Hedging Errors Induced by Discrete Trading Under an Adaptive Trading Strategy

TL;DR

This paper analyzes how discrete rebalancing in hedging strategies affects errors, showing that errors converge at a specific rate and depend on a distributional limit as rebalancing thresholds decrease.

Contribution

It introduces a new analysis of hedging errors under adaptive rebalancing, revealing their convergence behavior and distributional properties as thresholds approach zero.

Findings

Expected squared hedging error converges at a specific rate.

Hedge ratio differences normalized by thresholds tend to a triangular distribution.

Results depend on a new theorem linking hedge ratio differences to a triangular distribution.

Abstract

Discrete time hedging in a complete diffusion market is considered. The hedge portfolio is rebalanced when the absolute difference between delta of the hedge portfolio and the derivative contract reaches a threshold level. The rate of convergence of the expected squared hedging error as the threshold level approaches zero is analyzed. The results hinge to a great extent on a theorem stating that the difference between the hedge ratios normalized by the threshold level tends to a triangular distribution as the threshold level tends to zero.