Modelling Illiquid Stocks Using Quantum Stochastic Calculus

TL;DR

This paper introduces a novel approach to model illiquid stocks by extending the classical Black-Scholes framework with Quantum Stochastic Calculus, capturing liquidity breakdowns and their effects on asset price distributions.

Contribution

It applies Quantum Stochastic Calculus to incorporate liquidity issues into option pricing models, a new approach in financial mathematics.

Findings

Widening bid-ask spreads affect asset price distributions.

Quantum Stochastic Calculus effectively models liquidity breakdowns.

Extended model provides more realistic pricing under illiquidity.

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.