A Hybrid GARCH and LSTM Model for Forecasting Volatility and Investment Horizons

Abstract

Accurately forecasting financial volatility is a critical component of modern finance, underpinning tasks such as risk management, asset pricing, and portfolio optimization. However, the stochastic and dynamic nature of financial markets poses significant challenges for existing models. Econometric approaches like Generalized Autoregressive Conditional Heteroskedasticity (GARCH) models are effective at capturing short-term volatility clustering but are limited in addressing nonlinearities and long-term dependencies in financial time series. Machine learning models such as Long Short-Term Memory (LSTM) networks can model complex patterns and sequential dependencies but often lack the interpretability and theoretical grounding of traditional econometric methods.

This thesis develops a hybrid GARCH-LSTM model designed to improve the precision of volatility forecasts by combining the strengths of both methodologies. The hybrid model uses GARCH to estimate conditional volatilities and feeds these estimates, along with historical price data, into an LSTM network for further refinement. A central application of this hybrid approach lies in solving a practical investment problem: determining the maximum time horizon an investor can remain invested without exceeding a predefined loss tolerance, given a specific confidence level.

The time horizon is estimated by combining the hybrid model's volatility forecasts with Monte Carlo simulations, which generate potential price paths based on predicted volatilities. These simulations provide a probabilistic framework for quantifying the likelihood of maintaining an investment within acceptable loss thresholds.

By focusing on optimizing investment time horizons, this thesis contributes a model for integrating advanced forecasting techniques into practical financial decision-making. Additionally, the results aim to equip investors and risk managers with tools to make informed decisions in the face of uncertainty.