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

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  • Miklavž Mastinšek

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. Copyright Springer-Verlag 2006

Suggested Citation

  • Miklavž Mastinšek, 2006. "Discrete–time delta hedging and the Black–Scholes model with transaction costs," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 64(2), pages 227-236, October.
    • Handle: RePEc:spr:mathme:v:64:y:2006:i:2:p:227-236
    DOI: 10.1007/s00186-006-0086-0
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    References listed on IDEAS

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    Keywords

    Delta hedging; Transaction costs;

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