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.Model misspecification, duplication of bonds, volatility mismatch, optimal selection of hedging instruments

How to Avoid a Hedging Bias

In this paper, the effects of so-called model misspecification and the effects of dropping the assumption that continuous rebalancing is possible are examined. Strategies which are robust if applied continuously fail to be robust if applied in discrete time. Therefore, the hedging bias which originates from the effects of time-discretising strategies is analysed. It turns out that a systematic hedging bias can only be avoided if a discrete-time hedging model is used. It is shown how the robustness property for convex payoffs is recovered while at the same time the hedging bias is avoided.Model misspecification, hedging strategies, convex payoffs, superhedging, discrete-time trading

Effectiveness of Hedging Strategies under Model Misspecification and Trading Restrictions

We consider a standard two-player all-pay auction with private values, where the valuation for the object is private information to each bidder. The crucial feature is that one bidder is favored by the allocation rule in the sense that he need not bid as much as the other bidder to win the auction. Analogously, the other bidder is handicapped by the rule as overbidding the rival may not be enough to win the auction. Clearly, this has important implications on equilibrium behavior. We fully characterize the equilibrium strategies for this auction format and show that there exists a unique pure strategy Bayesian Nash Equilibrium.Incomplete markets, model misspecification, trading restrictions, hedging, super-hedging, martingale measure, duplication costs, discretisation costs

Robustness of Gaussian Hedges and the Hedging of Fixed Income Derivatives

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.Interest rates, misspecification, Gaussian hedges, market models