WilsonMongwe

library(httr)
library(httpuv)
library(RColorBrewer)
library(twitteR)
library(tm)
library(wordcloud)
library(base64enc)
library(devtools)
library(ROAuth)

WilsonMongwe

#This is the code for the negative log likelihood function
#for the JUmp-difusion model

nll_jumps<-function(w)
{
  mu=w[1] # drift
  s=(w[2]) # diffsuive vol
  lam=(w[3]) # jump frequency
  mu_j=w[4] # jump size

WilsonMongwe

simulateJump=function(mu_,ss_,lambda_,mu2_,sigma_,TotalTime,delta)
{
  Sn=0
  times <- c(0)
  while(Sn <= TotalTime)
  {
    n <- length(times)
    u <- runif(1)
    expon <- -log(u)/lambda_
    Sn <- times[n]+expon

WilsonMongwe

library(DEoptim)

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

WilsonMongwe

first_moment<-function(s_0,r,TotalTime)
{
  (s_0*(exp(r*TotalTime)-1))/(r*TotalTime)
}

second_moment<-function(s_0,r,s,TotalTime)
{
  part1 = (2*s_0^2)/(r*(r+s^2)*(2*r+s^2)*TotalTime^2)
  
  part2 = r*exp((2*r+s^2)*TotalTime)-(2*r+s^2)*exp(r*TotalTime)+r+s^2