instruments in interest-rate, currency and ... - Volksbank AG

Monte Carlo simulation/Variance/covariance approachIf this premise is not acceptable, then it is necessary to resort to the Monte Carlo simulation or the variance/covariance approach (with assumed distribution). The Monte Carlo Simulation does not require any historical dataand works on only a few premises. However, this method is mathematically more demanding.The variance/covariance approach on the other hand has a considerable advantage over the historical simulation.Instead of long series of data containing historical observations, only two parameters - the mean value and thevolatility are required for the value at risk calculation. A requirement for using this model is a normal distributionof value fluctuations or returns of a stock or portfolio (normal Gaussian distribution or bell curve). The normaldistribution assumption is one of the basic premises for theoretical models for portfolios.The following parameters are required for the variance/covariance approach:nnnThe underlying’s current valueIts volatilityA factor which indicates the quality of the generated result (= the confidence level)The volatility factorWhat volatility is used for the calculation? For the holding period of one day, it is not necessarily essential toknow the daily volatility. The volatility can be statistically scaled up or down to fit the desired holding period.ExampleThe EUR/JPY volatility for a period of 1 year is assumed as being 15.0%.What is the volatility for a single working day?xd = Number of days for which the volatility should be calculated1Y = the annual volatility= The year is calculated as having 250 working daysVol p.a. Holding period Vol xd Price Possible loss15% 1 year 15.00% 100 15.0015% 1 day 0.95% 100 0.9515% 5 days 2.12% 100 2.1215% 10 days 3.00% 100 3.0015% 20 days 4.24% 100 4.2415% 30 days 5.20% 100 5.2063