Developing Bid-Ask Probabilities for High-Frequency Trading

Lester Ingber

Working Paper Article Version 3 This version is not peer-reviewed

Version 1 : Received: 9 March 2019 / Approved: 11 March 2019 / Online: 11 March 2019 (09:32:39 CET)
Version 2 : Received: 19 March 2019 / Approved: 20 March 2019 / Online: 20 March 2019 (15:12:59 CET)
Version 3 : Received: 17 April 2019 / Approved: 17 April 2019 / Online: 17 April 2019 (11:15:37 CEST)
Version 4 : Received: 7 May 2019 / Approved: 8 May 2019 / Online: 8 May 2019 (08:47:44 CEST)

Methods of path integrals are used to develop multi-factor probabilities of bid-ask variables for use in high-frequency trading (HFT). Adaptive Simulated Annealing (ASA) is used to fit the nonlinear forms so developed to a day of BitMEX tick data. Maxima algebraic code is used to develop the path integral codes into C codes, and sampling code is used for the fitting process. After these fits, the resultant C code is very fast and useful for forecasting upcoming ask, bid, midprice, etc., when narrow and wide windows of incoming data are used. A bonus is the availability of canonical momenta indicators (CMI) useful to forecast direction and strengths of these variables.

path integral; financial markets; high-frequency trading

Physical Sciences, Applied Physics

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Developing Bid-Ask Probabilities for High-Frequency Trading

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