Monte Carlo simulations are hypothetical simulations complying with the dependency structure of risk factors. The hypothetical simulation method consists of simulating the random values of risk factors and revalues accordingly the instruments from such multiple simulations. The methodology is identical to Monte Carlo simulations. Each simulation of the set of risk factor values is a hypothetical scenario. The methodology still relies on the variance-covariance matrix for conducting such simulations. The methodologies for simulating dependent variables are expanded in the dependencies chapters. When the linear approximation collapses, as for options, we need to revert to full valuation technique. The full revaluation method avoids the drawback of relying on the constant sensitivity assumption, as with historical simulations.

The main drawback of Monte Carlo simulation is that it is calculation intensive. This drawback is magnified when dealing with instruments for which no closed formula exists, such as look-back options valued with simulations. In such cases, revaluation of derivatives requires simulations within each hypothetical scenario, or "simulations within simulations," making the process overly complex.

Because of these complexities, several techniques help simplifying the process. Historical simulation with full revaluation is a first technique that reduces the calculations to historical data and avoids dealing explicitly with dependencies embedded in past data. It is discussed above. Another way to address the calculation intensive process is to minimize the number of simulations. There are variations around these common principles. The simplest ones include:

• grid simulations

• full Monte Carlo simulations.

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