[R-SIG-Finance] Cumulative Multivariate Normal Distribution

Krishna Kumar kriskumar at earthlink.net
Sat Sep 20 01:00:30 CEST 2008

Hi Ben,

Have you looked at pmvnorm  in package mvtnorm.? This is Genz's method, 
I am working with Jan-Dash on a new approximation
for cumulative normal and I have some semi-tested code of that, we are 
currently testing it for Worst-of and other rainbow type options.

The alternative to price these would be to use monte-carlo to do the 
integration and just price them using that, see for example
 the attached R code which generates multi-variate paths. You can then 
use these paths to then compute the discounted payoff function.

Hope this helps,


ps:  the drift is simply the risk-neutral drift however for currencies 
you have to factor in the quanto adjustment.
Also this piece of code was written about 4 years ago so pardon the 
coding standards.


Chiquoine, Ben wrote:
> Hi,
> Does anyone know of a function similar to the CBND function for
> multivariate distributions?  I've seen a couple but what I am really
> looking for is one that will take (x1,x2,x3,cor112,cor113) as inputs.
> Alternatively, does anyone know of a package with built in functions for
> pricing a worst of three color rainbow options?  Any help along these
> lines would be greatly appreciated.  
> Thanks,
> Ben
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