The accounting of illiquidity and transaction costs during the delta-hedging

The article is devoted to the study of optimal time interval for re-hedging in the presence of illiquidity and transaction costs. A nonlinear Black – Scholes type equations are obtained for the case when the function of illiquidity costs is linear and quadratic. To determine the transaction costs, a risk-adjusted pricing methodology (RAPM) model is used. In order to demonstrate its practical application, the optimal time interval for the delta hedging is considered using an example of an optional combination «long butterfly».