I'm developing a software to calculate the implied volatility of an option using the Black & Scholes formula and a trial-and-error method. The implied volatility values I get are correct, but I noticed that they are not the only possible ones.
For example, with a given set of parameters, my trial-and-errors lead me to an implied volatility of 43,21%, which, when used on B&S formula, outputs the price I started with. Great!
But I realized this 43,21% value is just a fraction of a much wider range of possible values (let's say, 32,19% - 54,32%).
Which value should I, then, pick as the 'best' one to show to my user?