Market risk in volatile times: a comparison of methods for calculating Value at Risk

Sammanfattning: Three standard approaches of finding Value at Risk; age weighted historical simulation, volatility weighted historical simulation and t – distribution were compared with Value –at – Risk calculated using generalized extreme value theory during the period 2000 to 2010 to see which approach that would give the most accurate forecast of actual losses during the two volatile times within the time frame. One important aspect was also to see if the results would differ depending on the holding period and quantile used. The Value- at – Risk estimates were updated once per month for the three standard approaches and once per five month for the extreme value approach during the entire ten year period. Value – at- Risk during this period was calculated for two different confidence levels, 95% and 99% and two different holding periods, one and ten days. As previous research had shown that extreme value theory gave the most accurate forecasts for the period during the Global Financial Crises similar results were expected but, at the contrary, the approach to provide the most accurate forecasts of actual losses differed according to Kupiec test for every holding period and confidence level used. As the Basel II Accord states that the Value –at- Risk should be calculated for a holding period of ten days using a 99% confidence level the results from Kupiec test, which tested the model for each approach during a two year period from 2000- 2009, accepted all standard approaches for every two year period but with highest p values for volatility weighted approach during all but one of the two year periods. The only approach which the model was not accepted for all two year periods was generalized extreme value theory. As the purpose was to see if the two volatile periods during the chosen ten year time frame could be best estimated with the same approach regardless of the holding period or the confidence level used the conclusion that can be drawn from these result states that no such approach existed. The result depend on the window chosen for the historical simulation approaches, the accuracy of the estimated parameters to calculate the volatility in the volatility weighted historical simulation, the accuracy of the parameters estimated to calculate Value- at- Risk according to generalized extreme value theory and the assumptions made about the underlying profit/loss distribution. The generalized extreme value theory assumes a distribution based on the highest value in every block but when approaching the time of the Global Financial Crises that distribution seemed to change giving lower Value- at- Risk estimates than, for example, volatility weighted historical simulation which adapted to the new market conditions of higher volatility faster.