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Monte Carlo simulation for VaR estimation

5 messages · David Reiner, andrija djurovic, Arun Kumar Saha

Original
David Reiner
# 
I'm guessing that you would want to specify the correlation as given as you have the volatilities,
hence use a covariance matrix in MASS::mvrnorm to generate your 'sh'.
That shuld get you started anyway.
Rolling your own with use of Cholesky is OK, too, of course, but others have done lots of hard work do give you better results.

(
There are many other functions in various packages to generate multivariate normal samples if you look; e.g.,
found 532 matches;  retrieving 20 pages, 400 matches.
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
)

HTH,
-- David


-----Original Message-----
From: r-sig-finance-bounces at r-project.org [mailto:r-sig-finance-bounces at r-project.org] On Behalf Of andrija djurovic
Sent: Friday, November 18, 2011 3:02 AM
To: r-sig-finance at r-project.org
Subject: [SPAM] - [R-SIG-Finance] Monte Carlo simulation for VaR estimation - Email found in subject

Dear users,
I need help in understanding steps of Monte Carlo simulation for VaR estimation. Here is the simplified example of what i was trying to do, but I suppose this is not appropriate way for performing MC simulation.

Suppose that our portfolio consist of x1 and x2 (with equal weights), which returns are given:

sh<-matrix(c(rnorm(100,0,0.01),rnorm(100,0,0.015)),ncol=2)
colnames(sh)<-c("x1","x2")
w<-matrix(c(0.5,0.5),ncol=1)
pr<-sh%*%w
pmu<-mean(pr)
sigma<-cov(sh)
pvar<-t(w)%*%sigma%*%w

Now I was trying to generate 10 scenarios (keeping the correlation between
x1 and x2). Then calculate portfolio mean for each scenario and from that mean distribution  calculate 95% VaR. Here I am sure  these aren't good steps and I that I am missing something in part of keeping a correlation between x1 and x2:

l<-list("vector",10)
cd<-chol(cov2cor(sigma))
#generate 10 scenarios#
mu<-apply(sh,2,mean)
sd<-apply(sh,2,sd)
for (i in 1:10)
{
l[[i]]<-matrix(c(rnorm(10,mu[1],sd[1]),rnorm(10,mu[2],sd[2])),ncol=2)%*%cd
}

mc<-sapply(l,function(x) mean(x%*%w))

quantile(mc,p=0.05)


Thanks in advance and any help is really appreciated.

Andrija


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2 days later
Arun Kumar Saha
# 
Hi Andrija, I am not sure why you need to replicate 10 times. Instead you
should want to replicate once with, say, 1000 simulation and then get the
5th percentile of the portfolio return distribution. Here you go:

l<-list("vector",1) 
mu<-apply(sh,2,mean) 
sigma<-cov(sh) 
#generate 1 replication
l<-list("vector",1) 
for (i in 1:1) 
{ 
l[[i]]<-rmnorm(1000,mu,sigma) # this will generate 1000 possible asset
returns based on the same statistical characteristic as in 'sh'
							  # I assume, 'sh' is your historical asset return
} 

l <- l[[1]]
pr_simulated <- apply(l, 1, function(x) return(sum(x * c(0.5, 0.5)))) #
simulated portfolio return
quantile(pr_simulated, 0.05, type = 3) # your Portfolio VaR (95%)

PS: I used rmnorm() function for drawing random number from a multivariate
normal, which is from 'mnormt' package.

HTH,

Thanks and regards,
_____________________________________________________

Arun Kumar Saha, FRM
QUANTITATIVE RISK AND HEDGE CONSULTING SPECIALIST
Visit me at: http://in.linkedin.com/in/ArunFRM
_____________________________________________________


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