ESGtoolkit (version 0.2.0)

simshocks: Underlying gaussian shocks for risk factors' simulation.

Description

This function makes simulations of correlated or dependent gaussian shocks for risk factors.

Usage

simshocks(
  n,
  horizon,
  frequency = c("annual", "semi-annual", "quarterly", "monthly", "weekly", "daily"),
  method = c("classic", "antithetic", "mm", "hybridantimm", "TAG"),
  family = NULL,
  par = NULL,
  par2 = NULL,
  type = c("CVine", "DVine"),
  seed = 123
)

Arguments

n

number of independent observations for each risk factor.

horizon

horizon of projection.

frequency

either "annual", "semi-annual", "quarterly", "monthly", "weekly", or "daily" (1, 1/2, 1/4, 1/12, 1/52, 1/252).

method

either classic monte carlo, antithetic variates, moment matching, hybrid antithetic variates + moment matching or "TAG" (see the 4th reference for the latter).

family

the same as CDVineSim from package CDVine. A d*(d-1)/2 integer vector of C-/D-vine pair-copula families with values 0 = independence copula, 1 = Gaussian copula, 2 = Student t copula (t-copula), 3 = Clayton copula, 4 = Gumbel copula, 5 = Frank copula, 6 = Joe copula, 7 = BB1 copula, 8 = BB6 copula, 9 = BB7 copula, 10 = BB8 copula, 13 = rotated Clayton copula (180 degrees; "survival Clayton"), 14 = rotated Gumbel copula (180 degrees; "survival Gumbel"), 16 = rotated Joe copula (180 degrees; "survival Joe"), 17 = rotated BB1 copula (180 degrees; "survival BB1"), 18 = rotated BB6 copula (180 degrees; "survival BB6"), 19 = rotated BB7 copula (180 degrees; "survival BB7"), 20 = rotated BB8 copula (180 degrees; "survival BB8"), 23 = rotated Clayton copula (90 degrees), 24 = rotated Gumbel copula (90 degrees), 26 = rotated Joe copula (90 degrees), 27 = rotated BB1 copula (90 degrees), 28 = rotated BB6 copula (90 degrees), 29 = rotated BB7 copula (90 degrees), 30 = rotated BB8 copula (90 degrees), 33 = rotated Clayton copula (270 degrees), 34 = rotated Gumbel copula (270 degrees), 36 = rotated Joe copula (270 degrees), 37 = rotated BB1 copula (270 degrees), 38 = rotated BB6 copula (270 degrees), 39 = rotated BB7 copula (270 degrees), 40 = rotated BB8 copula (270 degrees)

par

the same as CDVineSim from package CDVine. A d*(d-1)/2 vector of pair-copula parameters.

par2

the same as CDVineSim from package CDVine. A d*(d-1)/2 vector of second parameters for pair-copula families with two parameters (t, BB1, BB6, BB7, BB8; no default).

type

type of the vine model: 1 : C-vine 2 : D-vine

seed

reproducibility seed

Value

If family and par are not provided, a univariate time series object with simulated gaussian shocks for one risk factor. Otherwise, a list of time series objects, containing gaussian shocks for each risk factor.

Details

The function shall be used along with simdiff, in order to embed correlated or dependent random gaussian shocks into simulated diffusions. esgplotshocks can help in visualizing the type of dependence between the shocks.

References

Brechmann, E., Schepsmeier, U. (2013). Modeling Dependence with C- and D-Vine Copulas: The R Package CDVine. Journal of Statistical Software, 52(3), 1-27. URL http://www.jstatsoft.org/v52/i03/.

Genz, A. Bretz, F., Miwa, T. Mi, X., Leisch, F., Scheipl, F., Hothorn, T. (2013). mvtnorm: Multivariate Normal and t Distributions. R package version 0.9-9996.

Genz, A. Bretz, F. (2009), Computation of Multivariate Normal and t Probabilities. Lecture Notes in Statistics, Vol. 195., Springer-Verlag, Heidelberg. ISBN 978-3-642-01688-2.

Nteukam T, O., & Planchet, F. (2012). Stochastic evaluation of life insurance contracts: Model point on asset trajectories and measurement of the error related to aggregation. Insurance: Mathematics and Economics, 51(3), 624-631. URL http://www.ressources-actuarielles.net/EXT/ISFA/1226.nsf/0/ab539dcebcc4e77ac12576c6004afa67/$FILE/Article_US_v1.5.pdf

See Also

simdiff, esgplotshocks

Examples

# NOT RUN {
# Number of risk factors
d <- 6

# Number of possible combinations of the risk factors
dd <- d*(d-1)/2

# Family : Gaussian copula for all
fam1 <- rep(1,dd)

# Correlation coefficients between the risk factors (d*(d-1)/2)
par1 <- c(0.2,0.69,0.73,0.22,-0.09,0.51,0.32,0.01,0.82,0.01,
        -0.2,-0.32,-0.19,-0.17,-0.06)

                 
# Simulation of shocks for the 6 risk factors
simshocks(n = 10, horizon = 5, family = fam1, par = par1)


# Simulation of shocks for the 6 risk factors
# on a quarterly basis
simshocks(n = 10, frequency = "quarterly", horizon = 2, family = fam1, 
par = par1)


# Simulation of shocks for the 6 risk factors simulation
# on a quarterly basis, with antithetic variates and moment matching. 
s0 <- simshocks(n = 10, method = "hyb", horizon = 4, 
family = fam1, par = par1)

 
s0[[2]]
colMeans(s0[[1]])
colMeans(s0[[5]])
apply(s0[[3]], 2, sd)
apply(s0[[4]], 2, sd)

# }