simulationStudy.R

library(DEoptim)

# Parameters
mu_= 0.05
ss_= 0.3
lambda_= 25
mu2_=0.01
sigma_=0.1
TotalTime = 50
delta=1/252
simulationSize = 100

# Store the results 
par = matrix(0,simulationSize,5)

lower = c(-100,0.00001,0.00001,-100,0.001) #lower bounds of the search
upper = c(100,100,100,100,100) #upper bounds of the search

for(i in 1:simulationSize)
{
  print(paste("Simulation Number :",i))
  
  #Simulate the path
  set.seed( as.integer((as.double(Sys.time())*1000+Sys.getpid()) %% 2^31) )
  x = diff(simulateJump(mu_,ss_,lambda_,mu2_,sigma_,TotalTime,delta)[,2])

  #Using the default settings for DEoptim
  set.seed(1234)
  outDEoptim = DEoptim(nll_jumps, lower = lower,upper = upper)
  
  #Store the parameters
  par[i,] = outDEoptim$optim$bestmem
}

# Convergence plot
plot(outDEoptim, plot.type = "bestvalit", type = 'b')

mean(par[,1])
mean(par[,2])
mean(par[,3])
mean(par[,4])
mean(par[,5])

sd(par[,1])
sd(par[,2])
sd(par[,3])
sd(par[,4])
sd(par[,5])


hist(par[,1], 
     main="Histogram for the drift", 
     xlab=expression(mu), 
     border="blue", 
     xlim=c(-0.2,0.2),
     las=1, 
     breaks=10,prob=TRUE)
abline(v=0.05,col="red")
lines(density(par[,1]),col="black")
legend("topright", legend=c("True value"),
       col=c("red"), lty=1:2, cex=0.8)


hist(par[,2], 
     main="Histogram for the diffusive vol", 
     xlab=expression(sigma), 
     border="blue", 
     xlim=c(0.29,0.31),
     las=1, 
     breaks=8,prob=TRUE)
abline(v=0.3,col="red")
lines(density(par[,2]),col="black")
legend("topright", legend=c("True value"),
       col=c("red"), lty=1:2, cex=0.8)


hist(par[,3], 
     main="Histogram for the jump intensity", 
     xlab=expression(lambda), 
     border="blue", 
     xlim=c(21,28),
     las=1, 
     breaks=10,prob=TRUE)
abline(v=25,col="red")
lines(density(par[,3]),col="black")
legend("topright", legend=c("True value"),
       col=c("red"), lty=1:2, cex=0.8)


hist(par[,4], 
     main="Histogram for the mean jump size", 
     xlab= "mean jump size", 
     border="blue", 
     xlim=c(0.001,0.02),
     breaks=10,prob=TRUE)
abline(v=0.01,col="red")
lines(density(par[,4]),col="black")
legend("topright", legend=c("True value"),
       col=c("red"), lty=1:2, cex=0.8)


hist(par[,5], 
     main="Histogram for the jump size standard deviation", 
     xlab="jump size standard deviation", 
     border="blue", 
     xlim=c(0.085,0.11),
     las=1, 
     breaks=10,prob=TRUE)
abline(v=0.1,col="red")
lines(density(par[,5]),col="black")
legend("topright", legend=c("True value"),
       col=c("red"), lty=1:2, cex=0.8)