Let's assume I was able to imply dividends from liquid options for the next 3 years, but I want to price an option expiring in the 4rd year from now. How would practitioners normally extrapolate implied dividends? Thanks
While I no longer do this (only trade Indexes and non-dividend instruments now), I previously collected the dividend history, and merely projected it to occur in the future. -- Only viable if you are willing to assume no change to prior periods. (you can tweak for expected dividend growth, etc)
Your question embeds the answer - either extrapolate or if the firm has had a history of growing dividends a growth model. Not a totally easy answer as the carry function in long-dated is much more important than in short-dated. This is one of the reasons b/a spread in long-dated are so generous. As you go longer in time the carry function becomes much more critical than expected volatility. BTW keep in mind for long-dated you can model anything - it's finding a desk that will make a market in an option longer than the listed LEAP or arbing the listed LEAPS with you carry estimate
For option pricing, there is also a matter of fixed vs proportional dividends. I.e. if you are pricing a $10 dollar stock that pays a $1 dollar worth dividends, in 4 years it's forward will be $6. So if you are pricing a European option, you want to decide that at some point in the future the stock will start paying dividends proportional to the stock price instead of fixed dollars.
If you got all option chains you can find every implied discrete div and implied ex-div date with a high degree of accuracy for a given maturity (mult div). Its hard, time consuming but doable. For an option expiring in 4 years without option quotes, knowing the 3 yearly implied div and ex-div dates, imho (without any add information) your best guess would be the last implied discrete div, and the best guess for ex div date would be to add an equal time interval forward .
Thanks a lot for your insight! Besides, from what i've observed there is a significant risk premium in implied dividends far out (implied divs are sold at discount). Actually the dividend term structure is declining. Therefore probably it makes more sense to extrapolate implied dividend rather than historical growth. Am I right?
As ajacobson told you, all that kind of stuff is associated with your hability to find a desk that would take the other part of the deal.
Depends on the market. I would value spx divs flat to up as payouts are more stable. For sx5e I would project earnings and use stated payout ratios. This is as a buysider looking for an opportunity. As a sellsider, I would mark against the longest dated that I can hedge to and then shock the forward div to give me a confidence interval to quote around.