BlackSholes.R

## Black-Scholes Function
BS <- function(S, K, T, r, sig, type="C"){
    d1 <- (log(S/K) + (r + sig^2/2)*T) / (sig*sqrt(T))
    d2 <- d1 - sig*sqrt(T)
    if(type=="C"){
      value <- S*pnorm(d1) - K*exp(-r*T)*pnorm(d2)
    }
    if(type=="P"){
      value <- K*exp(-r*T)*pnorm(-d2) - S*pnorm(-d1)
    }
    return(value)
}


## Function to find BS Implied Vol using Bisection Method
implied.vol <-
  function(S, K, T, r, market, type){
    sig <- 0.20
    sig.up <- 1
    sig.down <- 0.001
    count <- 0
    err <- BS(S, K, T, r, sig, type) - market 
    
    ## repeat until error is sufficiently small or counter hits 1000
    while(abs(err) > 0.00001 && count<1000){
      if(err < 0){
        sig.down <- sig
        sig <- (sig.up + sig)/2
      }else{
        sig.up <- sig
        sig <- (sig.down + sig)/2
      }
      err <- BS(S, K, T, r, sig, type) - market
      count <- count + 1
    }
    
    ## return NA if counter hit 1000
    if(count==1000){
      return(NA)
    }else{
      return(sig)
    }
  }