Several files for numerical or financial Math, free for download and with no warranty.
22.02.2015: what is new?

 Contents: More stuff: some special functions hypergeometric function 2F1 complex case for parameters and variable some (older) Maple files Garch, NIG, bivariate normal external callings with Maple DLLs and call-backs PARI Open source CAS and also fine for Numerics (allowing arbitrary precison and complex values), DLLs and examples how to use it from Maple or Excel. LCC-WIN32 'free' Win compiler admitting 100 decimals of precision, DLLs and examples how to use it from Maple or Excel. feedback is welcome & if you want to drop me any comment ...

classical binomial model

CRR_optimized.zip
Simplifying algebraic terms in the binomial model of Cox-Ross-Rubinstein for american options the
speed against the usual solution (cf Haug's book for a code) is improved by a factor of 40 - 50.
That file contains the Excel code (with inline comments as user docu) and examples for testing.
But it does not heal the combinatorical curse of double looping for American options ...

LeisenReimer_NP.zip
A binomial Leisen-Reimer tree avoids the oscillations of the usual binomial trees through a proper
choice of the tree parameters. Besides that the geometry is the same as for CRR the speed
is improved by a factor better than 40. The Excel file contains code and examples for testing.

LeisenReimer_properties.zip
The code for the above has been translated into a DLL (C source code included) for better speed to
play with the properties of the model within Excel (like extrapolation or what may happen through
numerical differentiation). I am somewhat too lazy to comment the various results.
Speed is about 880 prices per second for a 257 step tree and a 4-point Richardson extrapolation
gives an exactness of 6 - 7 digits for the european case (starting with 65 steps), while extrapolation
is not really helpfull in the case of early exercise.

pricing

BS&Vol_CodyMiller.xls.zip
This uses an improved version of the former through a better cumulative normal distribution (due to
Miller and Cody) and gives almost IEEE correctness in Excel (relativ error ~ 2 DBL_EPSILON).
On my Office PC it needs ~ 1 sec for 100000 prices, computing volatility needs 10 times more.
It also works for non-practical situations of data (strike=1.5*spot, time=some days, vol ~ 0.25%).

BS&Vol.xls.zip, BS&Vol_increased.xls.zip
Excel sheets to compute Black-Scholes prices and retrieve volatility. Yes, there are many such files.
The point is: these here are robust (working with the option premium and switch to 'normed' situations)
and the volatility is computed in the spirit of a fairly good initial guess (similar to Jaeckel).
The 2nd Excel file shows how one can increase the usual solution for vol and still gets given prices.
This (partially) solves the problem, that vol numerical is not well-defined as the inverse of a price.
It even works in extreme situations (like vol ~ 10% and small time or very far off the money).
A more sound solution has to use C code (or similar), but it is just a stripped down version of that.
Of course that depends on the quality of the pricing function and to judge it one can not use Excel.

perf_tst.zip
Performance test for Black-Scholes prices for pure VBA vs a C DLL (docu)

pdf_pricing.zip
BS pricing through integrating the pay off against the risk neutral density, both over spots and
logarithmic moneyness (i.e. Breeden-Litzenberger). That Excel sheet uses the DLL of the
integrator in integratorXL. A Maple sheet (as pdf) is included explaining the manipulations and
gives estimations, where to cut off to restrict to integration to finite intervalls

Simple example for Madan & Carr's Fourier method on option pricing: the case of constant volatility
(which means: Fourier method for Black-Scholes) using integration (instead of FFT).

stochastic volatility / Heston

Heston93-Check.pdf
Heston's model using characteristic functions (Maple)

Heston93_opt.zip
Optimized Excel solution for Heston's model using Gauss integration (undiscounted option values),
including reference values (from Maple) and graphics for the integrands (VolVol = 0 is missing),
short documentation.

Heston93_pdf.zip
Smiles and probability function (RND) for Heston's model with Excel; if strikes are extreme that may
fail for the smiles

Heston93_withDLL.zip
DLL version for Heston in Excel: one fast and one exact solution, gives back prices and/or volatility,
VolVol=0 is still missing (as I found to allow reaching it my solution become instable due to oscillation)

Heston-MC.pdf
A Monte-Carlo simulation for the Heston market model in Maple, somewhat slow ...
and I should have added 'reflecting/absorbing barrier' to be chosen ...

