Practical estimation of Value at Risk and Expected Shortfall: Are complex methods really necessary?

Sammanfattning: This paper tests the parametric estimation method for Value at Risk and Expected Shortfall estimation together with the historical simulation method to find out if the historical simulation could yield accurate enough estimations in stormy and calm periods. Given that the parametric estimation proved superior, the thesis examines which volatility forecasting models, using which distribution assumptions, would yield the best estimations. To test this, six different GARCH, two different EWMA and two different historical simulation models were examined. Together, all tests were conducted on 10 of the worlds largest stock indices for their relevance in index investing, on two different periods of varying financial stability. The results showed that the EWMA, especially the Gaussian EWMA, consistently gave satisfying results in both the crisis and post crisis period, while the one year-HS also yielded acceptable results in the post crisis period. Other models yielded disappointing results compared to the simpler EWMA model. To answer the initial question: parametric estimation, with the EWMA model, is clearly superior to historical simulation in both stormy and calm periods, though historical simulation yielded acceptable results in calmer periods. Value at Risk and Expected Shortfall estimation should thus be conducted with parametric estimation using the Gaussian distribution EWMA model for all periods. Although, if simplicity is highly regarded by the estimating individual, historical simulation can be used in periods of high financial stability.