# [R-SIG-Finance] Cumulative Multivariate Normal Distribution

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

-----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
Kumar
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.
http://arxiv.org/pdf/cs.CE/0611061

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,

Best
Krishna

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.

>assetPath<-multiassetpath(c(2,3),c(-0.1,-0.2),2,matrix(c(1,0.2,0.2,1),2
,2),1,100,2)

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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