Approximation and comparison of the empirical liquidity cost function for various futures contracts
Аннотация
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.
Литература
[1] Kyle A. S., “Continuous auctions and insider trading,” Econometrica, 53, No. 6, 1315–1335 (1985).
[2] Korajczyk R. A. and Sadka R., “Pricing the commonality across alternative measures of liquidity,” J. Financ. Econ., 87, No. 1, 45–72 (2008).
[3] Black F., “Toward a fully automated stock exchange, Part I,” Financ. Analysts J., 27, No. 4, 28–35 (1971).
[4] Degryse H., De Jong F., Van Ravenswaaij M., and Wuyts G., “Aggressive orders and the resiliency of a limit order market,” Rev. Finance, 9, No. 2, 201–242 (2005).
[5] Foucault T., Kadan O., and Kandel E., “Limit order book as a market for liquidity,” Rev. Financ. Stud., 18, No. 4, 1171–1217 (2005).
[6] Large J., “Measuring the resiliency of an electronic limit order book,” J. Financ. Markets, 10, No. 1, 1–25 (2007).
[7] Olbrys J. and Mursztyn M., “Estimation of intraday stock market resiliency: short-time Fourier transform approach,” Phys. A: Stat. Mech. Appl., 535, 122413 (2019).
[8] Giot P. and Grammig J., “How large is liquidity risk in an automated auction market?” Empirical Econ., 30, No. 4, 867–887 (2006).
[9] Obizhaeva A. A. and Wang J., “Optimal trading strategy and supply/demand dynamics,” J. Financ. Markets, 16, No. 1, 1–32 (2013).
[10] Roch A. F. and Mete Soner H., “Resilient price impact of trading and the cost of illiquidity,” Int. J. Theor. Appl. Finance, 16, No. 06 (2013).
[11] Rogers L. C. G. and Singh S., “The cost of illiquidity and its effects on hedging,” Math. Finance, 20, No. 4, 597–615 (2010).
[12] Malo P. and Pennanen T., “Reduced form modeling of limit order markets,” Quant. Finance, 12, No. 7, 1025–1036 (2012).
[13] Margins Handbook, National Futures Association (1999). https://www.nfa.futures.org/members/member-resources/files/margins-handbook.pdf
[14] ICE Risk Model, Intercontinental Exchange (2018). https://www.theice.com/publicdocs/clear europe/ice risk model tool user guide.pdf
[15] Margin Methodology, Options Clearing Corporation (2021). https://www.theocc.com/Risk-Management/Margin-Methodology
[16] Initial Margin, Moscow Exchange (2020). https://www.moex.com/s1696
[17] Search by Contracts, Moscow Exchange (2020). https://www.moex.com/en/derivatives/contracts.aspx?p=act
[18] Market Data Subscription, Moscow Exchange (2021). https://www.moex.com/en/orders/historicaldata
[19] Sandås P., “Adverse selection and competitive market making: empirical evidence from a limit order market,” Rev. Financ. Stud., 14, No. 3, 705–734 (2001).
[20] Roşu I., “A dynamic model of the limit order book,” Rev. Financ. Stud., 22, No. 11, 4601–4641 (2009).
[21] Bouchaud J.-P., Farmer J. D., and Lillo F., “Chapter 2. How markets slowly digest changes in supply and demand,” in: Handbook of Financial Markets: Dynamics and Evolution (T. Hens and K. R. Schenk-Hopp´e, eds.), Handbooks in Finance, pp. 57–160, North-Holland (2009).
[22] Cont R., Stoikov S., and Talreja R., “A stochastic model for order book dynamics,” Oper. Res., 58, No. 3, 549–563 (2010).
[23] Kelly F. and Yudovina E., “A Markov model of a limit order book: thresholds, recurrence, and trading strategies,” Math. Oper. Res., 43, No. 1, 181–203 (2018).
[24] Parlour C. A., “Price dynamics in limit order markets,” Rev. Financ. Stud., 11, No. 4, 789–816 (1998).
[25] Korolev V. Y., Chertok A. V., Korchagin A. Y., and Zeifman A. I., “Modeling high-frequency order flow imbalance by functional limit theorems for two-sided risk processes,” Appl. Math. Comput., 253, 224–241 (2015).
[26] Gould M. D., Porter M. A., Williams S., McDonald M., Fenn D. J., and Howison S. D., “Limit order books,” Quant. Finance, 13, No. 11, 1709–1742 (2013).
[27] Lehoczky J. and Schervish M., “Overview and history of statistics for equity markets,” Annu. Rev. Stat. Appl., 5, 265–288 (2018).
[28] Dyshaev M. M., “On measuring the cost of liquidity in the limit order book,” Chelyab. Fiz. Mat. Zhurn., 5, No. 1, 96–104 (2020).
[29] Harris L. and Hasbrouck J., “Market vs. limit orders: the SuperDOT evidence on order submission strategy,” J. Financ. Quant. Anal., 31, No. 2, 213–231 (1996).
[30] Ranaldo A., “Order aggressiveness in limit order book markets,” J. Financ. Markets, 7, No. 1, 53–74 (2004).
[31] Escribano A. and Pascual R., “Asymmetries in bid and ask responses to innovations in the trading process,” Empirical Econ., 30, No. 4, 913–946 (2006).
[32] Dyshaev M. M., “Values, distributions and approximations of the empirical liquidity cost function for various futures contracts” (2021). https://zenodo.org/record/5522451
[33] Izergin D. B. and Dyshaev M. M., “The visualization of the dynamics of the empirical liquidity cost function (for the Brent futures contracts)” (2021). https://zenodo.org/record/4461771
Поступила в редакцию
10-05-2021
Как цитировать
Dyshaev, M., Izergin, D. и Fedorov, V. (2022) Approximation and comparison of the empirical liquidity cost function for various futures contracts, Математические заметки СВФУ, 28(4), сс. 101-113. doi: https://doi.org/10.25587/SVFU.2021.37.62.008.
Выпуск
Раздел
Математическое моделирование
Это произведение доступно по лицензии Creative Commons «Attribution» («Атрибуция») 4.0 Всемирная.