The presentation will include examples relevant to finance. Attendees will gain an understanding of how NAG’s mathematical and statistical software can be integrated into many different programs and environments, including Excel, MATLAB (using the NAG Toolbox for MATLAB®), C, C++, and C#.

1. Numerical Excellence in Finance
John Holden
Banking on Monte Carlo and GPUs
Paris, FRANCE
28th January 2010
Experts in numerical algorithms
and HPC services

2. Agenda
 NAG – An Introduction
 NAG – Numerical Libraries
Numerical Excellence in Finance – January 2010 2

3. Introduction to NAG
 Founded in 1970 as a co-operative project in UK
 Operates as a commercial, not-for-profit organization
 Worldwide operations
 Oxford & Manchester, UK
 Chicago, US
 Tokyo, Japan
 Taipei, Taiwan
 Over 3,000 customer sites worldwide
 Staff of ~100, over 50% technical, over 25 PhDs
 £7m+ financial turnover
January 10 Numerical Excellence in Finance – January 2010 3

4. Portfolio
 Numerical Libraries
 Highly flexible for use in many computing languages, programming
environments, hardware platforms and for high performance
computing methods
 Connector Products for Excel, MATLAB and Maple and
 Giving users of the Excel and mathematical software packages
MATLAB and Maple access to NAG’s library of highly optimized and
often superior numerical routines and allowing easy integration
 NAG Fortran Compiler and GUI based Windows
Compiler: Fortran Builder
 Visualization and graphics software
 Build data visualization applications with NAG’s IRIS Explorer
 Consultancy services
Numerical Excellence in Finance – January 2010 4

5. Why bother?
 Numerical computation is difficult to do accurately
 Problems of
 Overflow / underflow
 How does the computation behave for large / small numbers?
 Condition
 How is it affected by small changes in the input?
 Stability
 How sensitive is the computation to rounding errors?
 Importance of
 error analysis
 information about error bounds on solution
Numerical Excellence in Finance – January 2010 5

6. NAG development philosophy
 First priority: accuracy
 Second priority: performance
 How fast do you want the wrong answer?
 Algorithms chosen for
 usefulness
 robustness
 accuracy
 stability
 speed
Numerical Excellence in Finance – January 2010 6

7. Why Use NAG Maths Libraries?
 Global reputation for quality – accuracy,
reliability and robustness…
 Extensively tested, supported and maintained
code
 Reduce development time
 Concentrate on your key areas
 Components
 Fit into your environment
 Simple interfaces to your favourite packages
 Regular performance improvements!
Numerical Excellence in Finance – January 2010 7

8. NAG Library and Toolbox Contents
 NAG provides high-level maths and stats components
 Nonlinear equation solvers
 Summation of series and transformations, FFTs
 Quadrature
 ODEs, PDEs and integral equations
 Approximation and curve and surface fitting
 Optimization and operations research
 Dense linear algebra, including LAPACK
 Sparse linear systems and eigenproblems
 Special functions
 Random Number Generators
 ...
Numerical Excellence in Finance – January 2010 8

9. Use of NAG Software in Finance
 Portfolio analysis / Index tracking / Risk management
 Optimisation, linear algebra, copulas…
 Derivative pricing
 PDEs, RNGs, multivariate normal, …
 Fixed Income/ Asset management / Portfolio
Immunization
 Operations research
 Data analysis
 Time series, GARCH, principal component analysis, data smoothing,
…
 Monte Carlo simulation
 RNGs
 ……
Numerical Excellence in Finance – January 2010 9

10. Don’t take our word for it….
Financial Maths Professors speed up their optimization
Numerical Excellence in Finance – January 2010 10

