Abstract
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.
Highlights
High-frequency trading (HFT) is a relatively new development in financial markets, it has become a primary force in market pricing
This paper shows how complex algorithms can be developed, with parameters optimized by using simulated annealing, to produce code that can be used in real time
A library is created, within a desired range of ’s that are “reasonably” close to the ideal, by doing multiple Adaptive Simulated Annealing (ASA) fits to return data. This defines a library of probabilities that can be used as described here, yielding a range of choices to be made during high-frequency trading (HFT), e.g., as required to take into account latencies of trades being posted
Summary
High-frequency trading (HFT) is a relatively new development in financial markets, it has become a primary force in market pricing. This paper shows how complex algorithms can be developed, with parameters optimized by using simulated annealing, to produce code that can be used in real time In this context, this paper applies a previously developed statistical mechanics of financial markets (SMFM) (Ingber, 1984; Ingber, 1990; Ingber, 1996a; Ingber, 1996b; Ingber, 2000; Ingber, 2010; Ingber, 2017a; Ingber et al, 2001; Ingber & Mondescu, 2001; Ingber & Mondescu, 2003; Ingber et al, 1991; Ingber & Wilson, 1999; Ingber & Wilson, 2000), here applied to developing joint bid-ask probabilities to high-frequency data, using two methods of fitting price data or returns data to (a) the distribution and (b) fitting the returns.
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