Black Scholes Implied Volatility: Inputs Guidance

As usual, we will use an example to explain the requirements. So let's assume, we want to compute the implied volatility of a 2-year maturity, 2,300 strike call option on a non-divided paying stock, which has a current price of 2,500. Let's assume the price of the call option is 745, and the risk free discount rate is 5%(0.05). The inputs will be entered as follows:

Stock Price 2,500
Strike Price 2,300
Discount Rate 0.05
Dividend Yield 0.0
Maturity (years) 2.0
Option Price 745
Option Type Call

That is all there is to it. As for the price calculator's inputs, a few things that might cause some confusion are:

  • The time to maturity is in years, so a maturity of 15 months will be inputed as 1.25 (=1.0+3/12).
  • The discount rate and dividend yield are not formated with %, e.g., 5% is entered as 0.05.
  • The stock price, strike price, and maturity should be non-negative. If any of these is negative, it will be replaced with zero.

One more thing to add to the above: If the given price is too high or too low, then the algorithm may not be able to find the implied volatility that can produce the given option price. This should be indicated in the outputs.