Modelling Illiquid Stocks Using Quantum Stochastic Calculus

Paper: arXiv 2302.05243

Authors: Will Hicks

Abstract

Quantum Stochastic Calculus can be used as a means by which randomness can be introduced to observables acting on a Hilbert space. In this article we show how the mechanisms of Quantum Stochastic Calculus can be used to extend the classical Black-Scholes framework by incorporating a breakdown in the liquidity of a traded asset. This is captured via the widening of the bid offer spread, and the impact on the nature of the resulting probability distribution is modelled in this work.

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 2.5/10
• Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper introduces an innovative theoretical framework applying Quantum Stochastic Calculus to model market illiquidity and widening bid-ask spreads. However, it relies heavily on dense abstract mathematics while lacking empirical validation, real-world data testing, or reproducible code.

Research Flowchart

  flowchart TD
    A[Research Goal: Model Illiquid Stocks via Quantum Stochastic Calculus] --> B[Inputs: Classical Black-Scholes Framework & Bid-Ask Spread Dynamics]
    B --> C[Methodology: Apply Quantum Stochastic Calculus to Hilbert Space Observables]
    C --> D[Computational Process: Model Market Liquidity Breakdown & Widening Spreads]
    D --> E[Key Outcome: Extended Option Pricing Framework for Illiquid Assets]
    E --> F[Key Outcome: Quantified Impact on Asset Probability Distributions]