An engineer that specialized in trains confronts his investor, telling him that steam engines have three properties: speed, safety, and cheapness and that due to some fundamental laws of physics, steam engines can only be designed with two of the three properties. There is an old engineering joke involving steam engines.
In many cases the effect is too small to make a difference - but in some cases, found in financial engineering and other demanding applications, better results are obtained if independent random number sequences (streams) are used for each distribution in the model. Most Monte Carlo simulation tools generate a single sequence of random numbers, which introduces a subtle dependence between the samples for all distributions in one trial. Risk Solver offers multiple streams of random numbers. For low to moderate dimensional problems, Sobol numbers offer the "best of both worlds" - the speed of Standard Monte Carlo with the "coverage" of Latin Hypercube sampling. They are widely used by developers in quantitative finance. Sobol numbers - generated with a random shift for "Randomized Quasi Monte Carlo" - are an innovation in Risk Solver that's not found in other risk analysis products for Excel. Latin Hypercube sampling is a well-know method for reducing sample variance, enabling you to obtain more accurate simulation results with fewer Monte Carlo trials. Risk Solver can generate Monte Carlo samples from a wide range of probability distributions, using any of three methods: Standard Monte Carlo, Latin Hypercube, and Sobol numbers. Mersenne Twister generator of Matsumoto and Nishimura: period of 2 19937-1, but samples are not as 'equidistributed' as for the WELL1024 and CMRG generators.Well Equidistributed Long-period Linear (WELL1024) generator of Panneton, L'Ecuyer and Matsumoto: period of 2 1024 with very good statistical independence.Combined Multiple Recursive Generator (CMRG) of L'Ecuyer: period of 2 191, and excellent statistical independence of samples.Park-Miller 'Minimal' Generator with Bayes-Durham shuffle and safeguards: traditional random number generator with a period of 2 31-2.Risk Solver's Options dialog lets you choose among four high-quality random generators: Random numbers form the basis of Monte Carlo simulation.
Risk Solver gives you more choices for random number generation and more sampling methods than other risk analysis products for Excel. Powerful Random Number Generators & Sampling Methods