2019/11/26 by Will Hicks, Hicks, Will
Economics, Econometrics and Finance · #FOS: Economics and business #Mathematical Finance (q-fin.MF) #q-fin.MF
paper · pdf · doi:10.48550/arxiv.1911.11475
arxiv created 2020/01/24 · arxiv updated 2020/01/27
In this article we model a financial derivative price as an observable on the market state function. We apply geometric techniques to integrating the Heisenberg Equation of Motion. We illustrate how the non-commutative nature of the model introduces quantum interference effects that can act as either a drag or a boost on the resulting return. The ultimate objective is to investigate the nature of quantum drift in the Accardi-Boukas quantum Black-Scholes framework which involves modelling the financial market as a quantum observable, and introduces randomness through the Hudson-Parthasarathy quantum stochastic calculus. In particular we aim to differentiate randomness that is introduced through external noise (quantum stochastic calculus) and randomness that is fundamental to a quantum system (Heisenberg Equation of Motion).