Monte Carlo simulation is a mathematical model that uses historical statistical data to generate millions of different financial results by randomly inserting components into each run that can influence the final result, such as account returns, volatility or correlations. It is used for personal financial planning, portfolio evaluation, valuation of bonds and bond options, and in corporate or project financing. The simulation offers several distinct advantages over other forms of financial analysis, including the ability to create graphs and charts and to understand the positive and negative interdependent relationships between variables.
A Monte Carlo simulation is a mathematical model for calculating the probability of a specific outcome by testing or randomly sampling a wide variety of scenarios and variables. First used by Stanilaw Ulam, a mathematician who worked on the Manhattan Project during World War II, simulations give analysts an avenue to make tough decisions and solve complex problems that have multiple areas of uncertainty. Named after the casino resort populated in Monaco, the Monte Carlo simulation uses historical statistical data to generate millions of different financial results by randomly inserting components into each run that can influence the final result, such as account returns, volatility or correlations. Once the scenarios are formulated, the method calculates the probabilities of achieving a particular outcome. Unlike standard financial planning analyzes that use long-term averages and estimates of future growth or savings, Monte Carlo simulation, available in software and web applications, can provide a more realistic means of managing variables and measuring the probabilities of financial risk or reward.
Monte Carlo methods are often used for personal financial planning, portfolio evaluation, valuation of bonds and bond options, and in corporate or project financing. Although probability calculations are not new, David B. Hertz pioneered finance in 1964 with his article, “Risk Analysis in Equity Investing,” published in the Harvard Business Review. Phelim Boyle applied the method to the valuation of derivatives in 1977, publishing his paper, “Options: A Monte Carlo Approach,” in the Journal of Financial Economics. The technique is more difficult to use with US options, and because the results depend on the underlying assumptions, there are some events that the Monte Carlo simulation cannot predict.
Simulation offers several distinct advantages over other forms of financial analysis. In addition to generating the probabilities of the possible endpoints of a given strategy, the data formulation method makes it easy to create graphs and charts, encouraging better communication of results to investors and shareholders. The Monte Carlo simulation highlights the relative impact of each variable on the bottom line. Using this simulation, analysts can also see exactly how certain combinations of inputs affect and interact with each other. Understanding the positive and negative interdependent relationships between variables allows for a more accurate risk analysis of any instrument.
Risk analysis using this method involves the use of probability distributions to describe the variables. A well-known probability distribution is the normal or bell curve, with users specifying the expected value and a standard deviation curve defining the variance. Energy prices and inflation rates can be represented by bell curves. Normal distributions record positive variables with unlimited potential to increase, such as oil reserves or stock prices. Uniform, triangular, and discrete are examples of other possible probability distributions. The values, which are taken at random from the probability curves, are sent in sets called iterations.
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