On the Choice between Two Delta-Hedging Strategies

Abstract

This paper studies the choice between two popular hedging strategies by assuming that the hedge position (delta) follows a Markov chain with boundary conditions. We give the formula for long-run cost per unit time under two different cost structures: (I) a fixed transaction cost and (II) a non-fixed transaction cost. Then we consider the case where the hedge position follows a random walk; we show that (i) re-balancing delta to the initial position is always more cost-efficient than re-balancing it to the edge for a fixed transaction cost; (ii) under certain conditions, re-balancing delta to the initial position is less cost-efficient than re-balancing it to the edge for a non-fixed transaction cost. In addition, we quantify the magnitude of the efficiency in both cases.

Keywords: Cost of hedging, Re-balancing, Markov chain, Random walk, Fixed transaction cost, Non-fixed transaction cost.

JEL Classification: C02, G22.