Computing implied volatilities for exchange-traded options on dividend-paying stocks

Abstract

We present an algorithm and its software implementation that computes implied volatilities for exchange-traded stock options. The stocks underlying the options are assumed to pay out dollar cash dividends. The Leisen-Reimer (LR) binomial tree is used for the option pricing that is at the core of the root-finding procedure in searching for the implied volatilities. The Brent's method is used for the root-finding, and the option pricing code is optimised for performance. Tests were made on call and put options traded on the stocks of Microsoft Corporation and Apple Inc. In 0.046 and 0.226 s, respectively, the implemented software program completed the computation for 154 Microsoft and 823 Apple call options. © 2014 Springer Science+Business Media Dordrecht.