Multiple Discrete Dividends

Question

Using the recombining tree model as described in Haug's Option Pricing Forumla one can factor in multiple future discrete dividends when calculating the option value and greeks.

What's unclear is how does one handle a stock that pays a regular quarterly dividend but has only declared (as is standard) the next quater's dividend. If the option expires in one year, the next dividend is know, but the remaining three dividends have not yet been declared.

Should one use past dividends as a reference?

Do you only use the [single] declared dividend (even though it's assumed there will be 4 dividends during the life of the option)?

My assumption is they you'd plug in the known and use the past dates / amounts as a reference for the other 'future' dividends' and revise those with the actual information when they are finally declared, but that's only an assumption.

Answer 1

I found that sometimes going back to the source gets me the farthest. Here is what you are probably looking for:

http://www.math.ku.dk/kurser/2005-1/finmathtowork/ODD.pdf

Discrete dividends that have not been declared yet need to be estimated. Estimating and updating dividend expectations is part of the job of every single stock vol trader. You are asking how: Well, most traders use street estimates, Bloomberg and other data providers provide dividend estimates. The funny thing is that such estimate perceptions are very similar to the Black-Scholes perceptions. Everyone knows the assumptions are wrong but as long as everyone more or less agrees on the setup then traders are fine with faulty assumptions. It is all about beating peers (but do not make the mistake in assuming the battle is fought over dividend assumptions) and (at least on the sell-side) directing traffic to your book. In fact, the short time I traded single stock vol a long time ago I frequently discussed the dividend assumptions with my counter parties at DB, GS, ..., in order to arrive at a pricing level that made sense to both parties. Obviously different implied volatility assumptions make up for the largest pricing difference between counter parties thus most are happy to share their dividend curves in a more or less subtle way. If you do not have access to such data services or counter parties then I recommend you build your own dividend curves by extrapolating from past dividend payments. You can get fancy if you want and take into account changes in the company's guidance in regards to revenues or earnings but I would not go overboard with that if I were you. However, what is important is that you get the equation right as soon as dividends have been declared and adjustments have to be made on known information, especially that you are always aware of the ex-date of any underlying whose options you price/trade. There is no magic formula or one way as in most things in pricing financial assets, so a little imagination on your end is in order.