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Cumulative Multivariate Normal Distribution

4 messages · Chiquoine, Ben, davidr at rhotrading.com, Krishna Kumar

davidr at rhotrading.com
# 
Espen Haug has code for a trivariate cum norm in his second edition, p.
482, section 13.4, due to Alan Genz.
(You also need cor_23)
HTH,

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 Chiquoine,
Ben
Sent: Friday, September 19, 2008 1:18 PM
To: r-sig-finance
Subject: [R-SIG-Finance] Cumulative Multivariate Normal Distribution

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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Krishna Kumar
# 
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:
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2 days later
davidr at rhotrading.com
# 
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
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.
,2),1,100,2)
Chiquoine, Ben wrote:
for