[R] The best solver for non-smooth functions?
Cren
oscar.soppelsa at bancaakros.it
Wed Jul 18 22:00:19 CEST 2012
# Hi all,
# consider the following code (please, run it:
# it's fully working and requires just few minutes
# to finish):
require(CreditMetrics)
require(clusterGeneration)
install.packages("Rdonlp2", repos= c("http://R-Forge.R-project.org",
getOption("repos")))
install.packages("Rsolnp2", repos= c("http://R-Forge.R-project.org",
getOption("repos")))
require(Rdonlp2)
require(Rsolnp)
require(Rsolnp2)
N <- 3
n <- 100000
r <- 0.0025
ead <- rep(1/3,3)
rc <- c("AAA", "AA", "A", "BBB", "BB", "B", "CCC", "D")
lgd <- 0.99
rating <- c("BB", "BB", "BBB")
firmnames <- c("firm 1", "firm 2", "firm 3")
alpha <- 0.99
# One year empirical migration matrix from Standard & Poor's website
rc <- c("AAA", "AA", "A", "BBB", "BB", "B", "CCC", "D")
M <- matrix(c(90.81, 8.33, 0.68, 0.06, 0.08, 0.02, 0.01, 0.01,
0.70, 90.65, 7.79, 0.64, 0.06, 0.13, 0.02, 0.01,
0.09, 2.27, 91.05, 5.52, 0.74, 0.26, 0.01, 0.06,
0.02, 0.33, 5.95, 85.93, 5.30, 1.17, 1.12, 0.18,
0.03, 0.14, 0.67, 7.73, 80.53, 8.84, 1.00, 1.06,
0.01, 0.11, 0.24, 0.43, 6.48, 83.46, 4.07, 5.20,
0.21, 0, 0.22, 1.30, 2.38, 11.24, 64.86, 19.79,
0, 0, 0, 0, 0, 0, 0, 100
)/100, 8, 8, dimnames = list(rc, rc), byrow = TRUE)
# Correlation matrix
rho <- rcorrmatrix(N) ; dimnames(rho) = list(firmnames, firmnames)
# Credit Value at Risk
cm.CVaR(M, lgd, ead, N, n, r, rho, alpha, rating)
# Risk neutral yield rates
Y <- cm.cs(M, lgd)
y <- c(Y[match(rating[1],rc)], Y[match(rating[2],rc)],
Y[match(rating[3],rc)]) ; y
# The function to be minimized
sharpe <- function(w) {
- (t(w) %*% y) / cm.CVaR(M, lgd, ead, N, n, r, rho, alpha, rating)
}
# The linear constraints
constr <- function(w) {
sum(w)
}
# Results' matrix (it's empty by now)
Results <- matrix(NA, nrow = 3, ncol = 4)
rownames(Results) <- list('donlp2', 'solnp', 'solnp2')
colnames(Results) <- list('w_1', 'w_2', 'w_3', 'Sharpe')
# See the differences between different solvers
rho
Results[1,1:3] <- round(donlp2(fn = sharpe, par = rep(1/N,N), par.lower =
rep(0,N), par.upper = rep(1,N), A = t(rep(1,N)), lin.lower = 1, lin.upper =
1)$par, 2)
Results[2,1:3] <- round(solnp(pars = rep(1/N,N), fun = sharpe, eqfun =
constr, eqB = 1, LB = rep(0,N), UB = rep(1,N))$pars, 2)
Results[3,1:3] <- round(solnp2(par = rep(1/N,N), fun = sharpe, eqfun =
constr, eqB = 1, LB = rep(0,N), UB = rep(1,N))$pars, 2)
for(i in 1:3) {
Results[i,4] <- abs(sharpe(Results[i,1:3]))
}
Results
# In fact the "sharpe" function I previously defined
# is not smooth because of the cm.CVaR function.
# If you change correlation matrix, ratings or yields
# you see how different solvers produce different
# parameters estimation.
# Then the main issue is: how may I know which is the
# best solver at all to deal with non-smooth functions
# such as this one?
--
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