, cf. El Karoui, Jeanblanc-Picque and Shreve (1998) and in particular for applications to fixed income derivatives Dudenhausen, Schlögl and Schlögl (1998). These results crucially depend on the choice of certain ``natural'' hedge instruments which are not always available in the market and fail to hold otherwise. In this paper, the problem of optimally selecting hedging instruments from a given set of traded assets, in particular of zero coupon bonds, is studied. Misspecified hedging strategies lead to a non-vanishing cost process, which in turn depends on the particular choice of instruments. The effect of this choice on the cost process is analyzed. Referring to bond markets, a thorough study of the implications of volatility mismatching is made and explicit results are stated for a broad range of volatility scenarios.