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Geometric Brownian Motion. The aim of this project is to gain an understanding of the Monte Carlo simulation method (Value-at-Risk measure) and to create a user-friendly piece of software that will allow investors to determine the potential risk a chosen

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Name: Tom Forward                                                          Year: 2010

Chapter 1: Introduction

A main factor that plays a big part in the price of a stock or shares is the economy, the economy was doing really well up until 2008 when the recession started, this caused share prices to drop dramatically and businesses having to close down. Customers began to spend less, this affected most companies as it caused a downturn in the economy. Investment levels dropped and businesses did not perform to the same standard. Investment became riskier as banks started to collapse, some even going bankrupt causing businesses to close down too. The recession in the past years (which is still ongoing) has led to fewer people investing and share prices decreasing. Due to this risk management has become important when investing.

1.1 Equity

Stocks are also known as equities or shares. An equity is when a stock or share is bought either privately or within a company, this can sometimes be risky because if the company does well in terms of valuation of the equity then the stock or shares bought would have been a good investment to the buyer and profit could be made, but if the company does badly, then the net worth of the stock or shares held is less than what its initial value was and a loss could be made through the returns generated. Risk measures need to be considered when investing in equities to avoid potential losses.

1.2 Aim of the project

The aim of this project is to gain an understanding of the Monte Carlo simulation method (Value-at-Risk measure) and to create a user-friendly piece of software that will allow investors to determine the potential risk a chosen stock has.

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In order to calculate a normally distributed random number with mean 0 and standard deviation 1 using this alternative method we need to implement the following formula:-


ε, is normally distributed random number

Riis simply a random number generated using the ‘rand()’ function found under ‘math & trig’.

In order to implement this function, 12 random numbers need to be generated using this generator. The values of the 12 figures will be added together using the ‘sum’ function and take 6 from this value. To generate more the row will just need to be copied down to the relevant number of rows needed, for example can be copied down to 1000. This will show 1000 normally distributed random numbers.

2.7 Historical data

The historical data needed has been collected in order for this project to be implemented and one way of creating a software that will allow investors to estimate future stock prices. The historical data is taken from DataStream via FTSE100 and will consist of three years’ worth of closing share prices for a number of various companies. Historical data is being used in order to estimate future stock prices. Stock prices are observed at fixed intervals of time that will be used in this project including daily, weekly and monthly. Volatility can be estimated by the movement of stock prices.

2.8 Risk Measure (V-a-R)

A well-known risk measure is Value at Risk (V-a-R); this was first used by major financial firms in the late 1980’s. This is a widely used risk measure of the risk of loss on a specific portfolio of financial assets and will be used in this project.Three different types of models exist for estimating Value at Risk, these include the variance-covariance (VCV) assuming that risk factor returns are always (jointly)

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The aims of the project have been met seeing that a user friendly software has been created in order to estimate future stock prices and calculate its V-a-R. Testing of the software has been successful with no errors and complications, results obtained have been appropriate easy to understand and can be based on real life financial situations.

From the initial design stage to the completion of the project there have been ups and downs throughout but with great motivation and support this has been a successful project!

Chapter 9: User Manual


This manual will guide the user through the software; each step will be illustrated and labelled, each label being explained. The main purpose of the software is to calculate stock prices using Geometric Brownian Motion, measuring its risk by V-a-R.

Before proceeding further the following requirements are needed; an operating system of Windows XP or newer and the software needed is Microsoft office 2007 (Excel). The software will need to be opened directly from the CD-Rom and not from a copied version on the system.

If the above are available to the user then it is time to get started!

Open the program from the CD-Rom into Microsoft Excel, ensure all security checks are in place, and enable macros. This will ensure that all functions will run accordingly. To enable macros click the ‘Office button’, this will be located on the top left hand corner of the Excel window, then go to ‘Excel options’ > ‘Trust center’ > ‘Trust center settings’ > ‘Enable all macros’.

Once all of the above are done and available to the user, the user can get started with using the software.

Chapter 10: References

Reading, to gain further understanding of the main topics:

Hull, John C., Options, Futures, and Other Derivatives, 5th ed., Prentice Hall, 2002.

Hull, John C., Fundamentals of futures and options markets, 7th ed., Pearson, 2011.

Neil A, Chriss., Black schools and beyond: Option pricing methods, McGraw-Hill companies,1997.

Tom Forward

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