Decay Factor Optimisation in Time Weighted Simulation - Evaluating VAR Performance

We propose an optimisation approach to determine the optimal decay factor in time weighted (BRW) simulation. The backtesting of the BRW simulation involving different decay factors together with a broad range of competing VaR models has been performed on a sample of seven stock indexes and two commodities - gold and WTI oil. The obtained results show that the BRW simulation with optimised decay factor in regard to Lopez (1998) size-adjusted function is among the best performing VaR models, second only to the conditional extreme value approach (McNeil, Frey, 2000). The optimised decay factors are sufficiently stable over time, giving economic justification to the optimisation since they do not change for longer time periods. Unlike most of the tested VaR models, in a large majority of cases, the optimised BRW model passes the Basel 2 criteria but yields significantly lower VaR forecasts if compared to the extreme value approaches, resulting thus in lower idle capital i.e. lower costs