Topics in computational finance

Abstract

This paper presents, compares and evaluates the strengths and weaknesses of four Value at Risk (VaR) approaches for measuring risk, namely the delta normal, delta gamma, Monte Carlo simulation and historical simulation. The analysis was based on an option (non-linear) and on a stock (linear) portfolio, computing the four approaches to one and five days’ time horizon with 95% and 99% of confidence level. It was concluded that the Monte Carlo Simulation provides the most accurate risk measure and delivers consistent results for both portfolios. Although delta gamma provided an accurate VaR for the option portfolio, it also showed to be complex, demanding a higher level of calculation which can be costly and also complicated. On the other hand, the conclusions from the historical simulation for the two portfolios were overestimated because this one is based on historical data. Additionally, the delta normal method proved to be a weak model because it doesn’t present proper accuracy even for the stock portfolio. This is due to the fact that the delta normal method is based on normal distributions and, in practice, fat tails are more frequent than what the model predicts. Additionally, this paper proved the improvement that portfolio diversification can have in the VaR measures, being the Monte Carlo simulation the one that presents the highest efficiency in the VaR measures. Lastly, this work suggests an approach to improve the VaR measures when dealing with extreme values in the sample, that is Extreme Value Theory (EVT).