Essays on Portfolio Optimization, Volatility Modelling and Risk Measurement

This study comprises of three essays on the subject of financial risk management with applications in the fields of portfolio optimization, continuous and discrete time stochastic volatility (SV) modelling. We jointly consider two risk measures: Value-at-Risk (VaR) and conditional Value-at-Risk (CVaR) to measure the financial market risk. In order to model the distribution of financial asset returns which is characterized by skewness, heavy tails and leptokurtosis, we employ the Asymmetric Laplace distribution (ALD) in the first and third essay while constructing the risk model on the basis of the Heston stochastic volatility (SV) model in the second essay. Specifically, in the first essay, we provide a comprehensive empirical examination of the viability of the new proposed Mean-CVaR-Skewness optimization model under ALD by Zhao et al. (2015). In addition, we propose the Mean-VaR-Skewness model under ALD by employing VaR as risk measure. The closed-form solution of the two optimization models is shown to be consistent and is obtainable by using the Lagrange Multiplier approach. In the second essay, we construct the VaR and CVaR models for the financial dynamics that do not have a closed-form probability density function. The only input required in our approach is the knowledge of the characteristic function of the underlying asset. In the numerical analysis, we investigate the elements that could impact the VaR and CVaR approximations in the Heston model. The third essay contributes to the existing literature by extending the ALD (Kotz et al., 2001) to the return error term of a standard discrete time SV model. We give the closed-form VaR and CVaR formulas for oil supply and demand. As additional contribution, we propose a new scale mixture of uniform (SMU) representation for the AL density so that the model can be implemented efficiently within the Bayesian Markov Chain Monte Carlo framework.