Ph.D. Thesis Defense: Alireza Khodaei
Friday, August 1, 2025
10:30 AM
SEC C207 (Scott Engineering Center)
"Volatility Estimation Under Structural Market Changes Using GARCH Modeling and Quantum Computing"
Volatility forecasting plays a foundational role in financial analysis, with the Generalized Autoregressive Conditional Heteroscedastic (GARCH) model serving as a central tool for modeling time-varying market risk. While Maximum Likelihood Estimation (MLE) has traditionally been used to estimate GARCH parameters, the non-convex and often nondifferentiable nature of the GARCH likelihood surface presents serious limitations for classical optimization techniques. In this dissertation, I introduce a quantum-enhanced alternative to classical estimation by leveraging Quantum Annealing (QA) to perform Maximum Likelihood Estimation through a Quadratic Unconstrained Binary Optimization (QUBO) formulation. By encoding the low-altitude smooth likelihood landscape and stability constraints into the QUBO structure, the proposed quantum MLE (qMLE) framework enables robust global optimization in noisy, structurally volatile, and regime-shifting financial time series. The method is evaluated across diverse market conditions—including crisis, recovery, and speculative regimes—using historical S&P 500 stock data. Hypothesis testing confirms that the quantum estimator consistently diverges from classical forecasts in structurally meaningful ways in almost all markets. Backtesting against realized volatility further reveals that the quantum model outperforms classical GARCH in turbulent markets, while showing limitations in ultra-stable conditions. These results demonstrate the potential of quantum computing to reshape likelihood-based financial modeling by improving estimation stability, agile adaptability, and out-of-sample generalization in volatility forecasts.
Committee Chair:
Prof. Jerry Hudgins