Volatility and Dividends II - Consistent Cash Dividends

Abstract

We discuss a time-homogeneous equity stock price modelling approach with a consistent dividend process such that at any point, conditional on the state variables of the model, short-term implied dividends are cash-like (constant) and long-term dividends are proportional.Our approach is based on a general representation for dividend paying stocks where we prove that the stock price process is the sum of an inner process plus the sum of the expectation of all future (appropriately discounted) dividends under the risk-neutral measure.This note summarizes results presented in 2012 at Global Derivatives. We discuss dividend dynamics in the proposed approach; calibration to dividend options and the equity implied volatility surface are only touched upon.