A Further Study of the Choice between Two Hedging Strategies - The Continuous Case
14 Pages Posted: 11 Apr 2016 Last revised: 30 Oct 2017
Date Written: October 29, 2017
In our previous work, the choice between two popular hedging strategies was studied under the assumption that the hedge position of the underlying portfolio follows a discrete-time Markov chain with boundary conditions. This paper aims to investigate the same problem for the continuous case. We first assume that the underlying hedge position follows an arbitrary continuous-time Markov process; we give the general formulas for long-run cost per unit time under two cost structures: (1) a fixed transaction cost (2) a non-fixed transaction cost. Then we consider the case where the underlying hedge position follows a Brownian motion with drift; we show that (i) re-balancing the hedge position to the initial position is always more cost-efficient than re-balancing it to the boundary for a fixed transaction cost; (ii) when the cost function satisfies certain conditions, re-balancing the hedge position to the initial position is more cost-efficient than re-balancing it to the boundary for a non-fixed transaction cost.
Keywords: Cost of hedging; continuous-time Markov process; first hitting time; Brownian motion with drift; fixed transaction cost; non-fixed transaction cost
JEL Classification: C02; G22
Suggested Citation: Suggested Citation