Numerical Excellence in Finance


                                                     John Holden
                       ...
Agenda




 NAG – An Introduction
 NAG – Numerical Libraries




                Numerical Excellence in Finance – Janua...
Introduction to NAG
 Founded in 1970 as a co-operative project in UK
 Operates as a commercial, not-for-profit organizat...
Portfolio
 Numerical Libraries
      Highly flexible for use in many computing languages, programming
       environment...
Why bother?
 Numerical computation is difficult to do accurately
 Problems of
      Overflow / underflow
           Ho...
NAG development philosophy

 First priority: accuracy
 Second priority: performance
     How fast do you want the wrong...
Why Use NAG Maths Libraries?
 Global reputation for quality – accuracy,
    reliability and robustness…
   Extensively t...
NAG Library and Toolbox Contents
 NAG provides high-level maths and stats components
      Nonlinear equation solvers
  ...
Use of NAG Software in Finance
 Portfolio analysis / Index tracking / Risk management
      Optimisation, linear algebra...
Don’t take our word for it….
Financial Maths Professors speed up their optimization




                 Numerical Excelle...
Don’t take our word for it…...
Senior Quant @ Tier 1 bank
 “concerning the ‘nearest correlation’ algo.
 I have to say, it ...
NAG Libraries Ease of Integration
   C++ (various)                        Excel
   C# / .NET                           ...
NAG and Excel..
 Our libraries are
  easily accessible
  from Excel
      Calling DLLs using VBA
      NAG provide VB
 ...
NAG and .NET
NAG solutions for .NET
1. Call NAG C (or Fortran) DLL from C#

2. NAG Library for .NET (beta)
  “a more natur...
NAG Toolbox for MATLAB

 Contains essentially all NAG functionality
     not a subset
 Currently runs under Windows (32...
Case study – e04uc vs fmincon
A problem from a customer from a European
 bank.
The problem involves 48 variables and has...
Subset of Eigenvalues and Eigenvectors
Speedup




 Sunday, 31 January 2010   Numerical Excellence in Finance – January 2...
Best Advice – Use the Decision Trees




         Numerical Excellence in Finance – January 2010   18
NAG Library and Toolbox – recent additions
 Global optimization                More Copulas
 ANOVA – Analysis of       ...
Other NAG software
 NAG’s High Performance libraries
     NAG SMP Library (for multi/many core/processor)
     NAG Para...
Summary
 NAG for Quality, World-leading Numerical
  Software Components
     accurate, reliable, robust
     extensivel...
NAG Key Contacts
www.nag.com

Technical Support and Help
  support@nag.co.uk

Sales in France
  francois.cassier@nag.com
 ...
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Numerical Excellence In Finance N A G Jan2010

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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#.

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Numerical Excellence In Finance N A G Jan2010

  1. 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. 2. Agenda  NAG – An Introduction  NAG – Numerical Libraries Numerical Excellence in Finance – January 2010 2
  3. 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. 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. 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. 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. 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. 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. 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. 10. Don’t take our word for it…. Financial Maths Professors speed up their optimization Numerical Excellence in Finance – January 2010 10
  11. 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. 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. 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. 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. 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. 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. 17. Subset of Eigenvalues and Eigenvectors Speedup Sunday, 31 January 2010 Numerical Excellence in Finance – January 2010 NAG Toolbox for MATLAB 17 17
  18. 18. Best Advice – Use the Decision Trees Numerical Excellence in Finance – January 2010 18
  19. 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. 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. 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. 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

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