Monte Carlo Simulation

Monte Carlo Simulation Natalia A. Humphreys  April 6, 2012 University of Texas at Dallas

 Aknowledgement 

Wayne L. Winston, “Microsoft Excel Data Analysis and Business Modeling” , 2004

 Aknowledgement 

Wayne L. Winston, “Microsoft Excel Data Analysis and Business Modeling” , 2004

Overview 

Part I 

Questions answered with the help of MCS

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History

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Typical simulations

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Part II: Simulation examples

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Part III: Advantages Advantages of MCS over deterministic analysis

Challenges 

We are constantly faced with uncertainty, ambiguity, and variability. variability.

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Risk analysis is part of every decision we make.

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We’d like to accurately predict (estimate) the probabilities probabilities of uncertain events.

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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?

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How should a car dealership determine how many cars to order?

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What is the probability that a new product’s cash flows will have a positive net present value (NPV)?

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What is the riskiness of an investment portfolio? 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.

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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.

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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)

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Procter and Gamble (P&G)

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Eli Lilly

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Wall Street firms

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Sears

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Financial planners

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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

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Predict structural costs and purchasing costs

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Determine its susceptibility to different risks: 

Interest rate changes

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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

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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