A new formula for computing implied volatility

摘要

This paper considers the explicit formulas for computing the implied volatility from the Black–Scholes option pricing model. The existing formulas in the literature are summarized and a uniform framework for deriving the formulas is given. A new explicit formula for computing the implied volatility is provided. The new formula is valid for a wide band of option moneyness and time to expiration. It is shown that the new formula is more accurate than the existing ones. Moreover, the new formulas can be easily implemented in spreadsheet applications. Thus the proposed formula is particularly important for the calculation of intra-day implied volatility in real time.