Dynamic Coupling in Order Book: Quantum Framework

Quantum coupled-wave theory of price formation in financial markets: Price measurement, dynamics and ergodicity

“…Apart from imbalance 𝐼 being eliminated at fair value, coupling between levels is also eliminated since there is no reason for probability transfer. This indicates that 𝜅~𝐼 [16]. This…”

“…Apart from imbalance being eliminated at fair value, coupling between levels is also eliminated since there is no reason for probability transfer. This indicates that ~ [16]. This dependence is what ensures price stabilization by creating a point of stability with = 0.…”

“…In reality of course 𝐼 will fluctuate being symmetrically dispersed around 0 value with some probability distribution 𝑄(𝐼). That probability distribution tends to be narrower for more liquid securities and wider for less liquid ones [16].…”

“…The end result of the measurement depends on the SPECIFICS of how that measurement is performed! Following these considerations, quantum theory of price formation was proposed and developed by the author in [9][10][11][12][13][14][15][16][17], treating price formation as a quantum-chaotic process rather than classical-chaotic process. In this approach securities are governed by the stochastic price operator, whose spectrum defines the prices that the security can attain when it is transacted.…”

“…This quantity can span from 1, when orders are certain to execute at 𝑠 𝑎𝑠𝑘 to −1, when orders are certain to execute at 𝑠 𝑏𝑖𝑑 , and is equal to 0 when execution probabilities are equal. Execution imbalance should not be confused with order imbalance, introduced in [16]. Given that phase is random our interest in system's state is now limited to execution imbalance.…”