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.
Highlights
In this article, we consider hedging problems for the European-type contingent claim taking into account the position of the claim on the basis-risk model
We show the linear increment of the hedge error risk for the mean-variance hedging strategy
The risk amount measured by R(k) for the mean-variance hedging strategy varies in a linear way with respect to the claim volume k, i.e., R(k) R(1)
Summary
We consider hedging problems for the European-type contingent claim taking into account the position of the claim on the basis-risk model We consider both exponential hedging and mean-variance hedging for multiple units of claim. Ilhan et al [4] summarized that the utility indifference price converges to the no arbitrage price with the minimal martingale measure when either risk-averse coefficient or claim volume goes to zero. This fact is shown in this article too. Mania and Schweizer [12] showed that the exponential hedging strategy with the utility indifference price converges to the strategy of the mean-variance hedging when the risk-averse coefficient goes to zero.
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