Heston_MC_hf_10.pdf
A speed-improved version of the above in Maple 10, almost 100 times faster

stochastic volatility / other models

NIG_tiny_withDLL.zip
Normal Inverse Gauss option pricer (with Esscher transform correction), Excel + DLL, and
a Maple worksheet with short explanations, cf Schoutens book "Levy Proccess in Finance"

VG_Pricer_short(Maple).pdf
A 'brute' option pricer for the Variance Gamma model (Madan, Carr, Chang 1998) in Maple

VG_small.zip
Variance Gamma model in Excel + DLL; it uses a gamma distribution pdfGamma(a,x)
which accepts large numerical arguments, short docu

Correction for VG (both Maple and Excel+DLL, 02. Jan 2014)
The paper has a typo. To get the correct values one has to use  - theta instead of + theta.
With that change of sign on input level the values are correct (without modifying the code),
see the discussion here.

volatility smile

GatheralSmileExample.zip
Example for Gatheral's parsimonious arbitrage-free implied volatility parametrization, in Maple as pdf
(24 Oct 2004: corrected some errors in that sheet)

GatheralSmile_Vola.zip
Fitting Gatheral's model to a given, empirical volatility smile. The estimates for initial parameters are
computed from data only. This is a pure Excel solution with least square fitting likewise either through
Excel's solver or a Levenberg-Marquardt method included as VBA project, short docu

GatheralSmile_Vola_DLL.zip
This is the same as above, but uses a DLL for fitting to speed things up.

PatSmile.zip
Continous family of smiles produced by the SABR model of Pat Hagan et al

SABR.pdf
Code in C and Visual Basic SABR_Code_VB_and_C.txt  and some graphs for the SABR model

various

European_Dividend_Alan_Example.pdf
Numerical example for european options and discontinous dividends, valuation method due to Alan Lewis

ExtremeSmiles.htm
Example using actual historical data for 'extreme' smiles and vol term structures after crashes

VolaTermDAX.zip
Example using actual historical data for 'visible volatility ATM term structure', if front month expires

Div1Year.gif
Dividend strip for the Swiss market regarding tax (both tax variants) in money and SMI points

Exane.gif
Example for sticky strike vs sticky delta from exane.com

Risk neutral density

a_brute_way_to_get_a_RND_from_option_prices.pdf
Using polynomial approximations and normal distribution for tails one can find a RND (over log
space), which is good enough to recover option prices and to get reasonable statistical results.

From_a_brute_RND_to_a_NIG_estimation.pdf
Having descriptive statistics for a RND one can fit a normal inverse Gauss model against option prices

RND_statistics_example.zip
This Excel sheet (with pure VBA code) shows, how one can estimate the descriptive statistics for
a RND directly from option prices using an approach similar to the VIX construction (where I use
a somewhat different discretization), no interpolation of volatility or prices is needed.
Here is a sketchy explanation for the method: Explaining the method in RND_statistics_example.pdf.

Numerics / Excel

Testing Excel 2010.pdf
This is a test report about Excel 2010 (beta), which seems to be a good improvemet over older versions.
For testing essentially taking an input in decimal number it is converted to the nearest IEEE 754 double, then
it is feed to Maple to be evaluated with higher precision, which then is rounded to the nearest IEEE again
to have a correct result (as far as it can be correct).  Only then it makes sense to compare against some
floating point result given by Excel.
For that a work around for the limitation of 15 decimal places in Excel is needed and provided as well.

Numerics / Excel / various financial stuff

simpleGarch11.zip
A simple GARCH(1,1) in Excel (using optimizer for the maximum likelihood and the statistics
for the time series) to estimate DAX spot volatility

Hist_Vol.zip
How to compute historical volatility in Excel with a variable time frame

Numerics / Excel / fitting

LMfit_logistic.zip
Example for Levenberg-Marquardt in Excel (pure VBA), which shows the essential algorithm
(ie: the linear algebra and the numerics), short documentation

LMfit3_with_weights.zip
It contains the complete usual Levenberg-Marquardt in Excel (pure VBA, dim = 1) and a version,
which allows weightings of data points

LeastSquareFitting.zip
An Excel interface to a DLL (containing a Levenberg-Marquardt method) for fitting curves against
data and estimating the parameters of the curve. The objective function is given within VBA and
can be chosen freely, short docu. As example Gatheral's SVI volatility smile is treated.

LMfit_logistic.zip
Example for Levenberg-Marquardt in Excel (pure VBA), which shows the essential algorithm
(ie: the linear algebra and the numerics), short documentation

LMfit3_with_weights.zip
It contains the complete usual Levenberg-Marquardt in Excel (pure VBA, dim = 1) and a version,
which allows weightings of data points

LeastSquareFitting.zip
An Excel interface to a DLL (containing a Levenberg-Marquardt method) for fitting curves against
data and estimating the parameters of the curve. The objective function is given within VBA and
can be chosen freely, short docu. As example Gatheral's SVI volatility smile is treated.

