# 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.

1. What are common stochastic models for dividends that allow pricing of such derivatives respectively risk analysis?
2. What are practitioner approaches to pricing and risk analysis of dividend futures/options?

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This is very broad (you have at least 5 questions). You'd likely get (better) answers if you split this into 2-4 more specific questions. –  Joshua Ulrich Apr 2 '13 at 2:13
@JoshuaUlrich You are right - I will split the first 2 points and the second up. Thanks for this suggestion. –  Richard Apr 2 '13 at 14:50
This is a very interesting topic: Hans Buehler has several papers and presentation on stochastic dividends and dividend derivatives that might be useful (quantitative-research.de). If you have some experience with dividend derivatives perhaps you might help me here: quant.stackexchange.com/questions/7841/… –  sets Jun 20 '13 at 13:34

Have you read Options, Futures and Other Derivatives by John Hull? I have the (ancient) 3rd edition and dividends are covered in section 11.12. (The latest edition is viciously expensive, but getting a used copy of one version back can halve the price.)

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Can you summarize that section with regards to the question? –  chrisaycock Apr 3 '13 at 2:01
I have a newer version and quickly browsing it again I don't see anything on derivatives on dividends. I only see remarks on things like Black-Scholes for dividend paying assets - there might be connections (due to arbitrage, just guessing) but nothing directly related. –  Richard Apr 3 '13 at 8:07
@Richard, I see the same, so I think I misunderstood your question. Sorry it was no help. –  Darren Cook Apr 3 '13 at 12:24

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.

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thank you for your detailed answer about options on dividend-paying assets. But my question is about derivatives (e.g. futures) on dividends. This is related but a totally different story ... it is about instruments like this: globalderivatives.nyx.com/stock-indices/nyse-liffe/… –  Richard Apr 4 '13 at 7:16
@Richard as long as you can synthically replicate the other securities the meathod should work. –  ash Apr 4 '13 at 14:28
sorry, but this is binomial pricing ... this does not directly help with futures on dividends what my question is about. I hope for a more specific answer to the question. Thanks for posting but this is too basic and too little related to my question. –  Richard Apr 4 '13 at 14:54
If I apply this scheme to a dividend process then it would mean that dividends pay dividends ... I can hardly imagine this. So this is off-topic - sorry. –  Richard Apr 4 '13 at 14:55
@Richard ATM I dont have time to do anymore on this. I will wait for someone to cook the solution –  ash Apr 4 '13 at 17:15