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This page includes files and associated videos that address Monte Carlo simulation in finance. When I first began studying Monte Carlo simulation in the early 1990’s I quickly became addicted to the process. You can make beautiful frequency distributions, show fancy time series equations and directly associate risks with mathematical statistics (i.e. volatility and mean reversion). I have also noticed that academics like to apply Monte Carlo to many problems so they show how smart they are. More recently I have seen that much of the application of Monte Carlo simulation to finance is rubbish. Incorrect measurement of mean reversion can mess things up and many times Monte Carlo does not really measure anything at all.

I do still believe that Monte Carlo can be helpful in certain situations. For example, if you are evaluating how much a cash flow sweep reduces default probability, you can use Monte Carlo simulation. You could measure the default probability with and without a sweep using Monte Carlo simulation. I also find Monte Carlo simulation useful to prove statistical concepts. I did not really believe the Mean Square Error can be used to add up standard deviation, but with simulation this can be demonstrated. Finally, if you want to demonstrate risks associated with holding different portfolios of short-term and long-term debt, the potential risks can be effectively displayed with Monte Carlo Simulation.

The following Examples of Models apply that Include Monte Carlo Simulation. These models create time series variable(s) and use a simple macro to apply these in a simulation Framework. The video below discusses how to set-up a spreadsheet for creating a Monte Carlo simulation.

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= Monte Carlo Exercises =



The exercises in the files help you walk through how to add a Monte Carlo Simulation to your financial models.

The first two simple exercises begin with a simple Monte Carlo simulation created without a macro below. The next exercise performs a similar Monte Carlo simulation using Brownian Motion, but uses a simple macro to perform the simulation. The third exercise includes mean reversion and price boundaries in the Monte Carlo simulation The fourth exercise includes correlation amoung variables in the simulation.



To add Monte Carlo Simulation to your financial models, follow a two step process:
 * 1) Run the Monte Carlo simulation for one or more input variables in the cash flow model (e.g. oil prices, gas prices and interest rates). This file allows you to incorporate Monte Carlo simulation with mean reversion, price boundaries, price jumps, correlations and other factors to any input variables
 * 2) Save the Monte Carlo results in a summary file by running the "strip files" macro
 * 3) With the original financial model open and the summary Monte Carlo file open, select the Simulation Template Model



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 * Subject ||  || Excel Exercise File ||   || Video ||   || Chapter Reference ||   || Page Reference ||
 * Working with Normal Distribution ||  || Exercise 1: Normal Distribution Functions ||   || https://www.youtube.com/watch?v=7s2GiemfZdg ||   || Chapter 21 ||   || 278 ||
 * Working with Wiebull Distribution ||  || Exercise 2: Weibull Distribution Functions ||   ||   ||   ||   ||   ||   ||
 * Creating Basic Time Series Distribution with Normal Distribution ||  ||   ||   ||   ||   ||   ||   ||   ||
 * Creating Time Series with Weibull Distribution ||  ||   ||   ||   ||   ||   ||   ||   ||
 * Graphing Distribution ||  ||   ||   ||   ||   ||   ||   ||   ||
 * Adding Time Series to Financial Model ||  ||   ||   ||   ||   ||   ||   ||   ||
 * Mean Reversion in Time Series Models ||  ||   ||   ||   ||   ||   ||   ||   ||
 * Boundaries in Time Series Models ||  ||   ||   ||   ||   ||   ||   ||   ||
 * Correlation in Time Series Models ||  ||   ||   ||   ||   ||   ||   ||   ||
 * Black Sholes Model ||  ||   ||   ||   ||   ||   ||   ||   ||
 * Monte Carlo Simulation and Black Sholes Model ||  ||   ||   ||   ||   ||   ||   ||   ||
 * Testing Time Series for Normal ||  || Commodity Price Analysis ||   ||   ||   ||   ||   ||   ||
 * Simple Time Series Analysis in Excel without Mean Reversion ||  ||   ||   || https://www.youtube.com/watch?v=WliOwYepmHo ||   ||   ||   ||   ||
 * Monte Carlo with Mean Reversion ||  ||   ||   || https://www.youtube.com/watch?v=2mLJEo2ubsw ||   ||   ||   ||   ||
 * Monte Carlo Distribution Graphs ||  ||   ||   || https://www.youtube.com/watch?v=_oVz9TT6a5g ||   ||   ||   ||   ||
 * Monte Carlo with Mean Reversion ||  ||   ||   || https://www.youtube.com/watch?v=2mLJEo2ubsw ||   ||   ||   ||   ||
 * Monte Carlo Distribution Graphs ||  ||   ||   || https://www.youtube.com/watch?v=_oVz9TT6a5g ||   ||   ||   ||   ||