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Journal of Stochastic Analysis

Modelling Illiquid Stocks Using Quantum Stochastic Calculus

Will Hicks

Published Mar 15, 2023• 5 citations
Publisher

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.

DOI
10.31390/josa.4.1.05

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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.
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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.
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