Faster Implied Volatilities via the Implicit Function Theorem

Michael Kelly

The Financial Review, 2006, vol. 41, issue 4, 589-597

Abstract: We present a faster, more accurate technique for estimating implied volatility using the standard partial derivatives of the Black‐Scholes option‐pricing formula. Beside Newton‐Raphson and slower approximation methods, this technique is the first to provide an error tolerance, which is essential for practical application. All existing noniterative approximation methods do not provide error tolerances and have the potential for large errors.

Date: 2006
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