ABSTRACT
The concept of volatility is extremely important in measuring investment risk, pricing and portfolio performance. The growing number of financial crises, political uncertainties, various policies and technological innovations increase the complexity of markets. For this reason, accurate forecasting of volatility is required. Over the last four decades, there have been significant advances in the field of volatility forecasting from statistical and econometric models through machine learning and deep learning models. However, despite many achievements in the field, the current scientific literature lacks the synthesis of results regarding the comparative analysis of volatility forecasting approaches and its implications for portfolio optimization.
The goal of the paper is to conduct systematic and comprehensive review of the development of volatility forecasting models and its impact on portfolio optimization process. This paper presents the systematic literature review of the development of traditional statistical methods, GARCH family models, stochastic volatility models, machine learning and deep learning models and hybrid volatility forecasting models. Special attention is paid to the capability of each of these models to account for the stylized facts of financial time series: volatility clustering, leverage effect, persistence, long memory, nonlinearity and regimes.
This paper also studies the influence of volatility forecasts on portfolio optimization using different portfolio optimization methods: mean-variance optimization, minimum variance portfolios, risk parity portfolios and dynamic asset allocation portfolios. It is shown that more accurate volatility forecasts help improve risk measurement, asset allocation effectiveness, diversification and risk-adjusted returns of portfolios. Nevertheless, there are several problems associated with interpretability of the model, robustness of volatility forecasts in stressful periods, macroeconomic uncertainty and evaluation of volatility forecasting model performance from the economic perspective.
Based on systematic literature review, this paper develops the conceptual framework showing relationships between volatility forecasting models, risk measurement and portfolio optimization. Also, the research gaps in this field are outlined and the future research agenda including explainable artificial intelligence in volatility forecasting, hybrid econometric-machine learning approaches, regime-dependent volatility forecasting models, alternative data and uncertainty-aware portfolio optimization models is suggested.

Keywords: Volatility Forecasting, Portfolio Optimization, GARCH Models, Machine Learning, Deep Learning, Hybrid Forecasting Models, Dynamic Asset Allocation.