Modelling Uncertain Volatility Using Quantum Stochastic Calculus: Unitary vs Non-Unitary Time Evolution

Paper: arXiv 2407.04520

Authors: Will Hicks

Abstract

In this article we look at stochastic processes with uncertain parameters, and consider different ways in which information is obtained when carrying out observations. For example we focus on the case of a the random evolution of a traded financial asset price with uncertain volatility. The quantum approach presented, allows us to encode different volatility levels in a state acting on a Hilbert space. We consider different means of defining projective measurements in order to track the evolution of a traded market price, and discuss the results of different Monte-Carlo simulations.

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 3.0/10
• Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents a sophisticated theoretical framework combining Quantum Stochastic Calculus with uncertain volatility modeling in finance. However, it relies heavily on analytical formulations and theoretical Monte-Carlo setups with no real-world market data backtesting or empirical validation.

Research Flowchart

  flowchart TD
    A[Research Goal: Model Asset Price with Uncertain Volatility via Quantum Calculus] --> B[Inputs: Financial Asset Price & Discrete Volatility Levels]
    B --> C[Methodology: Encode Volatility in Hilbert Space States]
    C --> D[Model Evolution: Compare Unitary vs Non-Unitary Dynamics]
    D --> E[Computation: Apply Projective Measurements & Monte-Carlo Simulations]
    E --> F[Outcomes: Framework for Tracking Prices under Different Observation/Information Regimes]