# MONTE CARLO METHOD

Monte Carlo methods—named after the famous European gambling casino—are a means of numerically simulating chance events in order to predict the most likely future outcome. In other words, Monte Carlo simulations are used to predict a range of different outcomes from a given set of decisions. The decisions are held constant, but the outcomes are allowed to vary depending on changes in some key influence, such as sales volume, interest rates, market volatility, and so forth. Monte Carlo simulations are distinguished from other types of simulation techniques by their extensive use of random numbers and repeated trials. The predictive value of Monte Carlo simulations lends itself to a diverse field of business applications, ranging from risk management to financial planning to economic modeling.

Monte Carlo simulations can be used in decision making to provide potential solutions to complex problems. As intimated above, the simulations effectively provide an understanding of the possible outcome come of a given decision. They are useful when the environment surrounding a problem is too complex for the effects of a decision or set of decisions to be described with a single outcome. Indeed, Monte Carlo simulations can provide a range of potential results based on the same decision(s). As shown in the example below, the simulations typically involve (1) a decision variable that is chosen and changed by the person running the simulation; (2) a randomly changing variable; and (3) a key performance indicator that is influenced by the decision variable and the random variable.

As a simple example, assume that the owner of a rolling hot dog stand earns an average of \$75 in profit per day. He sells hot dogs for \$3 each, and expects daily sales to vary between 100 and 200 hot dogs. All hot dogs that do not sell spoil and are a total loss, and he puts 200 hot dogs in his stand each morning just in case he has a big day. Using Monte Carlo analysis techniques, the owner could study the effects of various business decisions based on the performance of a key indicator, such as daily profit. For example, he could test the profit impact of the decision to start each day with only 175 hot dogs in his cart. He could then generate a series of random numbers to represent daily hot dog sales over a given period to determine his average daily profits. He may find, for instance, that profits rise when he starts out with only 175 hot dogs, despite the fact that he will run out of hot dogs on some days.

The party running a Monte Carlo simulation must adhere to several parameters for the simulation to be useful. For example, the random variable(s)—the number of hot dogs sold in a day in the above example—must reflect the underlying uncertainty of the problem. For this reason, Monte Carlo simulations can be highly complex and require the application of advanced statistical techniques. Because they allow the modeling of complex environments, they are often used to simulate difficult scientific and financial problems. Advanced Monte Carlo methods involve the use of Markov chains and the Gibbs sampler, statistical tools that consider the probability of moving through a multistage process given multiple variables and uncertainties. Because Monte Carlo simulations are by nature computationally intensive, they are usually done on a computer.

Chorafas, Dimitris N. Chaos Theory in the Financial Markets: Applying Fractals, Fuzzy Logic, Genetic Algorithms, Swarm Simulation & the Monte Carlo Method to Manage Market Chaos and Volatility. Chicago: Probus Publishing Co., 1994.

Fishman, George S. Monte Carlo: Concepts, Algorithms, and Applications. New York: Springer-Verlag, 1996.

Sobol, Ilya M. A Primer for the Monte Carlo Method. Boca Raton: CRC Press, 1994.