Applications › Pricing, risk and forecasting under non-standard dynamics
Applications · Finance & econometrics
Pricing, risk and forecasting under non-standard dynamics
Quantum and quantum-inspired formalisms applied to option pricing, portfolio risk and macroeconomic forecasting — including markets whose dynamics carry memory.
The problem
Standard financial models assume that the future depends on the present and not on the path that got there. Real markets are not so obliging: volatility clusters, shocks persist, and correlations change under stress in ways a memoryless model does not capture.
Two lines of work follow from that. The first asks whether a quantum formalism describes price dynamics better than a classical stochastic one — the Black–Scholes equation, with variable parameters, turns out to map onto a generalised Schrödinger equation. The second applies fractional and fractal methods, where the order of a derivative is not an integer and the system explicitly remembers its own history.
Reformulation of pricing equations in quantum-mechanical terms; fractional-calculus models with explicit memory kernels; quantum and quantum-inspired optimisation for portfolio construction; and quantum-econometric methods for macroeconomic series. The econometrics and quantitative analysis group works alongside the algorithm and foundations pillars on this.
Monte Carlo, GARCH-family models and conventional stochastic calculus remain the working tools of the field and are very well understood. The claim here is not that they are obsolete; it is that certain memory-carrying and non-local behaviours are awkward for them and natural for a fractional or quantum formulation.
Published theory, with numerical validation. Several results appear in Q1 finance and information-processing journals. Not deployed in a production trading or risk system.
Derivative pricing under realistic dynamics; portfolio and risk optimisation; macroeconomic forecasting for policy and planning.
Historical series at sufficient resolution; a clearly specified objective and risk measure; and, for the optimisation side, access to annealing or hybrid solvers. Institutional validation against an existing benchmark model is essential before any operational use.
Evidence
- “Black–Scholes equation in quantitative finance with variable parameters: a path to a generalized Schrödinger equation.” Financial Innovation (2026). doi
- “Qualitative financial modelling in fractal dimensions.” Financial Innovation 11, 42 (2025). doi
- “Modeling stochastic Langevin dynamics in fractal dimensions.” Physica A 667, 130570 (2025). doi
Talk to us about this
The econometrics and quantitative analysis group works with institutions on applied forecasting problems as well as on the theory.
Last updated 14 September 2026.