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# WilsonMongwe/Simulation.R Secret

Last active Oct 6, 2015
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 #### Author: Wilson Mongwe #### Date: 05/10/2015 #### Website: www.wilsonmongwe.co.za #### Title: Formular for Lee and Mykland Test(2008) simulateJump=function(mu_,ss_,lambda_,mu2_,sigma_,TotalTime,delta,compare,size) { Sn=0 times <- c(0) while(Sn <= TotalTime) { n <- length(times) u <- runif(1) expon <- -log(u)/lambda_ Sn <- times[n]+expon times <- c(times, Sn) } times=times[-length(times)] #the last time is beyond TotalTime, so i delete from the vector times indicator=seq(from=0,to=0,length=TotalTime) # if there are jumps or not between two times jumpSize=seq(from=0,to=0,length=TotalTime) # stores the size of the jump delta=1/252 t=(0:(length=(TotalTime)-1)) for(m in 2:length(times)) { for(k in 2: length(t)) { if( t[k-1]<=times[m] && times[m]<=t[k]) { indicator[k]=1 if(compare) { u = runif(1,0,1) signA=1 if(u<=0.5) { signA=-1} jumpSize[k]=ss_*size*signA } else { jumpSize[k]=rnorm(1,mean=mu2_,sd=sigma_) } } } } stock=seq(from=0,to=0,length=TotalTime) stock[1]=10 for(i in 2:TotalTime) { stock[i]=stock[i-1]+(mu_-0.5*ss_^2)*delta+ss_*sqrt(delta)*rnorm(1)+jumpSize[i]*indicator[i] } final=cbind(stock) return(final) } simulateGBM=function(mu_,ss_,TotalTime,delta) { stock=seq(from=0,to=0,length=TotalTime) stock[1]=10 for(i in 2:TotalTime) { stock[i]=stock[i-1]+(mu_-0.5*ss_^2)*delta+ss_*sqrt(delta)*rnorm(1) } indicator=stock*0 final=cbind(stock) return(final) }