Three essays on volatility forecasting, option pricing, and value at risk forecasting using neural network models

This thesis consists of three chapters, each addressing important topics in financial forecasting using a combination of traditional and modern approaches. The first chapter explores the application of a hybrid GARCH-LSTM model to forecast market volatility. By integrating traditional econometric models with long short-term memory (LSTM) networks, the study demonstrates the potential of combining machine learning with established methods to improve volatility forecasting accuracy. The second chapter introduces the Stochastic-Local-Jump Volatility Option Pricing Model (SLJV-OPM), which combines stochastic volatility (Heston model), jump diffusion (Merton model), and local volatility (Dupire model). This model formalizes their integration using the Expectation-Maximization (EM) algorithm, providing a systematic method for calibrating the contributions of each component. To the best of our knowledge, this is the first formal use of the EM algorithm to combine stochastic, jump, and local volatility models in option pricing. After presenting this novel method, machine learning models, specifically LSTM networks, are applied according to the proposed framework for enhancing option pricing models. Finally, the third chapter investigates the use of LSTM models for forecasting Value at Risk (VaR). This chapter highlights the effectiveness of the proposed methodology in estimating financial VaR. Together, these chapters contribute to the growing literature on financial forecasting and risk modeling, demonstrating the versatility of both traditional and machine learning-based methods.