Duration: 3 days
 Monte Carlo Simulation in Finance
 Random Number Generation
 Cholesky Decomposition
 Binomial Lattice Models
 Stochastic Differential Equations
 Variance Reduction Techniques
 Pricing Exotic Options
 Measuring Value at Risk
The objective of this advancedlevel course is to give the participants a good understanding of the
Monte Carlo Method and its applications in finance. We shall start by motivating the use of Monte
Carlo methods and we shall give an overview of the widespread use of Monte Carlo methods in
securities and derivatives pricing and in risk management. We then give an indepth explanation of
the Monte Carlo method, enumerating its fundamental building blocks. We shall work our way through
generation of pseudorandom numbers including numbers drawn from arbitrary probability
distributions, discrete as well as continuous. We explain how the “Cholesky decomposition”
technique can be used when sampling from multivariate distributions, when assets are correlated. We
will use latticepricing models to price exotic options using various stochastic processes,
including BlackScholes as a benchmark. Further, we will show how to construct discrete versions of
widely used Stochastic Differential Equations. These versions will be used to simulate trajectories
of assets and to measure the Value at Risk of a portfolio of securities. Finally, we present quite
a few variance reduction techniques for use with Monte Carlo Simulation, including the use of
antithetic variables, control variates and importance sampling. The effect of these techniques on
computational accuracy and/or performance will be evaluated. Throughout the course the participants
will be given the opportunity to work on exercises, gaining handson experience with some of the
Monte Carlo methods. (Excel and Visual Basic). The exercises/workshops will be based upon Microsoft
Excel 2000 and Visual Basic.
Day One
09.00  09.15 Welcome Address
09.15  12.00 Introduction to Monte Carlo Simulation
 What is "Monte Carlo Simulation"?
 Advantages/Disadvantages of MCS
 Applications of Monte Carlo Simulation in Finance
 A Couple of Examples of What You Can Do
 Introductory Exercise
The Monte Carlo Toolkit

Generating Random Numbers
 Random number generators  how they work
 Testing the Excel/VB random number generator
12.00  13.00 Lunch
13.00  16.30 The Monte Carlo Toolkit (cont' d)

Statistical Distributions
 Uniform, normal and lognormal distributions
 Binomial distribution
 Other distributions

Sampling Techniques
 Generating normally distributed random numbers
 Drawing form multivariate distributions
 Stochastic Differential Equations
 Exercises
Day Two
09.00  09.15 Recap
09.15  12.00 Pricing Options Using Monte Carlo Simulation
 Overview of Option Pricing Models
 Pricing Standard European Options

Pricing "Path Dependent" Options
 Barrier options
 Lookback
 Asian
 Range Floaters/EARNs
 Pricing American Options
 Greeks in Monte Carlo
 Exercises/Workshop
12.00  13.00 Lunch
13.00  16.30 Calculating "ValueatRisk"

What is "ValueatRisk"?
 VaR due to market risk
 VaR due to credit risk
 Approaches to Calculating VaR

Calculating VaR Using Monte Carlo Simulation
 VaR for Single Asset Portfolios
 Formulating the price process
 Discretising the price process
 Constructing the P&L Histogram
 Inferring the VaR
 Exercises
Day Three
09.00  09.15 Recap
09.15  12.00 Calculating ValueatRisk (continued)

VaR for Multiple Asset Portfolios
 When prices are independent
 When prices are perfectly correlated
 When prices are imperfectly correlated
 Choleksky decomposition
 Constructing the P&L Histogram
 Inferring the VaR
 Stress Testing
 Exercises/Workshop
12.00  13.00 Lunch
13.00  16.00 Making Monte Carlo Simulation More Efficient

Problems with Conventional MCS
 "Clustering" and other problems
 QuasiMonte Carlo Approaches
 Scrambled Nets Approach
 Scenario Simulation  an Alternative Approach
 Examples and Exercises
16.00  16.30 Recap, Evaluation and Termination of the Seminar