Discrete-time delta hedging and the Black-Scholes model with transaction costs

Author: Mastinšek, Miklavž

Source: Mathematical Methods of Operations Research, Volume 64, Number 2, October 2006 , pp. 227-236(10)

Publisher: Springer

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Abstract:

The paper deals with the problem of discrete-time delta hedging and discrete-time option valuation by the Black-Scholes model. Since in the Black-Scholes model the hedging is continuous, hedging errors appear when applied to discrete trading. The hedging error is considered and a discrete-time adjusted Black-Scholes-Merton equation is derived. By anticipating the time sensitivity of delta in many cases the discrete-time delta hedging can be improved and more accurate delta values dependent on the length of the rebalancing intervals can be obtained. As an application the discrete-time trading with transaction costs is considered. Explicit solution of the option valuation problem is given and a closed form delta value for a European call option with transaction costs is obtained.

Keywords: Delta hedging; Transaction costs

Document Type: Research article

DOI: http://dx.doi.org/10.1007/s00186-006-0086-0

Affiliations: 1: Email: mastinsek@uni-mb.si

Publication date: 2006-10-01