[R-SIG-Finance] Cumulative Multivariate Normal Distribution

davidr at rhotrading.com davidr at rhotrading.com
Mon Sep 22 15:11:24 CEST 2008

Just be aware that the output of pmvnorm is not deterministic.
Genz's method for trivariate (given in Haug) is deterministic.

David L. Reiner, PhD
Head Quant
Rho Trading Securities, LLC

-----Original Message-----
From: r-sig-finance-bounces at stat.math.ethz.ch
[mailto:r-sig-finance-bounces at stat.math.ethz.ch] On Behalf Of Krishna
Sent: Friday, September 19, 2008 6:01 PM
To: Chiquoine, Ben
Cc: r-sig-finance
Subject: Re: [R-SIG-Finance] Cumulative Multivariate Normal Distribution

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
> pricing a worst of three color rainbow options?  Any help along these
> lines would be greatly appreciated.  
> Thanks,
> Ben
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