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Monte Carlo Acceleration A new procedure is presented to accelerate the convergence of Monte Carlo simulations using the Default Correlation model. It is found that the modifications have been implemented correctly, and that the modifications result in a substantial improvement in the convergence rate of the Monte Carlo simulation models. A particular benefit of the model is a dramatic improvement in the stability of delta computations, allowing more accurate and timely risk management of basket trades. The reason for the improvement in stability of the deltas is a change in the method of their calculation. The new method is found to be quite accurate for low and moderate correlations and is explained in detail in the next section. The new method generates small negative delta amounts in certain cases. Based on the numerical results, these negative deltas are not confined to situations of high correlation and/or large spread differences between credits. The negative deltas do seem, however, to be consistent with zero and to therefore be the result of a noise component introduced in certain cases by the acceleration algorithm. A typical Monte Carlo simulation algorithm assigns each simulation run, or path, an identical probability weight. If we allow, however, a different probability to be assigned to each simulation path, we allow more flexibility in the simulation and can thus shape the simulation in accordance with our needs. For example, we can choose the probabilities of each path in manner such that the simulation is guaranteed to reproduce the prices of “benchmark” securities, whose prices are known from market data. A simulation thus calibrated to benchmarks will then price off-market securities in a realistic manner. The technique of assigning probability weights has, at least theoretically, the additional benefits of accelerating the convergence of the simulation, as well as allowing the sensitivities of the simulated price with respect to the benchmark securities to be computed without needing to perform additional simulations.
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