bino tree.R

#'@title Construct a binowmial Tree
#'@description
#'\code{bino} Constructs the binomial tree for an american option and calculates
#'the option price by taking type,strike price(k),Strike Price(st),volatility(vol),
#'dividend yield(yield),Risk free rate of return(rf),time to maturity(time),n is the number of steps
#'@param type for call option 0 for put option 1
#'@param k strike price
#'@param st stock price
#'@param volatility vol volatility(e.g 30 for 30%)
#'@param yield dividend yield(e,g 3 for  3%)
#'@param rf risk free rate(e.g 6.5 for 6.5%)
#'@param time time to maturity(e.g 3 for 3 months)
#'@param n number of steps(e.g 2 for 2 steps)
bino<-function(type,k,st,vol,yield,rf,time,n){

    m_price<-matrix(nrow=n+1,ncol=n+1)
        m_payoff<-matrix(nrow=n+1,ncol=n+1)
        u<-exp((vol/100)*sqrt(time/(12*n)))
        print(u)
        d<-1/u
        print(d)
        deltaT<-time/(12*n)
        p<-(exp((rf-yield)*deltaT/100)-d)/(u-d)
        print(p)
        q<-1-p
        price<-st
        n<-n+1

        for(i in 1:n){
            m_price[i,i]<-st*(d^(i-1))
                if(type==1){
                    m_payoff[i,i]<-max(m_price[i,i]-k,0)
                }
                else{
                    m_payoff[i,i]<-max(k-m_price[i,i],0)
                }
            price<-m_price[i,i]
                for(j in i:n){
                    m_price[i,j]<-price
                        if(type==1){
                            m_payoff[i,j]<-max(m_price[i,j]-k,0)
                        }
                        else{
                            m_payoff[i,j]<-max(k-m_price[i,j],0)
                        }
                    price<-price*u
                }
        }
    m_final<-matrix(nrow=n,ncol=n)
        for(i in n:1){
            for(j in 1:(i-1)){
                m_final[j,i-1]<-max(exp(-rf*deltaT/100)*(m_payoff[j,i]*p+m_payoff[j+1,i]*q),m_payoff[j,i-1])
            }
        }
    print(q)
        print(m_payoff)
        print(m_final)
#if fOptions is not installed
#install.packages("fOptions")
        library(fOptions)
        BinomialTreePlot(m_final,xlab="n",ylab="Option Value",xlim=c(0,8))
}