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Handbook in Monte Carlo Simulation: Applications in Financial Engineering, Risk Management, and Economics by Paolo Brandimarte

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Chapter One

Introduction to Monte Carlo Methods

The term Monte Carlo is typically associated with the process of modeling and simulating a system affected by randomness: Several random scenarios are generated, and relevant statistics are gathered in order to assess, e.g., the performance of a decision policy or the value of an asset. Stated as such, it sounds like a fairly easy task from a conceptual point of view, even though some programming craft might be needed. Although it is certainly true that Monte Carlo methods are extremely flexible and valuable tools, quite often the last resort approach for overly complicated problems impervious to a more mathematically elegant treatment, it is also true that running a bad Monte Carlo simulation is very easy as well. There are several reasons why this may happen:

We are using a wrong model of uncertainty:
– Because we are using an unrealistic probability distribution
– Or because we are missing some link among the underlying risk factors
– Or because some unknown parameters have been poorly estimated
– Or because the very nature of uncertainty in our problem does not lend itself to a stochastic representation
The output estimates are not reliable enough, i.e., the estimator variance is so large that a much larger sample size is required. ...

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