Approximation and comparison of the empirical liquidity cost function for various futures contracts

The article is dedicated to the study and comparison of the empirical liquidity cost function for various futures contract. The function is determined by the current state of the limit order book (LOB). Comparing the liquidity cost of futures contracts, we suggest the use of the initial margin instead of the number of lots or asset units. The form of the empirical liquidity cost function is obtained and a number of approximations for practical use are proposed. The approximations were achieved by quadratic, linear and power functions. The explanation of the difference in the distribution of the values of the liquidity cost function depending on the required initial margin is proposed. These results can be used for optimal execution of large orders, including portfolio hedging.