11. Don’t take our word for it…...
Senior Quant @ Tier 1 bank
“concerning the ‘nearest correlation’ algo.
I have to say, it is very fast, it uses all the power
of my pc and the result is very satisfactory.”
www.walkingrandomly.com
“I really like the NAG toolbox for MATLAB for the
following reasons (among others):
It can speed up MATLAB calculations – see my
article on MATLAB's interp1 function for
example, and it has some functionality that can't
currently be found in MATLAB.”
Numerical Excellence in Finance – January 2010 11
11

12. NAG Libraries Ease of Integration
 C++ (various)  Excel
 C# / .NET  MATLAB
 CUDA  SciLab, Octave
 Visual Basic  Mathematica
 Java  Maple
 Borland Delphi  PowerBuilder
 Python  R and S-Plus
 F#  SAS
 …  …
 and more  …
 and more
Numerical Excellence in Finance – January 2010 12

13. NAG and Excel..
 Our libraries are
easily accessible
from Excel
 Calling DLLs using VBA
 NAG provide VB
Declaration
Statements and
Examples
Numerical Excellence in Finance – January 2010 13

14. NAG and .NET
NAG solutions for .NET
1. Call NAG C (or Fortran) DLL from C#
2. NAG Library for .NET (beta)
“a more natural solution”
 DLL with C# wrappers
 Integrated help
3. NAG Library for .NET (Work-in-Progress)
 as above pure C# functions
Numerical Excellence in Finance – January 2010 14

15. NAG Toolbox for MATLAB
 Contains essentially all NAG functionality
 not a subset
 Currently runs under Windows (32/64bit) or
Linux (32/64-bit).
 Installed under the usual MATLAB toolbox
directory
 Can be used with MATLAB compiler
Numerical Excellence in Finance – January 2010 15

16. Case study – e04uc vs fmincon
A problem from a customer from a European
bank.
The problem involves 48 variables and has 9
linear constraints. (No nonlinear constraints.)
No derivatives supplied.
fmincon required 1890 evaluations of the
objective function and tool 87.6 seconds
e04uc required only 1129 evaluations and took
49.4 seconds
Numerical Excellence in Finance – January 2010 16

17. Subset of Eigenvalues and Eigenvectors
Speedup
Sunday, 31 January 2010 Numerical Excellence in Finance – January 2010
NAG Toolbox for MATLAB 17
17

18. Best Advice – Use the Decision Trees
Numerical Excellence in Finance – January 2010 18

19. NAG Library and Toolbox – recent additions
 Global optimization  More Copulas
 ANOVA – Analysis of  Extreme Value Theory
Variance Statistics
 Nearest Correlation Matrix  Fast quantile selection
routine
 Partial Least Squares  Wavelets
Regression Analysis
 Adoption of LAPACK 3.1
 Prediction intervals for  New RNGs
fitted models  Scrambled Seq for QMC
 Option Pricing  Mersenne Twister
 Sobol Sequence generator
 Generalised Mixed Effect (50,000 dimensions)
Regression
Numerical Excellence in Finance – January 2010 19
19

20. Other NAG software
 NAG’s High Performance libraries
 NAG SMP Library (for multi/many core/processor)
 NAG Parallel Library (for clusters architectures - MPI)
 NAG Fortran Compiler
 Windows version with GUI & Debugger
 Automatic Differentiation (AD) enabled
 In collaboration with RWTH Aachen University
 Routines for SIMD architectures (GPUs etc)
 Early successes with Monte Carlo components on NVIDIA
hardware
 In collaboration with Professor Mike Giles
Numerical Excellence in Finance – January 2010 20

21. Summary
 NAG for Quality, World-leading Numerical
Software Components
 accurate, reliable, robust
 extensively tested, supported and maintained code
 updated for new architectures and new algorithms
Numerical Excellence in Finance – January 2010 21

22. NAG Key Contacts
www.nag.com
Technical Support and Help
support@nag.co.uk
Sales in France
francois.cassier@nag.com
Direct Dial +33 6 87 88 12 94
NAGNews http://www.nag.co.uk/NAGNews/Index.asp
Numerical Excellence in Finance – January 2010 22