ABSTRACT
Option pricing models are generally rather complex. Th us there is oft en no closed-form solution for the implied volatility. However, a root-fi nding technique, such as the NewtonRaphson method, can be used to obtain a solution for it. Because of the rather high volatility of prices, it is important to use an effi cient algorithm to obtain a solution for
the implied volatility. If the pricing function, like the Black-Scholes formula, is well behaved, and there is a closed-form solution for vega, the Newton-Raphson method can be an extremely effi cient method that can converge quadratically. However, if there are multiple local extrema, and vega must be estimated, other numerical methods (such as Brent’s method) or approximations (such as the Brenner-Subrahmanyam formula) may be more effi cient. For more details see Antia (2002) and Hallenbach (2004).
