A Quadratic Method for the Calculation of Implied Volatility Using the Garman–Kohlhagen Model

Abstract

Conventional techniques for evaluating the implied volatility from option prices involve iterative methods. The analytical algorithm presented in this article provides a simple, fairly accurate, and intuitive way of determining implied volatility. The discussion of this method is with reference to the Garman–Kohlhagen model for currency options, but the analysis is applicable to all options that can be priced using the Black–Scholes model. An improvement on a closed-form solution for implied volatility that is computationally more efficient is also presented.