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- The FinDer system is easy to use. One can use it in a
spreadsheet, which we provide. One simply goes to a drop down menu
called FinDer that is part of the tool bar at the top of the Excel
Spreadsheet. The FinDer gives several possibilities for different
methods of generating the LDS sequences.
One selects one and indicates
some simple inputs such as the number of dimensions and the number of
scenarios. One can also adjust parameters such as skip, which controls
the number of elements at the start of the sequence that are skipped.
There are a couple other technical parameters that the system
automatically sets defaults for but which you can adjust if desired.
Given these, one hits the button and the spreadsheet is filled with the
LDS numbers.
These can be distributed between 0 and 1 or be normally
distributed. These numbers are all uncorrelated. Correlations can be
introduced with your own application software. The MFC ESG will do this correlation for generating interest
rate and other variables. The user can use the MFC ESG to add additional variables for simulating and
adding whatever correlations are desired.
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- The idea behind LDS can be explained with reference to a system
that involves simulating two random variables only. This could be the
interest rate next month and the month after that. One can take these
two interest rates and plot them on a graph, the value of one on the
x-axis and the value of the other on the y-axis.
When one does this each
scenario of interest rates is one point on the graph. Given a single
point, we know the interest rate in both periods. For the first period
by looking at its x-coordinate, and for the second period by looking at
its y-coordinate.
If we use Monte Carlo to generate these points, we
will find that by random chance we get some points near previously
generated points. Likewise, we also find that some areas that had no
points, don't get any more points as we add more simulations. To measure
this effect, mathematicians developed quantitative measures. The book by
Harald Niederreiter, Random Number Generation and Quasi-Monte Carlo
Methods, 1992, Society for Industrial and Applied Mathematics, CBMS,
volume 63 explains these measures and gives references to their history
in simulation.
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- For applications in finance and insurance, work was done at
Columbia University on both new sequences and their application to
pricing financial instruments and calculating Value at Risk (VaR). Some
of this work is patented, but additional proprietary methods are
included in the FinDer™ software. Anargyoros Papageorgiou of Columbia
University is actively engaged in developing new enhancements to the
Columbia system and is adding new generators for LDS sequences to the
FinDer™ system.
- The FinDer™ system has been used in both pricing applications by
major Wall Street firms and by users in the insurance and actuarial
area. It has been applied both to pricing as well as to setting capital
levels and calculating tail VaR.
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- For ease of users in one stop shopping, especially in actuarial applications, Mathematical Finance Company is happy to be part of bringing
this leading research to the financial community.
On-line tutorial on low discrepancy sequences.
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- For more information about Finder, please see the following page at http://www.cs.columbia.edu/~ap/
or http://www.cs.columbia.edu/~traub/html/body_patent_information.html.
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