R/butterfly.spread.R

In FinancialMath: Financial Mathematics for Actuaries

butterfly.spread = function(S,K1,K2=S,K3,r,t,price1,price2,price3,plot=FALSE){

  all=list(S,K1,K2,K3,r,t,price1,price2,price3,plot)
  #NULL
  if(any(lapply(all,is.null)==T)) stop("Cannot input any variables as NULL.")
  #Length
  if(any(lapply(all,length) != 1)==T) stop("All inputs must be of length 1.")
  #Numeric
  num2=list(S,K1,K2,K3,r,t,price1,price2,price3)
  na.num2=num2[which(lapply(num2,is.na)==F)]
  if(any(lapply(na.num2,is.numeric)==F)) stop("S K1, K2, K3, r, t, price1, price2, and price3 must be numeric.")
  #NA
  if(any(lapply(all,is.na)==T)) stop("Cannot input any variables as NA.")

  NA.Neg=c(r,S,K1,K2,K3,t,price1,price2,price3)
  #Positive
  if(any(NA.Neg<=0)) stop("All numeric variables must be positive.")
  #Infinite
  if(any(NA.Neg==Inf)) stop("Cannot input any variables as infinite.")
  #Logical
  stopifnot(is.logical(plot))

  if(K1>=K2 | K2>=K3) stop("K1<K2<K3 condition must be met.")
  if(K3-K2 != K2-K1) stop("K1 and K3 must be equidistant to K2")
  if(K2 != S) stop("K2 must be equal to S.")

  #long
  callP1 = price1
  #short
  callP2 = price2
  #long
  callP3 = price3

  stock=unique(round(seq(0,K1,length.out=6)))
  stock=c(stock,round((K2-K1)/2+K1),K2,round((K3-K2)/2+K2))
  stock=c(stock,round(seq(K3,K3+K1,length.out=6)))
  stock=unique(stock)
  stock2=unique(round(c(seq(0,K1,length.out=6),K2,seq(K3,K3+K1,length.out=6))))
  payoff=rep(0,length(stock))
  profit=rep(0,length(stock))

  for(i in 1:length(stock)){
    if(stock[i]<=K1) payoff[i]=0
    if(stock[i]>=K3) payoff[i]=0
    if(stock[i]<=K2 & stock[i]>K1) payoff[i]=stock[i]-K1
    if(stock[i]>K2 & stock[i]<K3) payoff[i]=(stock[i]-K1)+(K2-stock[i])+(K2-stock[i])
    profit[i]=payoff[i]+(2*callP2-callP1-callP3)*exp(r*t)
  }

  if(plot==T){
    plot(stock,profit,type="l",xlab="Stock Price",main="Butterfly Spread\nPayoff and Profit",ylab="$",
         ylim=c(min(profit,payoff),max(profit,payoff)),xaxt='n',yaxt='n',col="steelblue",lwd=2)
    lines(stock,payoff,lty=2,lwd=2,col="firebrick")
    abline(h=0,lty=2,col="gray")
    y=round(seq(min(payoff,profit),max(payoff,profit),length.out=8))
    axis(2,at=y,labels=y,las=2)
    axis(1,at=if(K2-K1<7 | K3-K2<7) stock2[-which(stock2==K1 | stock2==K3)] else stock2,las=2)
    legend("topleft",c("Profit","Payoff"),lty=c(1,2),col=c("steelblue","firebrick"),lwd=c(2,2))  }


  out1=round(data.frame(stock,payoff,profit),2)
  names(out1)=c("Stock Price","Payoff","Profit")
  out2=matrix(c(callP1,callP2,callP3,callP1+callP3,callP2*2,(callP1+callP3)-callP2*2),nrow=6)
  rownames(out2)=c("Call (K1)","Call (K2)","Call (K3)","Total Pay","Total Receive","Net Cost")
  colnames(out2)=c("Premiums")
  out=list(Payoff=out1,Premiums=out2)
  return(out)
}