Mathematics

Accounting of transaction costs for delta-hedging of options

M. M. Dyshaev

Chelyabinsk State University, Chelyabinsk, Russia

Abstract: Some pricing models of options with modified volatility are considered. These models allow to take into account the presence of transaction costs during delta-hedging. Modified volatility formulas for each model are given. Usually, the value of transaction costs depends on the frequency and volume of hedging transactions. Using an example of risk adjusted pricing methodology (RAPM), a possible algorithm for obtaining the value of the optimal rebalancing interval is demonstrated. The numerical solution of the nonlinear equation with a modified volatility from the RAPM model is found. As a practical example, the dependence of the optimal delta-hedging interval on the price of the underlying asset and the time remaining until the exercise of the option is constructed. For the practical using of the optimal interval of the rebalancing some recommendations are made.

Keywords: Black — Scholes model, transaction costs, RAPM, delta hedging.

UDC: 517.957+336.76

Received: 29.09.2019
Revised: 25.10.2019

DOI: 10.24411/2500-0101-2019-14401

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