1 © 2011 The MathWorks, Inc.

Computing VaR with MATLAB

Martin Demel, Application Engineer

2

Agenda

• Introducing MathWorks

• Introducting MATLAB (Portfolio Optimization Example)

• Introducting Algorithmic Trading with MATLAB

Break

• Credit Risk Modeling with MATLAB

• Risk Management using various VaR

computation methods

• Overview of derivatives pricing capabilities and further

financial computing products

• Q&A

3

Computational Finance Workflow

Files

Databases

Datafeeds

Access

Reporting

Applications

Production

Share

Data Analysis and Visualization

Financial Modeling

Application Development

Research and Quantify

Builder NE

Builder EX

Builder JA

MATLAB Compiler

Rep

ort G

en

era

tor

Datafeed

Database

Spreadsheet Link EX

Financial

Statistics Optimization

Fixed Income Financial Derivatives Econometrics

MATLAB

Parallel Computing MATLAB Distributed Computing Server

4

Financial Modeling with MATLAB

Financial – Financial charting and analysis, portfolio

optimizations, risk analyses, asset allocations, fixed-income pricing

Fixed income – Determine the price, yield, and cash flows for

many types of fixed-income securities including mortgage-backed

Financial derivatives – Analyze and model equity and fixed-income

derivatives and securities contingent on interest rates

Econometrics – Perform Monte Carlo simulation of univariate

returns, perform pre- and post-estimation diagnostic and hypothesis testing, estimate parameters of general ARMAX/GARCH models

5

Statistics Toolbox

Organizing Data

Descriptive Statistics

Statistics Visualization

Probability Distributions

Random Number Generation

Hypothesis test

Analysis of variance

Regression analysis

Multivariate methods

Cluster Analysis

Classification

Markov models

Design of experiments

Statistical Process Control

Parallel Statistics

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Financial Toolbox

Performing common financial tasks

Portfolio analysis

Investment performance metrics

Credit Risk Analysis

Regression with missing data

Financial time series analysis

Using financial time series

Financial Time Series Tool and GUI

Trading Date Utilities

Technical Analysis

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Econometrics Toolbox

Time series modeling

Model Selection

Simulation

Estimation

Forecasting

Regression

Multiple time series

Lag Operator polynomials

Stochastic differential equations

Seasonal ARIMA, GARCH, EGARCH, and

GJR model objects for modeling

univariate time series data

9

Fixed Income Toolbox

Mortgage-Backed Securities

Debt instrument

Derivatives securities

Credit Default Swaps

Interest Rate Curve Objects and class reference

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Financial Derivatives Toolbox

Interest Rates Derivatives

Equity Derivatives

Hedging portfolios

Derivatives pricing options

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Types of Derivatives

Interest Rate Derivatives – Options: calls/put

– Caps / Floors

– Swaps, Swaptions

– Futures / Forwards

– Convertible bonds, putable/callable bonds, OAS

Equity Derivatives – Vanilla options: calls/puts

– Exotic options: Asian

Barrier

Compound

Lookback

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Fixed-Income and Fin. Derivatives Toolbox

– Single name CDS Options (credit default swaptions)

– Convertible bond pricing updated (put features, variable-rate

coupons, continuous dividend yields, and no exercise periods)

Financial Derivatives

– Interest-rate tree model in option adjusted spreads (OAS) for

callable and putable bonds

– Generalized Hull-White algorithm for interest-rate tree models

What are the honorable mentions?

Customers have asked for…

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Continuous

Nonlinear Minimization

Nonlinear Least-Squares

Nonlinear Equations

Nondifferentiable Optimization

Nonlinear Programming

Multi-Objective Optimization

Linear Programming

Quadratic Programming

Constrained Linear Least-Squares

Continuous Discontinuous

and Stochastic

Global Discrete and

Custom Data Types

Discrete

Binary Integer Programming

Unconstrained Constrained

Global Optimization

Toolbox

Optimization Toolbox

(Global) Optimization Toolbox

Mixed Integer Programming

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Curve Fitting Toolbox

Flexible graphical user interface for fitting and plotting surfaces (sftool)

Four types of surface

fitting algorithms:

– Linear regression

– Nonlinear regression

– Smoothing

– Interpolation

Storage of results from a fitting

operation in surface fit objects

Automatic MATLAB code generation for surface fits and plots from sftool

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Other toolboxes

of great interest for finance

Datafeed Toolbox

Database Toolbox

Spreadsheet Link Excel

Neural Network Toolbox

Parallel Computing Toolbox

MATLAB Compiler

MATLAB Builder JA

MATLAB Builder NE

MATLAB Report Generator

Symbolic Math Toolbox

Signal Processing Toolbox

Control System Toolbox

Wavelet Toolbox

Fuzzy Logic Toolbox

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Key take-aways

Fast and easy to use all-in-one

development environment

Huge number of built-in

functionality

Speed up your calculations with almost no code change

Easy to build a complete application

Share your code and applications royality free

• MATLAB

• Financial Toolbox™

• Econometrics Toolbox™

• Optimization Toolbox™

• Statistics Toolbox™

• Compiler Toolbox™

• Parallel Computing Toolbox™

Highlighted products :

17

Agenda

• Introducing MathWorks

• Introducting MATLAB (Portfolio Optimization Example)

• Introducting Algorithmic Trading with MATLAB

Break

• Credit Risk Modeling with MATLAB

• Risk Management using various VaR

computation methods

• Overview of derivatives pricing capabilities and further

financial computing products

• Q&A