Cumulative Bivariate Distribution error in the tails - BivariateCumulativeNormalDistributionWe04DP

Posted by Fabien Le Floc'h on Feb 21, 2013; 12:31pm
URL: http://quantlib.414.s1.nabble.com/Cumulative-Bivariate-Distribution-error-in-the-tails-BivariateCumulativeNormalDistributionWe04DP-tp14068.html

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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