Cumulative Multivariate Normal Distribution
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.
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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