The material below comprises excerpts from books by Dr. Johnathan Mun, our CEO and founder, such as Readings in Certified Quantitative Risk Management, 3rd Edition, and Quantitative Research Methods Using Risk Simulator and ROV BizStats Software: Applying Econometrics, Multivariate Regression, Parametric and Nonparametric Hypothesis Testing, Monte Carlo Risk Simulation, Predictive Modeling, and Optimization, 4th Edition ( All screenshots and analytical models are run using the ROV Risk Simulator and ROV BizStats software applications. Statistical results shown are computed using Risk Simulator or BizStats. Online Training Videos are also available on these topics as well as the Certified in Quantitative Risk Management (CQRM) certification program. All materials are copyrighted as well as patent protected under international law, with all rights reserved.

Monte Carlo simulation, named for the famous gambling capital of Monaco, is a very potent methodology. For the practitioner, simulation opens the door for solving difficult and complex but practical problems with great ease. Perhaps the most famous early use of Monte Carlo simulation was by the Nobel physicist Enrico Fermi (sometimes referred to as the father of the atomic bomb) in 1930, when he used a random method to calculate the properties of the newly discovered neutron. Monte Carlo methods were central to the simulations required for the Manhattan Project, where in the 1950s Monte Carlo simulation was used at Los Alamos for early work relating to the development of the hydrogen bomb and became popularized in the fields of physics and operations research. The RAND Corporation and the U.S. Air Force were two of the major organizations responsible for funding and disseminating information on Monte Carlo methods during this time, and today there is a wide application of Monte Carlo simulation in many different fields including engineering, physics, research and development, business, and finance.

Simplistically, Monte Carlo simulation creates artificial futures by generating thousands and even hundreds of thousands of sample paths of outcomes and analyzes their prevalent characteristics. In practice, Monte Carlo simulation methods are used for risk analysis, risk quantification, sensitivity analysis, and prediction. An alternative to simulation is the use of highly complex stochastic closed-form mathematical models. For analysts in a company, taking graduate-level advanced math and statistics courses is just not logical or practical. A brilliant analyst would use all available tools at his or her disposal to obtain the same answer in the easiest and most practical way possible. And in all cases, when modeled correctly, Monte Carlo simulation provides similar answers to the more mathematically elegant methods. In addition, there are many real-life applications where closed-form models do not exist and the only recourse is to apply simulation methods. So, what exactly is Monte Carlo simulation and how does it work?

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