I am attempting to create an R function to approximate sigma using Black-Sholes option pricing model and the following variables: Put = put option price, S0 = current stock price, K = strike price, r = risk-free rate, T =: remaining time to maturity, and sigma = standard deviation of underlying stock price.

The first line of the code should read:

sigma <- function (put, S0, K, r, T) {

As an example of creating a function with the same variables and Black Sholes option pricing model please see R function below used to calculate the put option price:

put <- function (S0, K, r, T, sigma) { d1 <- (log(S0/K) + (r + sigma^2/2)*T) / (sigma*sqrt(T)) d2 <- d1 - sigma*sqrt(T) value <- (K*exp(-r*T)*pnorm(-d2) - S0*pnorm(-d1)) return(value) }