On Asymptotic Behaviors of Exponential Hedging in the Basis-Risk Model

Abstract

In this article, we consider the exponential hedging and the mean-variance hedging in the basis-risk model. We construct hedging strategies for multiple units of claim and calculate hedging errors. We then observe how the hedge error risk increases when the investor raises trading volumes of the claim. Under our definition of the hedge error risk amount, the risk increases in a linear way, according to the claim volume for the mean-variance hedging. As to the exponential hedging, it does not, i.e., nonlinear increment. The hedging error for the exponential hedging, however, tends to have the same properties to the mean-variance hedging when either risk-averse parameter or claim volume goes to zero. We numerically demonstrate this fact. Our numerical demonstration with the results of the previous researches verifies that the indifference price converges to the mean-variance hedging cost when the claim volume goes to zero under the basis-risk model.