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

TL;DR

This paper explores modeling uncertain volatility in financial assets using quantum stochastic calculus, comparing unitary and non-unitary evolution, and analyzing measurement strategies through Monte Carlo simulations.

Contribution

It introduces a quantum framework for representing uncertain volatility and compares different measurement approaches in this context.

Findings

Quantum approach encodes multiple volatility levels in a Hilbert space state.

Different measurement strategies impact the tracking of market prices.

Monte Carlo simulations demonstrate the effectiveness of the quantum models.

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.