A note on a simple, accurate formula to compute implied standard deviations

We derive a simple, accurate formula to compute implied standard deviations for options priced in the classic framework developed by Black and Scholes (1973) and Merton (1973). When a stock price is equal to a discounted strike price, this formula reduces to a formula provided by Brenner and Subrahmanyam (1988). However, their formula's accuracy is sensitive to stock price deviations from a discounted strike price. The formula derived here extends the range of accuracy to a wide band of option moneyness.