Robust volatility measures and multivariate models for volatilities and returns with financial applications / Tan Shay Kee

• Main Author: Tan , Shay Kee
• Format: Thesis
• Published: 2022
• Subjects: Q Science (General); QA Mathematics
• Online Access: http://studentsrepo.um.edu.my/14725/2/Tay_Shay_Kee.pdf; http://studentsrepo.um.edu.my/14725/1/Tan_Shay_Kee.pdf; http://studentsrepo.um.edu.my/14725/

Volatility of asset prices in the financial market is not directly observable. Various return-based models have been proposed to estimate the volatility using daily closing prices. With the availability of intraday information such as the opening, highest, lowest and closing prices, many volatility measures were proposed to estimate the volatility directly. This thesis aims to improve these volatility measures and further proposes advanced volatility models to model these measures. We first apply Garman-Klass (GK) range-based volatility measure to measure the volatilities of 102 active cryptocurrencies and models the persistence and leverage features of the GK volatility measures using asymmetric bilinear conditional autoregressive range (CARR) model. Focus on the top five cryptocurrencies, we relate these features to their time of development and transaction speed. Since the accuracy of the volatility measures may be distorted by the occurrence of extreme prices, our second contribution proposes two unbiased quantile-based volatility measures, namely quantile Parkinson (QPK) and quantile Rogers-Satchell (QRS) to measure daily volatilities and shows how they can robustify the Parkinson (PK) and Rogers-Satchell (RS) measures in the presence of intraday extreme prices. Scaling factors for different interquantile range levels are provided to ensure the unbiasedness of QPK and QRS measures and simulation studies are performed to confirm their efficiencies relative to intraday squared returns (open-to-close) and their respective range-based volatility measures in the presence of extreme prices. To smooth out the noises in these quantile-based measures, the CARR model is fitted with different mean functions and error distributions as the first stage. The second stage imputes the best fitted volatilities into the return models to capture the heteroskedasticity of returns. This two-stage model is called CARR-return model. Risk measures such as value-at-risk (VaR) at different levels based on the return models are evaluated and tested. Empirical examples are provided to demonstrate the applicability of the proposed measures and the two-stage models. Our third contribution extends the CARR-return models to a multivariate setting to forecast cross dependency of multiple asset returns for portfolio risk assessments. Extensive comparisons are carried to evaluate the modelling and forecasting performances with the multivariate CARR-return models and multivariate GARCH models. Different levels of VaR based on the return models are evaluated and tested to confirm the accuracy of the VaR forecasts.