Apr 7

## Monte Carlo Methods for Beginners

Biao has writen several posts on Monte Carlo simulation method for option pricing and risk analysis, so what is indeed a Monte Carlo method? as this post is just a general introduction for beginners like me, please skip if you are familiar with it.

Monte Carlo methods or Monte Carlo Experiments, as they are commonly referred to as are a class of computational algorithms that use repeated random sampling to obtain the desired results. They find their use in simulating mathematical and physical systems. Since these rely heavily on repeated computation of pseudo-random or random or numbers therefore, they are better suited for calculation by a computer.

Systems having large number of coupled degrees of freedom like fluids, strongly coupled solids, cellular structures and disordered materials can be easily solved using these methods. These are also effective in solving complicated boundary conditions and multidimensional integral problems. Today, these methods are being widely used in oil as well as space explorations.

Monte Carlo is not a single method of problem solving. Instead, it is a class of approaches that helps in solving complicated problems. These approaches follow a defined pattern which includes defining the domain of possible inputs, generating input randomly from the domain, performing a deterministic computation and aggregating individual result to the final results. If you are familiar with the term “what if” scenario, then you should note that Monte Carlo methods are totally opposite of “what if” scenarios. These simulations or methods consider random sampling of the probability distribution functions as inputs to produce thousands of results.

Monet Carlo method was introduced in 1940’s by physicists working in Los Alamos National Laboratory. After its introduction many new methods came, but still Monte Carlo method is one of the most popular methods used for problem solving. The basis of this method is the probability theory, which also gave birth to a large number of methods. The popularity and use of Monte Carlo methods increased considerably after the introduction of computers in 1950’s. USAF and The Rand Corporation were among the major organizations which started use of these methods in their day to day operations.

For more technical posts, please search "Monte Carlo" in this blog. For instance, Variance reduction by antithetic variable.

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