Portfolio Value-at-Risk and Expected-Shortfall with Efficient Simulation Approaches

In many fields, particularly in the financial sector, risk management and control constitute an essential component for effective financial management and regulation. Management of risks often necessitates a holistic understanding of the risks borne by the financial institution and the measurement and communication of the risks to senior management. Thus, developing a powerful tool to efficiently and accurately measure risk is fundamental to making key financial and regulatory decisions; the more refined the risk estimation, the more accurate the predictive results and the more effective decisions based on the risk estimates. Risk speculation measures such as Value-at-Risk (VaR) and Expected-Shortfall (ES) have been predominantly used in financial risk assessment. However, evidence suggests that several of the approaches used in their computation produce estimates that are statistically far off their true values, and the simulation methods used are either slow or have more computational requirements, leading to longer computing efforts and inaccurate results. This thesis reviews VaR and ES, their calculation methods, and considers existing efficient simulation methods for their estimation to achieve faster computing speeds and more accurate results. It conducts an empirical study contrasting an Importance Sampling (IS) method based on a Gaussian mixture Model (GMM) of return distribution with an Expectation–Maximization (EM) algorithm for calibrating the model parameters with Geometric Brownian Motion (GBM) Monte Carlo methods.