findiff.R

#'@title Pricing option using the finite difference method
#'@desciption 
#'\code{findiff} function is used to find the price of the option using the 
#'finite difference method by taking the rate of return , standard deviation,
#'the stock price,the time to maturity,the strike price
#'@param r risk free rate of return
#'@param sd standard deviation
#'@param t time to maturity
#'@param x strike price
findiff<-function(r,sd,s,t,x,type = c("call","put")){
        dy<-(log(100*s)-log(1/s))/200
        y1<-seq(log(1/s),log(2*s),dy)
        nr<-length(y1)
        dt<-t/200
        r<-r/100
        sd<-sd/100
        t1<-seq(t,0,-dt)
        nc<-length(t1)
        m1<-matrix(nrow=nr,ncol=nc)
        w1<-0.5*((sd/dy)^2-(r-(sd^2)/2)/dy)*dt
        w3<-0.5*((sd/dy)^2+(r-(sd^2)/2)/dy)*dt
        w2<-1-((sd/dy)^2)*dt
        tp = type[1]
        if(tp=="call"){
        for(i in 1:nr){
        m1[i,nc]<-max(0,exp(y1[nr+1-i])-x)
        }
        m1[nr,]<-0
        for(i in (nc-1):1){
        for(j in (nr-1):1){
        if(j==1){
            m1[1,i]<-exp(y1[nr])*dy+m1[2,i]
        }
        else{
            m1[j,i]<-(w1*m1[j-1,i+1]+w2*m1[j,i+1]+w3*m1[j+1,i+1])/(1+r*dt)
        }
        }
        }
        }
        if(tp=="put"){
          for(i in 1:nr){
            m1[i,nc]<-max(0,x-exp(y1[nr+1-i]))
          }
          m1[nr,]<-0
          for(i in (nc-1):1){
            for(j in (nr-1):1){
              if(j==1){
                m1[1,i]<-exp(y1[nr])*dy+m1[2,i]
              }
              else{
                m1[j,i]<-(w1*m1[j-1,i+1]+w2*m1[j,i+1]+w3*m1[j+1,i+1])/(1+r*dt)
              }
            }
          }
        }
        
          
        
        nn<-m1[(nr-which(abs(y1-log(s)) == min(abs(y1-log(s))))),1]
        print(nn)

}