Yet Another Note on the Leland's Option Hedging Strategy with Transaction Costs

20 Pages Posted: 7 Nov 2005 Last revised: 7 Jan 2016

Valeriy Zakamulin

University of Agder - School of Business and Law

Date Written: December 20, 2005

Abstract

In a market with transaction costs the option hedging is costly. The idea presented by Leland (1985) was to include the expected transaction costs in the cost of a replicating portfolio. The resulting Leland's pricing and hedging method is an adjusted Black-Scholes method where one uses a modified volatility in the Black-Scholes formulas for the option price and delta. The Leland's method has been criticized on different grounds. Despite the critique, the risk-return tradeoff of the Leland's strategy is often better than that of the Black-Scholes strategy even in the case when a hedger starts with the same initial value of a replicating portfolio. This implies that the Leland's modification of volatility does optimize somehow the Black-Scholes hedging strategy in the presence of transaction costs. In this paper we explain how the Leland's modified volatility works and show how the performance of the Leland's hedging strategy can be improved by finding the optimal modified volatility. It is not claimed that the Leland's hedging strategy is optimal. Rather, the optimization mechanism of the modified hedging volatility can be exploited to improve the risk-return tradeoffs of other well-known option hedging strategies in the presence of transaction costs.

Keywords: option hedging, transaction costs

JEL Classification: G11, G13

Suggested Citation

Zakamulin, Valeriy, Yet Another Note on the Leland's Option Hedging Strategy with Transaction Costs (December 20, 2005). Available at SSRN: https://ssrn.com/abstract=839106 or http://dx.doi.org/10.2139/ssrn.839106

Valeriy Zakamulin (Contact Author)

University of Agder - School of Business and Law ( email )

Service Box 422
Kristiansand, N-4604
Norway
+47 38141039 (Phone)

HOME PAGE: http://vzakamulin.weebly.com/

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