Developing Bid-Ask Probabilities for High-Frequency Trading

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.