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

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  • 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.

Suggested Citation

  • Will Hicks, 2024. "Modelling Uncertain Volatility Using Quantum Stochastic Calculus: Unitary vs Non-Unitary Time Evolution," Papers 2407.04520, arXiv.org.
    • Handle: RePEc:arx:papers:2407.04520
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    References listed on IDEAS

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    1. Will Hicks, 2023. "Modelling Illiquid Stocks Using Quantum Stochastic Calculus," Papers 2302.05243, arXiv.org.
    2. T. J. Lyons, 1995. "Uncertain volatility and the risk-free synthesis of derivatives," Applied Mathematical Finance, Taylor & Francis Journals, vol. 2(2), pages 117-133.
    3. Will Hicks, 2023. "Modelling Illiquid Stocks Using Quantum Stochastic Calculus: Asymptotic Methods," Papers 2302.05256, arXiv.org.
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