Available at: https://digitalcommons.calpoly.edu/theses/3077
Date of Award
6-2025
Degree Name
MS in Mathematics
Department/Program
Mathematics
College
College of Science and Mathematics
Advisor
Dana Paquin
Advisor Department
Mathematics
Advisor College
College of Science and Mathematics
Abstract
In finance, risk is often quantified by volatility, and computing accurate volatility forecasts — while vital to financial decision making — remains one of the most challenging tasks in financial modeling. This thesis, motivated in part by the Black-Scholes-Merton Model and its limitations, adopts a statistical approach to volatility forecasting. The two main models of interest are the Exponential Weighted Moving Average (EWMA) model and the GARCH(1,1) model. Specifically, this work expands upon a potential adaptive lambda algorithm for EWMA models first proposed by Bernard Bollen (2014), and this work also utilizes the Momentum of Predictability (MoP) to generate adaptive model choice strategies. Models were trained and simulated over daily historical data for eight different companies, and their out-of-sample forecasts were analyzed using the two most robust loss functions MSE and QLIKE (Patton 2011). After forecasting losses were calculated, the MCS Test proposed by Hansen et al. in 2011 was used to identify which models significantly out performed their peers. Results show that adaptive parameter choice and model choice strategies did not work well with the EWMA model, but were unanimously effective when applied to the GARCH(1,1) model.