numerical excellence in finance n a g jan2010
DESCRIPTION
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#.TRANSCRIPT
Experts in numerical algorithms and HPC services
Numerical Excellence in Finance
John Holden
Banking on Monte Carlo and GPUsParis, FRANCE
28th January 2010
2Numerical Excellence in Finance – January 2010
Agenda
NAG – An Introduction
NAG – Numerical Libraries
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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
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PortfolioNumerical Libraries
Highly flexible for use in many computing languages, programmingenvironments, 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
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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
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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
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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!
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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
...
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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
……
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Don’t take our word for it….
Financial Maths Professors speed up their optimization
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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.”
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NAG Libraries Ease of Integration
C++ (various) C# / .NET CUDA Visual Basic Java Borland Delphi Python F# … and more
Excel MATLAB
SciLab, Octave
Mathematica Maple PowerBuilder R and S-Plus SAS … … and more
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NAG and Excel..
Our libraries are easily accessible from Excel Calling DLLs using VBA NAG provide VB
Declaration Statements and Examples
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NAG and .NET
NAG solutions for .NET1. 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
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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
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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
17Numerical Excellence in Finance – January 2010Sunday, 31 January 2010 17NAG Toolbox for MATLAB
Subset of Eigenvalues and Eigenvectors
Speedup
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Best Advice – Use the Decision Trees
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NAG Library and Toolbox – recent additions
Global optimizationANOVA – Analysis of
VarianceNearest Correlation MatrixPartial Least Squares
Regression AnalysisPrediction intervals for
fitted modelsOption PricingGeneralised Mixed Effect
Regression
More CopulasExtreme Value Theory
StatisticsFast quantile selection
routineWaveletsAdoption of LAPACK 3.1New RNGs
Scrambled Seq for QMC Mersenne Twister Sobol Sequence generator
(50,000 dimensions)
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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
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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
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NAG Key Contacts
www.nag.com
Technical Support and [email protected]
Sales in [email protected] Dial +33 6 87 88 12 94
NAGNews http://www.nag.co.uk/NAGNews/Index.asp