By Dempster M.A.H. (ed.)
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E. prices and rates). Uncertainty in value of market rates in the future Risk of fall in market value of portfolio. Simulate many scenarios of changes in market rates. Calculate resulting set of changes in portfolio market value. Change in portfolio market value. Simulated changes in market rates. g. USD/EUR USD/JPY USD/UKS SPOT WTI 1 ... ... ... 2 ... ... ... 3 ... ... ... 4 ... ... ... 5 ... ... ... ... ... ... N ... ... ... For a large firm: N, the number of simulated scenarios might be 5,000 or 10,000 for Monte Carlo simulation.
And so on. An unlimited set of parameters, representing higher order derivatives, could potentially be included. The minimum number of terms of a Taylor series expansion that are needed to achieve a speciﬁed degree of accuracy in the VAR calculation depends on the composition of the portfolio, the conﬁdence level at which VAR is to be measured and the relationship between the set of market factors used for simulation and the market factors on which the contract’s value depends. This latter point is not obvious and will be explained below.
An example of a one-dimensional grid for a linear and a nonlinear portfolio are illustrated in Figure 2. g. the changes in the value of the FX options portfolio which would result from a speciﬁed set of instantaneous, concurrent changes in the spot US$/Yen exchange rate and the US$/Yen implied volatility. In the limit of small incremental changes, the two-dimensional grid of factor sensitivities becomes a factor sensitivity surface. A Stress Test is a measurement of the change in the market value of a portfolio that would occur for a speciﬁed unusually large change in a set of market factors.