Models and Pricing Approaches for Dividend Derivatives
Summary
The document discusses pricing and risk analysis for derivatives on dividends paid by constituents of equity indices, with particular interest in dividend futures. One response distinguishes futures from options: dividend futures are linked directly to expected dividend values and can serve as hedging instruments, while options on dividends call for a model of dividend uncertainty. It notes early treatments that assume lognormal dividends, preserving a Black–Scholes-style framework for options on stocks, and later Markov-functional approaches built on Ornstein–Uhlenbeck dynamics to represent dividend-option smiles.
A second response sketches a binomial-tree method for a European call on a stock that pays a discrete dividend: adjust the stock-tree values for the dividend, compute terminal payoffs, then discount risk-neutral expected values backward. These are brief pointers rather than a full practitioner methodology. The discussion does not develop risk analysis, compare models empirically, or specify calibration and market-data procedures, so further references and validation are needed for implementation.
Key ideas
- Dividend futures are described as instruments tied to expected dividends and useful for hedging.
- Lognormal dividend assumptions have been used in early models of dividend options.
- Markov-functional models with Ornstein–Uhlenbeck dynamics can represent smiles in dividend options.
- A binomial tree can price a stock option with a discrete dividend by backward induction under risk-neutral probabilities.
- The responses provide model references and outlines, but little detail on calibration or risk management.
Tags
Full text
# Stochastic modelling of derivatives on dividends # Stochastic modelling of derivatives on dividends I consider pricing and risk analysis of derivatives on dividends of the members of equity indices (such as Dow Jones EuroStoxx). There are options but I focus on futures. - What are common stochastic models for dividends that allow pricing of such derivatives respectively risk analysis? - What are practitioner approaches to pricing and risk analysis of dividend futures/options? Who has references, experiences, comments? ## Answer by jherek (score 1) https://quant.stackexchange.com/a/69845 Futures on dividends are directly related to the expected value of the dividends. A model for the dividends is not going to help in pricing of those futures - they are the hedging instruments. For Options on dividends, early stochastic dividend models assume the dividend to be lognormal, see Geske (1978). This has the neat property that the Black-Scholes formula remains valid for Options on stocks. More recently, Markov-functional like models, on top of an Orstein-Uhlenbeck dynamic have been applied to represent the smile of the options on dividends, see Guennoun and Henry-Labordère (2019). ## Answer by ash (score -2) https://quant.stackexchange.com/a/7659 I will try to give you a way of "pricing" european call option on a stock that pays divided at t =1. You can extend it to American , more nodes etc In the end these 2 papers Paper 1 and Paper2 are quite good if you want a rigourous treatment using SDE. Lets define the underlined stock by(price ,up and down factors) $$ S = 100 , u = 1.1, d = 0.9, (1+r ) = 1.05 $$ Assume that the UL pays a $5 dividend at t = 1 You can have a binomial tree such that If it is a european Call option with maturity =2 and strike K = 90 then Node 2 is > MAX(115.5 - 90 , 0 ) = 25.5 MAX(94.5 - 90 , 0 ) = 4.5 MAX(93.5 - 90 , 0 ) = 3.5 MAX(76.5 - 90 , 0 ) = 0 Find risk nuetral probability of going up $$ q = (1+r)-d/(u-d)$$ and find price at node 1 and thereafter at node 0. Risk is a big problem in itself which I will leave for now for someone else.
Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.