Analytical conversion between implied volatilities based on different dividend models

Vladimir Lucic and Vladimir Jovanović

Abstract

The process of equity volatility marking involves constructing an implied volatility surface for an asset based on prices of liquid market instruments, typically call and put options. Assumptions about modeling asset dividends play a crucial role here, as different dividend models give rise to different implied volatilities. Volatilities are calibrated frequently and on a large scale (in terms of the number of underlyings). Thus, having a functional and stable numerical procedure for this conversion in practice is paramount. In this paper we derive an explicit formula for the conversion of implied volatilities corresponding to different dividend modeling assumptions. Our formula is both fast and accurate, and it is, to the best of the authors’ knowledge, the first efficient numerical method to cover such a wide range of strikes and maturities.