matmessМатематические заметки СВФУMathematical notes of NEFU2411-93262587-876XСеверо-Восточный федеральный университет имени М.К. Аммосова10.25587/SVFU.2021.37.62.008matmess-213Research ArticleМАТЕМАТИЧЕСКОЕ МОДЕЛИРОВАНИЕAPPROXIMATION AND COMPARISON OF THE EMPIRICAL LIQUIDITY COST FUNCTION FOR VARIOUS FUTURES CONTRACTSDyshaevM. M.

Mikhail M. Dyshaev,                     

Chelyabinsk State University, 129 Bratyev Kashirinikh Street, Chelyabinsk 454091, Russia 

mikhail.dyshaev@gmail.comIzerginD. B.

Dmitrii B. Izergin,

Chelyabinsk State University, 129 Bratyev Kashirinikh Street, Chelyabinsk 454091, Russia 

izergin@csu.ruFedorovV. E.

Vladimir E. Fedorov

Chelyabinsk State University, 129 Bratyev Kashirinikh Street, Chelyabinsk 454091, Russia

kar@csu.ruChelyabinsk State UniversityRussian Federation202102042026284101113Copyright © Dyshaev M.M., Izergin D.B., Fedorov V.E., 20262026Dyshaev M.M., Izergin D.B., Fedorov V.E.Dyshaev M.M., Izergin D.B., Fedorov V.E.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://matmess.elpub.ru/jour/article/view/213

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. 

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The authors declare that there are no conflicts of interest present.