Grid Simulations

Before generating a very large number of scenarios, it is tempting, for limiting the calculations, to restrict the approach to a small number of scenarios. The grid Monte Carlo approach uses an exact valuation for each grid point and uses a linear interpolation between points. Grid simulation consists of using a limited number of simulated values. The selected values should cover the maximum range of values of each parameter. The process is less calculation intensive than full Monte Carlo simulations because we limit the number of simulations and we use the interpolation technique between grid point simulations.

Full Monte Carlo Simulations

Under full Monte Carlo simulations, the process starts with modeling the stochastic processes of market parameters, doing the best to ensure that they capture recent worst-case situations. It is similar to historical simulations except that we look forward using simulated values rather than historical values. Modeling the inputs is a crucial issue. Inputs include volatilities and correlations whose measures raise issues with respect to their volatilities over time.

The next stage is the generation of random values of risk factors complying with this input structure. The last stage is portfolio revaluation for each set of values generated. Since the simulations capture all forward-looking information, as well as past information embedded in modeling inputs, we have the best of both worlds. The main drawback of the full-blown simulations is that it is calculation intensive. All instruments should be valued for all sets of markets parameter values and the number of runs has to be high enough to provide a sufficient accuracy for the portfolio value distribution.

By contrast, the correlation (delta-VaR) methodology uses the same variance-covariance matrix for all portfolios and the calculation requires only a product of matrices to obtain the portfolio volatility.