##### Monte Carlo Simulation

Monte Carlo simulation is a computerized mathematical technique to generate random sample data based on some known distribution for numerical experiments. This method is applied to risk quantitative analysis and decision making problems. This method is used by the professionals of various profiles such as finance, project management, energy, manufacturing, engineering, research & development, insurance, oil & gas, transportation, etc.

This method was first used by scientists working on the atom bomb in 1940. This method can be used in those situations where we need to make an estimate and uncertain decisions such as weather forecast predictions.

##### The Monte Carlo Simulation Formula

We would like to accurately estimate the probabilities of uncertain events. For example, what is the probability that a new product’s cash flows will have a positive net present value (NPV)? What is the risk factor of our investment portfolio? Monte Carlo simulation enables us to model situations that present uncertainty and then play them out on a computer thousands of times.

Many companies use Monte Carlo simulation as an important part of their decision-making process. Here are some examples.

• General Motors, Proctor and Gamble, Pfizer, Bristol-Myers Squibb, and Eli Lilly use simulation to estimate both the average return and the risk factor of new products. At GM, this information is used by the CEO to determine which products come to market.
• GM uses simulation for activities such as forecasting net income for the corporation, predicting structural and purchasing costs, and determining its susceptibility to different kinds of risk (such as interest rate changes and exchange rate fluctuations).
• Lilly uses simulation to determine the optimal plant capacity for each drug.
• Proctor and Gamble uses simulation to model and optimally hedge foreign exchange risk.
• Sears uses simulation to determine how many units of each product line should be ordered from suppliers—for example, the number of pairs of Dockers trousers that should be ordered this year.
• Oil and drug companies use simulation to value “real options,” such as the value of an option to expand, contract, or postpone a project.
• Financial planners use Monte Carlo simulation to determine optimal investment strategies for their clients’ retirement.