riskSimul {riskSimul}

Risk Quantification for Stock Portfolios under the T-Copula Model

Description

This package can estimate the tail loss probabilities and conditional excess for a stock portfolio. The log-returns are assumed to follow a t-copula model with generalized hyperbolic or t marginals.

Details

To simulate the tailloss probabilities of a portfolio for which the parameters of the t-copula model with generalized hyperbolic or t marginals are available the following two functions can be used.

SISTCopula() is the name of the function that uses stratified importance sampling (SIS) to estimate a single or several tailloss probabilities and the corresponding conditional excess in a very efficient way.

NVTCopula() estimates the same quantities using naive simulation (without variance reduction).

Author(s)

Wolfgang Hormann, Ismail Basoglu

References

I Basoglu, W Hormann. 2014. Efficient stratified sampling implementations in multiresponse simulation, in: Proceedings of the 2014 Winter Simulation Conference A. Tolk, S. Y. Diallo, I. O. Ryzhov, L. Yilmaz, S. Buckley, and J. A. Miller, eds.

I Basoglu, W. Hormann, and H. Sak. 2013. Optimally Stratified Importance Sampling for Portfolio Risk with Multiple Loss Thresholds. Optimization 62 (11): 1451-1471

Examples

R<- matrix(
c(1, 	0.554, 	0.632, 	0.419, 	0.400, 
  0.554,1, 		0.495, 	0.540, 	0.479,
  0.632,0.495, 	1, 		0.426, 	0.445,
  0.419,0.540, 	0.426, 	1, 		0.443,
  0.400,0.479, 	0.445, 	0.443, 	1),ncol=5)
  
pmg<- matrix(NA,ncol=5,nrow=5)  
colnames(pmg) <- c("lambda","alpha","beta","delta","mu")
pmg[1,] <- c(-0.602828, 8.52771, -0.533197, 0.014492, -0.000091)
pmg[2,] <- c(-1.331923, 2.72759, -2.573416, 0.019891, 0.001388)
pmg[3,] <- c(-1.602705, 3.26482, 1.456542, 0.035139, -0.001662)
pmg[4,] <- c(-1.131092, 15.13351, -1.722396, 0.014771, 0.001304)
pmg[5,] <- c(-0.955118, 31.14005, 0.896576, 0.015362, -0.000238)
 
portfo <- new.portfobj(nu=8.195,R=R,typemg="GH",parmg=pmg,c=rep(1,5),w=rep(0.2,5))

res1<- SISTCopula(n=10^4,npilot=c(10^3,3*10^3),portfobj=portfo,threshold=c(0.97,0.96,0.95,0.94),
                  stratasize=c(22,22),CEopt=FALSE,beta=0.75,mintype=0)