# simulation(lognormal)
mu<-0.1
sigma<-0.2
z<-rnorm(1000)
y<-matrix(mu+sigma*z,100,10)
Y<-matrix(rep(1,1000),100,10)
S<-matrix(rep(1,1000),100,10)
for (j in 1:10){
Y[,j]<-cumsum(y[,j])
S[,j]<-exp(Y[,j])
}
Y
S
# simulation(ar1)
mu<-0.1
sigma<-0.2
a<-0.7
Y<-matrix(rep(1,1100),100,11)
S<-matrix(rep(1,1100),100,11)
for (i in 1:100){
Y[i,1]<-mu@#l
S[i,1]<-exp(mu)@#l
for (j in 1:10){
Y[i,j+1]<-mu+a*(Y[i,j]-mu)+sigma*rnorm(1)
S[i,j+1]<-exp(Y[i,j+1])
}
}
Y[,-1] #1ڂO
S[,-1]@#
# simulation(garch)
mu<-0.1
alpha0<-0.0001
alpha1<-0.08
beta<-0.9
Y<-matrix(rep(1,1100),100,11)
sigma2<-matrix(rep(1,1100),100,11)
S<-matrix(rep(1,1100),100,11)
for (i in 1:100){
Y[i,1]<-mu@#l
S[i,1]<-exp(mu)@#l
sigma2[1,1]<-alpha0/(1-alpha1-beta)
for (j in 1:10){
sigma2[i,j+1]<-alpha0+alpha1*(Y[i,j]-mu)^2+beta*sigma2[i,j]
Y[i,j+1]<-mu+a*(Y[i,j]-mu)+sqrt(sigma2[i,j+1])*rnorm(1)
S[i,j+1]<-exp(Y[i,j+1])
}
}
Y[,-1] #1ڂO
S[,-1]@#
# simulation(RSLN2)
p12<-0.004
p21<-0.016
Y<-matrix(rep(1,1000),100,10)
S<-matrix(rep(1,1000),100,10)
K<-matrix(rep(1,1000),100,10)
mu<-c(0.2,-0.05)
sigma<-c(0.1,0.3)
for (i in 1:100){
z<-rnorm(1)
u<-runif(1)
if(u<0.2){rho<-1
}else {rho<-2}
Y[i,1]<-mu[rho]+sigma[rho]*z
S[i,1]<-exp(Y[i,1])
K[i,1]<-rho
for (j in 2:10){
u<-runif(1)
if(rho<2&u>p12){rho<-1
} else {rho<-2}
if(rho>1&u>p21){rho<-2
}else {rho<-1}
K[i,j]<-rho
z<-rnorm(1)
Y[i,j]<-mu[rho]+sigma[rho]*z
S[i,j]<-exp(Y[i,j])
}
}
K
Y
