R BlackSholes

 

BlackScholes <- function(TypeFlag=c("c", "p"), S, X, Time, r, b, sigma)
{
  # Check Type Flag:
  TypeFlag = TypeFlag[1]
  # Compute d1 and d2:
  d1 = ( log(S/X) + (b+sigma*sigma/2)*Time ) / (sigma*sqrt(Time))
  d2 = d1 - sigma*sqrt(Time)
  # Compute Option Price:
  if (TypeFlag == "c")
    price = S*exp((b-r)*Time)*pnorm(d1) - X*exp(-r*Time)*pnorm(d2)
  else if (TypeFlag == "p")
    price = X*exp(-r*Time)*pnorm(-d2) - S*exp((b-r)*Time)*pnorm(-d1)
  # Save Parameters:
  param <- list(TypeFlag=TypeFlag, S=S, X=X, Time=Time, r=r, b=b, sigma=sigma)
  ans <- list(parameters=param, price=price, option = "Black Scholes")
  class(ans) <- c("option", "list")
  # Return Value:
  ans
}

print.option <- function(x, ...)
{
  # Parameters:
  cat("\nOption:\n ")
  cat(x$option, "\n\n")
  # Parameters:
  cat("Parameters:\n")
  Parameter = x$parameters
  Names = names(Parameter)
  Parameter = cbind(as.character(Parameter))
  rownames(Parameter) = Names
  colnames(Parameter) = "Value:"
  print(Parameter, quote = FALSE)
  # Price:
  cat("\nOption Price:\n")
  cat(x$price, "\n")
  # Return Value:
  invisible()
}

S = 100 - 2 * exp(-0.1 * 0.25) - 2 * exp(-0.1 * 0.5)
r = 0.1
BlackScholes("c", S = S, X = 90, Time = 0.75, r = r, b = r, sigma = 0.25)

r = 0.1
q = 0.05
BlackScholes("p", S = 100, X = 95, Time = 0.5, r = r, b = r-q, sigma = 0.2)

FuturesPrice = 19
b = 0
BlackScholes("c", S = FuturesPrice, X = 19, Time = 0.75, r = 0.1, b = b, sigma = 0.28)


r = 0.06
rf = 0.08
BlackScholes("c", S = 1.56, X = 1.6, Time = 0.5, r = r, b = r-rf, sigma = 0.12)