Duration: 2 days
 Monte Carlo Simulation in Finance
 Random Number Generation
 Cholesky Decomposition
 Stochastic Differential Equations
 Variance Reduction Techniques
 Pricing Exotic and Hybrid Options
 Measuring Value at Risk
 Stress Testing
The objective of this advancedlevel course is to give the participants handson experience with the
use of advanced simulation techniques in finance. We start with an introduction to the Monte Carlo
method and we 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. Participants will work their way through the
generation of pseudorandom numbers including numbers drawn from arbitrary probability distributions,
discrete as well as continuous. Participants will also learn and try how the "Cholesky decomposition"
technique can be used when sampling from multivariate distributions, when assets are correlated. We use
latticepricing to price and risk assess exotic options such as Asian, barrier and lookback options
using various stochastic processes, including BlackScholes as a benchmark. Further, we show how to
construct discrete versions of widely used Stochastic Differential Equations. Participants will use
these to simulate trajectories of assets and to measure the Value at Risk of a portfolio of securities,
estimate the potential exposure of market driven instruments etc., and to perform "stress testing".
Finally, we present a number of variance reduction techniques for use with Monte Carlo Simulation,
including the use of antithetic variables, control variate and importance sampling methods. 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™).
Day One
09.00  09.15 Welcome and Introduction
09.15  12.00 Monte Carlo Simulation in Finance
 Applications of Monte Carlo Simulation in Finance
 Couple of Examples of What You Can Do
 Introductory Exercise
Implementing the Monte Carlo Toolkit
 Statistical Distributions
 Generating Normally Distributed Random Numbers in Visual Basic
 Drawing from Multivariate Distributions
 Programming Stochastic Differential Equations in Visual Basic
 Workshop: Participants Program Sampling Routines and Simulate Basic SDEs in Visual Basic
12.00  13.00 Lunch
13.00  16.30 Pricing Options Using Monte Carlo Simulation
 Overview of Option Pricing Models
 Pricing Standard European Options

Pricing "Path Dependent" Options
 Barrier options
 Lookback options
 Asian options

Pricing other Exotic Options
 Digital options and "range floaters"
 Basket and compound options
 Chooser and rainbow options
 Greeks in Monte Carlo
 Workshop: Participants Program a Generalized Routine in VB for Valuation of Standard and Exotic
Options
Day Two
09.00  12.00 Calculating "ValueatRisk" Using Monte Carlo Simulation

VaR for Single Asset Portfolios
 Formulating the price process
 Discretezising the price process
 Constructing the P&L Histogram
 Inferring the VaR
 Workshop: Participants Program Routine to Generate Full Distribution and Calculate VaR for
Single Asset

VaR for Multiple Asset Portfolios
 When prices are independent
 When prices are perfectly correlated
 When prices are imperfectly correlated
 Cholesky decomposition
 Constructing the P&L histogram
 Inferring the VaR
 Workshop: Participants Program Routine to Generate Full Distribution and Calculate VaR for
Asset Portfolio
12.00  13.00 Lunch
13.00  16.00 Calculating "ValueatRisk" for Option Portfolios
 Building a "Simulation within the Simulation"
 Constructing the Payoff Distribution and Inferring the VaR (market Risk + Counterparty
Risk)
 Workshop: Participants Construct Payoff Distribution for Option Portfolio and Infer VaR
Making Monte Carlo Simulation More Efficient
 Problems with Conventional MCS
 Variance Reduction Techniques
 QuasiMonte Carlo Approaches
 Scrambled Nets Approach
 Scenario Simulation – an Alternative Approach
 Workshop: Participants "Tune" their MC Applications
Evaluation and Termination of the Workshop