Q&A: How is Monte Carlo Simulation different from...

...analytical methods? Historical simulation?

CppQuant Answer

Monte Carlo simulation in finance involves identifying the risk factors associated with a problem, and the use of a computer to represent the operation of a complex financial system.

  • It provides only statistical estimates, not exact results: It is a complement to analytical methods.
  • It does not directly provide precise insights as analytical methods do. For example, it cannot reveal cause-and-effect relationships.
  • An integral part of simulation is the generation of a large number of random samples from a probability distribution. Monte Carlo simulation uses a random number generator with a specified distribution. In contrast, Historic simulation samples from a historical record of returns to simulate a process because the historical record provides the most direct evidence on distributions (and that the past applies to the future).

Bonus Points

  • A drawback of historical simulations is that any risk not represented in the time period selected will not be reflected in the simulation. For example, if a stock market crash did not take place in the sample period, such a risk will not be reflected in the simulation. Also, it does not lend itself to "what-if" analysis.
  • Monte Carlo simulation allows us to experiment with a proposed policy before actually implementing it to assess the risks. For example, it is used to simulate the interaction of pension assets and liabilities of defined benefit pension plans.
  • MC is widely used to develop estimates of Value at Risk (VAR). VAR involves estimating the probability that portfolio losses exceed a predefined level.
  • MC is used to value complex securities such as European options, mortgage-backed securities with complex embedded options.

Category: Quantitative Analysis

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