A Further Study of the Choice Between Two Hedging Strategies–the Continuous Case

Liang Hong ()
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Liang Hong: Robert Morris University

Methodology and Computing in Applied Probability, 2018, vol. 20, issue 4, 1189-1198

Abstract: 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; C02; G22 (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s11009-017-9604-1

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