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What is the Monte Carlo Method?

Monte Carlo MethodThe Monte Carlo method was invented in the late 1940s by Stanislaw Ulam, while he was working on nuclear weapon projects at the Los Alamos National Laboratory. It was named after the Monte Carlo Casino, where Ulam’s uncle often gambled. Ulam and John von Neumann programmed the ENIAC computer to carry out Monte Carlo calculations.

Monte Carlo Method in Finance

In finance, the Monte Carlo modeling is used to simulate the uncertainty that affects the value of an investment.The idea is to cover all conceivable real world possibilities in proportion to their likelihood. Monte Carlo Methods are used for personal financial planning, for option value determination and for business modeling.

For instance, if you want to determine the probability that you will outlive your retirement, by using the Monte Carlo method and simulating the overall market, the chances of outliving your retirement income from a 401(k) with a specific distribution schedule can be calculated. It can then be determined that based on a certain level of annual investment over the next “X” number of years before retirement, and then “Y” dollars of monthly withdrawals the investor would have a 25% chance of outliving his nest egg. This would necessitate a modification of the investment plan either requiring the investor to work longer or invest more prior to retirement.

Monte Carlo modeling can also be used in valuing an option, the simulation generates several thousand possible (but random) price paths for the underlying share, with the associated exercise value (i.e. “payoff”) of the option for each path. These payoffs are then averaged and discounted to today, and this result is the value of the option today.

Like the retirement example, Monte Carlo Methods are also used for portfolio balancing. The factors impacting the component instruments are simulated over time with the resulting value of each instrument calculated and then the portfolio value is observed to determine the optimal balance.

The key to developing an accurate Monte Carlo model is using the proper constraints for each variable with the proper relationship between variables taken into consideration. For example, because portfolio diversification is based on the correlation [Beta (β)] between various components of the portfolio, Monte Carlo modeling must take correlation into consideration when developing the model.

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About Tim McMahon

Work by editor and author, Tim McMahon, has been featured in Bloomberg, CBS News, Wall Street Journal, Christian Science Monitor, Forbes, Washington Post, Drudge Report, The Atlantic, Business Insider, American Thinker, Lew Rockwell, Huffington Post, Rolling Stone, Oakland Press, Free Republic, Education World, Realty Trac, Reason, Coin News, and Council for Economic Education. Connect with Tim on Google+

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