Quantum theory of securities price formation in financial markets

摘要

We develop a theory of securities price formation and dynamics based onquantum approach and without presuming any similarities with quantum mechanics.Disorder introduced by trading environment leads to probability distribution ofreturns that is not a smooth curve, but a speckle-pattern fluctuating in bothprice coordinate and time. This means that any given return can at timesacquire a substantial probability of occurring while remaining low on averagein time. Still, due to local character of order interaction during priceformation the distribution width grows smoothly, has a minimum value at smalltime scale and a square root behavior at large time scale. Examples ofcalibration to market data, both intraday and daily, are provided.