Approximate Inversion of the Black-Scholes Formula Using Rational Functions

European Journal of Operational Research, Vol. 185, No. 2, pp. 743-759, March 2008

Posted: 12 Feb 2008

Abstract

The Black-Scholes formula is often used in the backward direction to invert the implied volatility, usually with some solver method. Solver methods, being aesthetically unappealing, are also slower than closed-form approximations. However, closed-form approximations in previous works lack accuracy, often providing option pricing errors well exceeding the bid-ask spreads. We develop a new closed-form method based on the rational approximation. The rational approximation is much faster than typical solver methods and very accurate for both at-the-money and away-from-the-money options. Its accuracy can be further improved by one or two steps of Newton-Raphson iterations.

Keywords: Implied volatility, Black-Scholes formula, Rational functions

JEL Classification: C00, C14, G12, G13

Suggested Citation

Li, Minqiang, Approximate Inversion of the Black-Scholes Formula Using Rational Functions. European Journal of Operational Research, Vol. 185, No. 2, pp. 743-759, March 2008, Available at SSRN: https://ssrn.com/abstract=1091160

Minqiang Li (Contact Author)

Bloomberg LP ( email )

731 Lexington Avenue
New York, NY 10022
United States

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