Quantum Circuit Learning for Volatility Modeling: Multifractal Analysis of Realized Volatility Time Series

Battle Count: 81

The paper addresses volatility modeling, which is fundamental to quantitative trading for risk management, options pricing, and position sizing. However, the current work is primarily exploratory, focusing on whether a minimal quantum circuit can reproduce statistical properties of volatility rather than providing a practical forecasting tool. The anti-persistence finding (h(2)≈0.05-0.1 for IRV) is relevant for understanding volatility dynamics, but no trading strategy or forecasting performance is evaluated. The model's overestimation of kurtosis and lack of benchmarking limit immediate practical applicability.

The quantum circuit is extremely simple (single qubit, 3 parameters, 4 rotation gates + 1 variational gate), making it straightforward to implement using Qiskit. The MFDFA analysis is well-established with clear algorithmic steps. The COBYLA optimization is a standard derivative-free method. However, understanding the quantum circuit framework, angle encoding scheme, and multifractal analysis requires specialized knowledge. The overall pipeline is relatively simple compared to deep learning approaches.

The paper provides detailed mathematical formulations of the quantum circuit, encoding scheme, MFDFA procedure, and optimization algorithm. Data is available on GitHub. The use of Qiskit for numerical implementation is specified. However, the COBYLA optimization with random initialization may introduce some variability, and the paper notes convergence issues with certain initial values. The rolling window analysis parameters are clearly specified.