Expected liquidity cost under delta hedging process

Abstract

The expected liquidity cost when performing the delta hedging process of a European option is derived. It is represented by an integration formula that consists of European option prices and a certain function depending on the delta process. We define a unit liquidity cost and show that the liquidity cost is a multiplication of the unit liquidity cost, stock price, supply curve parameter, and the square of the number of options. With this formula, the expected liquidity cost before hedging can be calculated in much faster way than a Monte Carlo simulation.