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)
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.
Document Type: Research article
Publication date: 2006-10-01