Transcript Monte Carlo Simulation

Monte Carlo
Simulation
Natalia A. Humphreys
April 6, 2012
University of Texas at Dallas
Challenges
 We are constantly faced with uncertainty, ambiguity,
and variability.
 Risk analysis is part of every decision we make.
 We’d like to accurately predict (estimate) the
probabilities of uncertain events.
 Monte Carlo simulation enables us to model situations
that present uncertainty and play them out thousands
of times on a computer.
Questions answered with
the help of MCS
 How should a greeting card company determine how
many cards to produce?
 How should a car dealership determine how many
cars to order?
 What is the probability that a new product’s cash
flows will have a positive net present value (NPV)?
 What is the riskiness of an investment portfolio?
Modeling with MCS
 Monte Carlo Simulation (MCS) lets you see all the
possible outcomes of your decisions and assess the
impact of risk, allowing for better decision making
under uncertainty.
MCS: Where did the
Name Come From?
 During the 1930s and 1940s, many computer simulations
were performed to estimate the probability that the chain
reaction needed for the atom bomb would work
successfully.
 The Monte Carlo method was coined then by the physicists
John von Neumann, Stanislaw Ulam and Nicholas
Metropolis, while they were working on this and other
nuclear weapon projects (Manhattan Project) in the Los
Alamos National Laboratory.
 It was named in homage to the Monte Carlo Casino, a
famous casino in the Monaco resort Monte Carlo where
Ulam's uncle would often gamble away his money.
Who Uses MCS?
 General Motors (GM)
 Procter and Gamble (P&G)
 Eli Lilly
 Wall Street firms
 Sears
 Financial planners
 Other companies, organizations and individuals
MCS Use
 General Motors (GM), Procter and Gamble (P&G),
and Eli Lilly use simulation to estimate both the
average return and the riskiness of new products.
MCS Use: GM
 Forecast net income for the corporation
 Predict structural costs and purchasing costs

Determine its susceptibility to different risks:
 Interest rate changes
 Exchange rate fluctuations
MCS Use: Lilly
 Determine the optimal plant capacity that should be
built for each drug
MCS Use: Wall Street
 Price complex financial derivatives
 Determine the Value at Risk (VaR) of investment
portfolios.
 By definition, Value at Risk at security level p for a
random variable X is the number VaR_p(X) such that
Pr(X<VaR_p(X))=p
In practice, p is selected to be close to 1: 95%, 99%, 99.5%
MCS Use: Procter &
Gamble
 Model and optimally hedge foreign exchange risk
MCS Use: Sears
 How many units of each product line should be
ordered from suppliers
MCS Use: Financial
Planners
 Determine optimal investment strategies for their
clients’ retirement.
MCS Use: Others
 Value “real options”:
 Value of an option to expand, contract, or postpone a
project
MCS Applications

Physical Sciences

Engineering

Computational Biology

Applied Statistics

Games

Design and visuals

Finance and business (Actuarial Science)

Telecommunications

Mathematics
Part III: Advantages of
MCS
 In conclusion, we’ll discuss some advantages of MCS
over deterministic, or “single-point estimate” analysis.
Advantages of MCS
MCS provides a number of advantages over deterministic,
or “single-point estimate” analysis:
 Probabilistic Results
 Graphical Results
 Sensitivity Analysis
 Scenario Analysis
 Correlation of Inputs
Probabilistic Results
 Results show not only what could happen, but how
likely each outcome is.
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.
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.
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.
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 go up, others go up or down
accordingly.