Nonlocal Diffusions and The Quantum Black-Scholes Equation: Modelling the Market Fear Factor
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.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
PT Symmetry, Non-Gaussian Path Integrals, and the Quantum Black-Scholes Equation
The Accardi-Boukas quantum Black-Scholes framework, provides a means by which one can apply the Hudson-Parthasarathy quantum stochastic calculus to problems in finance. Solutions to these equations can be modelled using …
A Nonlocal Approach to The Quantum Kolmogorov Backward Equation and Links to Noncommutative Geometry
The Accardi-Boukas quantum Black-Scholes equation can be used as an alternative to the classical approach to finance, and has been found to have a number of useful benefits. The quantum Kolmogorov backward equations, and…
Relativistic Black-Scholes model
Black-Scholes equation, after a certain coordinate transformation, is equivalent to the heat equation. On the other hand the relativistic extension of the latter, the telegraphers equation, can be derived from the Euclid…
modelClosed Quantum Black-Scholes: Quantum Drift and the Heisenberg Equation of Motion
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 n…
Calibration and simulation of arbitrage effects in a non-equilibrium quantum Black-Scholes model by using semiclassical methods
An interacting Black-Scholes model for option pricing, where the usual constant interest rate r is replaced by a stochastic time dependent rate r(t) of the form r(t)=r+f(t) dW/dt, accounting for market imperfections and …