Monte Carlo

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Monte Carlo Method
Ouldsaid Nour El-imane
Mr Saadi
Audit Diagnostic des systèmes d’information
An Essay about: Monte-Carlo method
Abstract
Since the beginning of electronic computing, people have been interested in carrying out random
experiments on a computer. Such Monte Carlo techniques are now an essential ingredient in many
quantitative investigations.so what is monte carlo and why is it so important ?
Introduction :
Risk analysis is a part of every decision we make, we are Constantly faced with uncertainty,
Ambiguity and variability. And even though we have unprecedented access to information we can’t
accurately Predict the future . Monte Carlo simulation also known as the Monte Carlo the method
Lets you see All the possible outcomes of your decision and assess the impact of risk allowing for a
better decision making under uncertainty , Monte Carlo simulation uses random sampling and
statistical modeling to estimate mathematical functions and mimic the operations of complex
systems.
Definition of Monte Carlo Simulation
The Monte Carlo method was invented by scientists working on the atomic bomb in the 1940s, who
named it for the city in Monaco famed for its casinos and games of chance. Its core idea is to
use random samples of parameters or inputs to explore the behavior of a complex system or
process. The scientists faced physics problems, such as models of neutron diffusion, that were too
complex for an analytical solution -- so they had to be evaluated numerically. They had access to
one of the earliest computers -- MANIAC -- but their models involved so many dimensions that
exhaustive numerical evaluation was prohibitively slow. Monte Carlo simulation proved to be
surprisingly effective at finding solutions to these problems.
Monte Carlo simulation is a computerized mathematical technique that allows people to account for
risk in quantitative analysis and decision making. The technique is used by professionals in such
widely disparate fields as finance, project management, energy, manufacturing, engineering,
research and development, insurance, oil & gas, transportation, and the environment.
The simulation furnishes the decision-maker with a range of possible outcomes and the probabilities
they will occur for any choice of action.. It shows the extreme possibilities—the outcomes of going

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Monte Carlo Method
for broke and for the most conservative decision—along with all possible consequences for middle-
of-the-road decisions.
The Use of Monte Carlo Simulation:
Whenever you need to make an estimate, forecast or decision where there is significant uncertainty,
you'd be well advised to consider Monte Carlo simulation -- if you don't, your estimates or forecasts
could be way off the mark, with adverse consequences for your decisions! Dr. Sam Savage, a noted
authority on simulation and other quantitative methods, says "Many people, when faced with an
uncertainty ... succumb to the temptation of replacing the uncertain number in question with a
single average value. I call this the flaw of averages, and it is a fallacy as fundamental as the belief
that the earth is flat."
Most business activities, plans and processes are too complex for an analytical solution -- just like
the physics problems of the 1940s. But you can build a spreadsheet model that lets you evaluate
your plan numerically -- you can change numbers, ask 'what if' and see the results. This is
straightforward if you have just one or two parameters to explore. But many business situations
involve uncertainty in many dimensions -- for example, variable market demand, unknown plans of
competitors, uncertainty in costs, and many others -- just like the physics problems in the 1940s. If
your situation sounds like this, you may find that the Monte Carlo method is surprisingly effective
for you as well.
Knowledge Needed to Use monte carlo simulation
To use Monte Carlo simulation, you must be able to build a quantitative model of your business
activity, plan or process. One of the easiest and most popular ways to do this is to create
a spreadsheet model using Microsoft Excel -- and use Frontline Systems' Risk Solver as a simulation
tool. Other ways include writing code in a programming language such as Visual Basic, C++, C# or
Java -- with Frontline's Solver Platform SDK -- or using a special-purpose simulation modeling
language. You'll also need to learn (or review) the basics of probability and statistics. To deal with
uncertainties in your model, you'll replace certain fixed numbers -- for example in spreadsheet cells -
- with functions that draw random samples from probability distributions. And to analyze the
results of a simulation run, you'll use statistics such as the mean, standard deviation, and
percentiles, as well as charts and graphs. Fortunately, there are great software tools (like ours!) to
help you do this, backed by technical support and assistance.
The importance of monte carlo method career wise :
If your success depends on making good forecasts or managing activities that involve uncertainty,
you can benefit in a big way from learning to use Monte Carlo simulation. By doing so, you
can Avoid the Trap of the Flaw of Averages. As Dr. Sam Savage warns, "Plans based on average
assumptions will be wrong on average." If you've ever found that projects came in later than you
expected, losses were greater than you estimated as "worst case," or forecasts based on averages
have gone awry -- you stand to benefit!

