  In this paper, we establish a link between quantum stochastic processes, and
nonlocal diffusions. We demonstrate how the non-commutative Black-Scholes
equation of Accardi & Boukas (Luigi Accardi, Andreas Boukas, 'The Quantum
Black-Scholes Equation', Jun 2007, available at arXiv:0706.1300v1) can be
written in integral form. This enables the application of the Monte-Carlo
methods adapted to McKean stochastic differential equations (H. P. McKean, 'A
class of Markov processes associated with nonlinear parabolic equations', Proc.
Natl. Acad. Sci. U.S.A., 56(6):1907-1911, 1966) for the simulation of
solutions. We show how unitary transformations can be applied to classical
Black-Scholes systems to introduce novel quantum effects. These have a simple
economic interpretation as a market `fear factor', whereby recent market
turbulence causes an increase in volatility going forward, that is not linked
to either the local volatility function or an additional stochastic variable.
Lastly, we extend this system to 2 variables, and consider Quantum models for
bid-offer spread dynamics.
