Stochastic Proportional Dividends

Abstract

Motivated by recently increased interest in trading derivatives on dividends, we present a simple, yet efficient equity stock price model with discrete stochastic proportional dividends.

The model has a closed form for European option pricing and can therefore be calibrated efficiently to vanilla options on the equity. It can also be simulated efficiently with Monte-Carlo and has fast analytics to aid the pricing of derivatives on dividends.

While its efficiency makes the model very appealing, it has the twin drawbacks that dividends in this model can become negative, and that it does not price in any skew on either dividends or the stock price.

We present the model and also discuss various extensions to stochastic interest rates, local volatility and jumps.

(The 2012 revision corrects a minor mistake in the original paper)

Keywords: Options on Dividends, Stochastic Dividends, Dividend Yield, Dividend-Linked Derivatives

JEL Classification: G12