What volatility should be used for each option series

Question

What volatility should be used for each option series hence the theoretical Black–Scholes price and the market price are similar?

Answer 1

Though, we have the Black–Scholes formula as a function of volatility for option values, here is no formula for the implied volatility like a function of option value; this must be computed using several bisection, Newton–Raphson, or another numerical technique for getting zeros of a function. There plot these implied volatilities verses strike, one curve per expiration. It is the implied volatility smile. When you plot implied volatility against strike and expiration both as a three-dimensional plot then it is the implied volatility surface. Frequently you will find as the smile is quite flat for long-dated options, although getting steeper for short-dated options.