Volatility modeling of asset returns

Abstract

The research investigates financial market volatility modeling through an analysis of daily stock price data from Tallink Grupp together with OMX Baltic Index data spanning from 01 February 2007 until 10 October 2023. Financial econometric theory guides the analysis through the combination of Autoregressive Moving Average (ARMA) models with Generalized Autoregressive Conditional Heteroskedasticity (GARCH) frameworks to properly model heteroskedasticity. This research evaluates asymmetric GARCH extensions including TGARCH, EGARCH and other asymmetric variants to account for the leverage effect and examine how market shocks affect volatility differently based on their positive or negative nature. The ‘rugarch‘ package in R serves as a tool and provides a robust and flexible framework for specifying, fitting, and comparing various volatility models. The research further investigates heteroskedasticity and asymmetry characteristics in the volatility dynamics of Tallink Grupp stock prices and OMX Baltic Index data across three economic periods: the global financial crisis (2007–2010), the stable market phase (2011–2019), and the COVID-19 pandemic (2020–2023). The research provides both theoretical and practical value by advancing knowledge about risk-trade-off and the relationship between expected returns and associated risk. Advanced GARCH and asymmetric models which further support the performance of the models in capturing market shocks and volatility effects.