Hello,
Do your results show problems with double (x32) or long double (x64), or both? I am asking because I am using 64 bit Visual Studio, where long double is the same as double.
You should contact Graeme West about this; I’m sure he would be interested as the QuantLib algorithm is his modification of an algorithm published by Genz.
I am very interested in fast, accurate algorithms for the bivariate cumulative normal and t-distributions. Do you have sample code which illustrates this problem, and would you be willing to share it with me?
Thanks,
Dale Smith, Ph.D.
Senior Financial Quantitative Analyst
Risk & Compliance
Fiserv
Office: 678-375-5315
From: Fabien Le Floc'h [mailto:[hidden email]]
Sent: Thursday, February 21, 2013 7:32 AM
To: [hidden email]
Subject: [Quantlib-users] Cumulative Bivariate Distribution error in thetails - BivariateCumulativeNormalDistributionWe04DP
Hello,
BivariateCumulativeNormalDistributionWe04DP is imprecise in the tails: when the correlation is high and the x,y are very high (near +/-7), the results returned can exhibit some wiggling due to numerical noise. In practice this can lead to nonsensical greeks.
A simple fix is to evaluate the univariate cumulative normal distribution where it is most precise, that is in the lower tail rather than in the upper tail, because one can achieve much higher accuracy around 0.0 vs around 1.0 with double numbers.
Attached is a small patch for BivariateCumulativeNormalDistributionWe04DP along with a unit test.
Best regards,
Fabien Le Floc'h
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