Monte Carlo Simulation

Natalia A. HumphreysApril 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 MCSMCS 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.