An Explicit Implied Volatility Formula
24 Pages Posted: 1 Feb 2017 Last revised: 25 Jul 2018
Date Written: January 30, 2017
We show that an explicit approximate implied volatility formula can be obtained from a Black–Scholes formula approximation that is 2% accurate. The relative error of the approximate implied volatility is uniformly bounded for options with any moneyness and with arbitrary large or small option maturities and volatilities, including for long dated options and options on highly volatile underlying assets. For options within a large trading range, such as options with maturity less than five years and implied volatility less than 150%, the error of the approximate implied volatility relative to the Black–Scholes implied volatility is less than ten percentage points.
Keywords: Implied Volatility, Black-Scholes Model, Approximation Formula, Uniform Bounds
JEL Classification: C60, C63
Suggested Citation: Suggested Citation