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Monte Carlo Method
Go Beyond the Limits of 'What If' Analysis. A conventional spreadsheet model can take you only so
far. If you've created models with best case, worst case and average case scenarios, only to find
that the actual outcome was very different, you need Monte Carlo simulation! By
exploring thousands of combinations for your 'what-if' factors and analyzing the full range of
possible outcomes, you can get much more accurate results, with only a little extra work.
Know What Factors Really Matter. Tools such as Frontline's Risk Solver enable you to quickly
identify the high-impact factors in your model, using sensitivity analysis across thousands of Monte
Carlo trials. It could take you hours to identify these factors using ordinary 'what if' analysis.
Give Yourself a Competitive Advantage. If you're negotiating a deal, or simply competing in the
marketplace, having a realistic idea of the probability of different outcomes -- when your opponent
or competitor does not -- can enable you to strike a better bargain, choose the price that yields the
most profit, or benefit in other ways.
Be Better Prepared for Executive Decisions. The higher you go in an organization, the more you'll
find yourself dealing with uncertainty. Simulation or risk analysis might not be essential for routine
day-to-day, low-value decisions -- but you'll find it invaluable as you deal with higher-level, more
strategic -- and higher-stakes -- decisions.
Risk analysis is part of every decision we make. We are constantly faced with uncertainty,
ambiguity, and variability. And even though we have unprecedented access to information, we can’t
accurately predict the future. Monte Carlo simulation (also known as the Monte Carlo Method) lets
you see all the possible outcomes of your decisions and assess the impact of risk, allowing for better
decision making under uncertainty.
How Monte Carlo Simulation Works :
Monte Carlo simulation performs risk analysis by building models of possible results by substituting
a range of values—a probability distribution—for any factor that has inherent uncertainty. It then
calculates results over and over, each time using a different set of random values from the
probability functions. Depending upon the number of uncertainties and the ranges specified for
them, a Monte Carlo simulation could involve thousands or tens of thousands of recalculations
before it is complete. Monte Carlo simulation produces distributions of possible outcome values.
By using probability distributions, variables can have different probabilities of different outcomes
occurring. Probability distributions are a much more realistic way of describing uncertainty in
variables of a risk analysis.

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Monte Carlo Method
Common probability distributions include:
 Normal
Or “bell curve.” The user simply defines the mean or expected value and a standard deviation to
describe the variation about the mean. Values in the middle near the mean are most likely to occur.
It is symmetric and describes many natural phenomena such as people’s heights. Examples of
variables described by normal distributions include inflation rates and energy prices.
 Lognormal
Values are positively skewed, not symmetric like a normal distribution. It is used to represent values
that don’t go below zero but have unlimited positive potential. Examples of variables described by
lognormal distributions include real estate property values, stock prices, and oil reserves.
 Uniform
All values have an equal chance of occurring, and the user simply defines the minimum and
maximum. Examples of variables that could be uniformly distributed include manufacturing costs or
future sales revenues for a new product.
 Triangular
The user defines the minimum, most likely, and maximum values. Values around the most likely are
more likely to occur. Variables that could be described by a triangular distribution include past sales
history per unit of time and inventory levels.
 PERT
The user defines the minimum, most likely, and maximum values, just like the triangular
distribution. Values around the most likely are more likely to occur. However values between the
most likely and extremes are more likely to occur than the triangular; that is, the extremes are not

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Monte Carlo Method
as emphasized. An example of the use of a PERT distribution is to describe the duration of a task in a
project management model.
 Discrete
The user defines specific values that may occur and the likelihood of each. An example might be the
results of a lawsuit: 20% chance of positive verdict, 30% change of negative verdict, 40% chance of
settlement, and 10% chance of mistrial.
During a Monte Carlo simulation, values are sampled at random from the input probability
distributions. Each set of samples is called an iteration, and the resulting outcome from that sample
is recorded. Monte Carlo simulation does this hundreds or thousands of times, and the result is a
probability distribution of possible outcomes. In this way, Monte Carlo simulation provides a much
more comprehensive view of what may happen. It tells you not only what could happen, but how
likely it is to happen.
 Monte Carlo simulation provides a number of advantages over deterministic, or “single-
point estimate” analysis:
o Probabilistic Results. Results show not only what could happen, but how likely each
outcome is.
o Graphical Results. Because of the data a Monte Carlo simulation generates, it’s easy
to create graphs of different outcomes and their chances of occurrence. This is
important for communicating findings to other stakeholders.
o Sensitivity Analysis. With just a few cases, deterministic analysis makes it difficult to
see which variables impact the outcome the most. In Monte Carlo simulation, it’s
easy to see which inputs had the biggest effect on bottom-line results.
o Scenario Analysis: In deterministic models, it’s very difficult to model different
combinations of values for different inputs to see the effects of truly different
scenarios. Using Monte Carlo simulation, analysts can see exactly which inputs had
which values together when certain outcomes occurred. This is invaluable for
pursuing further analysis.
o Correlation of Inputs. In Monte Carlo simulation, it’s possible to model
interdependent relationships between input variables. It’s important for accuracy to
represent how, in reality, when some factors goes up, others go up or down
accordingly.
An enhancement to Monte Carlo simulation is the use of Latin Hypercube sampling, which samples
more accurately from the entire range of distribution functions.
Areas of application :
Monte Carlo methods are especially useful for simulating phenomena with significant uncertainty in
inputs and systems with many coupled degrees of freedom. Areas of application include:
Physical sciences: