Three essays on volatility and tail-risk

This thesis examines three interconnected topics: Option-implied Probability Density Functions (PDFs) during macroeconomic uncertainty, Extreme Value Theory (EVT) volatility-managed portfolios, and rough GARCH-type LSTM models for volatility forecasting. Using advanced econometric and machine learning methods, the study provides deeper insights into financial market dynamics. Chapter 2 investigates option-implied PDFs, which reveal investor expectations about future asset prices. Unlike traditional methods, PDFs provide a richer perspective by capturing a broader range of investor beliefs. The study employs non-parametric and parametric techniques to analyse the impact of macroeconomic uncertainty on these densities. It uses proxy Structural Vector Autoregressive (SVAR) models to study uncertainty shocks, while EVT tail shape parameters assess distribution tail decay. Findings highlight the link between anticipated uncertainty and its resolution, showing how uncertainty influences risk-taking behaviours. A Probit model indicates that low volatility periods often precede financial crises. Chapter 3 focuses on a volatility-managed portfolio strategy aimed at reducing tail risk and enhancing the Sharpe ratio. Built on the Fama-French Five-Factor Model, the strategy is compared with benchmarks like buy-and-hold and Moreira & Muir (2017) strategies. The chapter introduces EVT to better capture extreme loss risks by focusing on distribution tails, addressing limitations of Value at Risk (VaR). The analysis shows that EVT-based strategies effectively mitigate tail risk and improve returns, offering a novel volatility timing approach. Chapter 4 presents rough hybrid Long Short-Term Memory (LSTM) models, including rGARCH-LSTM, rEGARCH-LSTM, and rGE-LSTM, to improve volatility forecasting. These models combine financial time series roughness, LSTM predictive power, and GARCH-type model robustness. Tested on intraday SPX data, the hybrid models outperform conventional methods, enhancing volatility forecasts and risk management strategies. This thesis advances our understanding of volatility, tail risk, and uncertainty in financial markets, providing valuable insights for investors, policymakers, and financial institutions in risk management and investment decisions.