The estimation of implied volatility from the Black-Scholes model: some new formulas and their applications

This paper provides a more accurate formula for estimating the implied volatilities for at-the-money calls than the existing formula as developed previously by Brenner and Subrahmanyam (1988). New formulas are also given for estimating the implied volatilities of in- or out-of-the-money calls. These formulas are derived mathematically and assessed by using numerical tests. All the new formulas are easy to use and accurate for a wide range of option moneyness and time to expiration.