Numerics / Excel / cumulative normal distribution

cdfN2010_June.zip
This is my best cdf Normal in pure VBA. Absolute errors are fine, of course. The relative errors
are below 2 DBL_EPSILON or 3 ULPs over the full range (to be seen for negative inputs only)
as far as I am aware of it (i.e. I have no 'proof' for that, just tests, see the graphical test results).
Testing was done as sketched in the report "Testing Excel 2010.pdf" (so: precisely at IEEE level).
This is even much better than Excel 2010 (as of today), though I used my good old Excel 2000,
which I prefer (and yes, tiny relative errors at the left tail may be a little bit a matter of taste ...).
A short test docu sketches, how explicit test values and results can be achieved using Maple.

xmasNormDist.zip
cdf Normal (following George Marsaglia) for Excel, pure VBA with 19 digits (using data type CDec),
short documentation

cdfN_GMsimple_Test.zip
cdf Normal (following George Marsaglia) for Excel (pure VBA), simplified version, precise test
data calculated using Maple

bivariateNormal_Series.zip
This Excel sheet contains fast codes for the cumulative normal distribution in dimensions
1 and 2 through series developments up to machine precision in Excel, short documentation

cdfN_trivariate_mini.zip
This Excel sheet (with DLL for integration) compares implementations for the cumulative normal
distribution up to dimension 3 (references are given in the code and the short documentation), so
it is a kind of study (but not meant to be a complete overview). For high precision one would have
to switch to other environments of course, for example one can use LCC.

Numerics / Excel / random number generation

RNG_normal.xls.zip
This is an Excel solution with DLL for 3 very fast and good pseudo-random generators for normal
distributed numbers (Ziggurat [Marsaglia], ZIGNOR [Doornik], FastNorm3 [Wallace]). Speed is
about 1 sec for 10 Mio numbers.

Numerics / Excel / more ...

Brent_netlib.zip
Excel / VBA code for Brent's method to find Zeros or Minima in dimension 1. That are ports from
the Netlib C library. The original C sources have reasonable inline comments and serve as docu,
they are included.

integratorXL.zip
Numerical quadrature for Excel using a DLL which takes function names as arguments, short docu
applications: pricing by the risk neutral density (see above) and bi- and tri-variate normal densities
(to be done).

integratorXL_doubleIntegral.zip
The above integrator can be used to compute double integrals in Excel and as an example this is
shown for the cumulative bivariate normal distribution starting from a Gauss kernel only, short docu.

integrator_GaussKronrod.zip
An adaptive Gauss-Kronrod integrator, purely in VBA.

FFT_xl.zip
Fast Fourier Transform in Excel with VBA, that does not use Excel's slow and ugly built-in solution.
The docu explains conventions used, handling is shown by examples through a workbook.

Numerics / Excel / functional

wrapGSL.zip
Wrapper to use GSL from Excel: files
There is an Excel sheet enclosed how to work with function names as arguments (as Excel/VBA
does not have function pointers) for special functions and complex functions. One needs the free
GNU GSL lib to be installed and for a reasonable handling one should consult the documentation
for namings, arguments etc. That are the binary GSL files (DLLs) needed:  gslWIN32_1.3.zip
Documentation has to be done ...

Function_as_Arguments_in_Excel.zip
Several ways how to live with functions as arguments in Excel, VBA does not have this. Usually I do
not work with classes, but here it is seems to be one way out. That sheet grew from a discussion on
a forum, the main example is integration by Gauss-Legendre.

Working_with_Array_Functions_and_DLLs_in_Excel_VBA.pdf
This is a tutorial how to work with numerical arrays using Excel and DLLs: reading and writing from VBA
to DLL and vice versa (so it covers the old question "how to pass array data?"), using functions having
array arguments or array outputs.
It does not use SDK and all the overhead. And it is only through commented examples in C and VBA,
so it is a bit technical, but practical (and not thought as an introduction to DLL & VBA).
Here are the sources (Excel sheet, C code and DLL).

That tutorial is a short variant of "Working with Array Functions" having just implementation in mind.
Here are the sources (Excel sheet, C code and DLL).

This is for working with C-strings between VBA and a DLL, quite similar to the numerical case above.
Here are the sources (Excel sheet, C code and DLL).

All the VBA projects are unprotected while the source code for DLLs usually is not provided.
Many are just pure VBA code, but if a sheet uses a DLL then set the correct pathes within the
project. Open Excel's debug window to watch results being printed out.

31 Mar 2010: uploaded  Testing Excel 2010.pdf

11 May 2006: uploaded some files around the risk neutral density from option prices

18 Jan 2006: uploaded high precision for cumulative normal in dim <= 3 to the LCC subdirectory

17 Dec 2005: reorganized to give a better overview

12 Dec 2005: linked to my LCC files - giving 100 digits precision

23 Oct 2005: uploaded gslWIN32_1.3.zip (the DLLs for GSL)

06 Oct 2005: uploaded GatheralSmile_Vola_DLL, a DLL version

07 Jul 2005: uploaded Heston_MC_hf_10.pdf (speed in Maple 10 improved)

28 May 2005: uploaded Levenberg-Marquardt with weights

30 Jan 2005: uploaded bivariateNormal_Series (contains the deleted cdfN_Marsaglia_Taylor.txt)