A Further Study of the Choice between Two Hedging Strategies - The Continuous Case

14 Pages Posted: 11 Apr 2016 Last revised: 30 Oct 2017

See all articles by Liang Hong

Liang Hong

The University of Texas at Dallas

Date Written: October 29, 2017

Abstract

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

Hong, Liang, A Further Study of the Choice between Two Hedging Strategies - The Continuous Case (October 29, 2017). Available at SSRN: https://ssrn.com/abstract=2761019 or http://dx.doi.org/10.2139/ssrn.2761019

Liang Hong (Contact Author)

The University of Texas at Dallas ( email )

2601 North Floyd Road
Richardson, TX 75083
United States

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