I was assuming a single name option too. For indices I’d just use implied information from the brokers market - for spx you can find div swaps or forwards, for stoxx you can also use the div futures.
Actually my question was more single-stock oriented. For indices it's easier because there are div futures quoted with long expiries (up to 10y).
Impressive. Sounds you know how to do it. And as an expert, with all due respect, can you give me/us the way you would answer OP for say AAPL with a 2024 ATM call ?
Sure, I've made markets like these before, assuming * European option * no special div protection * reasonable size * reasonable moneyness
its the div treatment that is interesting (I used to price that kind of stuff 15+ years ago, and never went back to equity derivatives side. For sure there are updates that are worth to pay attention).
Overall, it's not a straight forward thing to price even the European version. There are various considerations besides the dividends too - vol is the primary one, then funding, corporate event protection etc. As I said, I am assuming I am protected from the special divs and mergers, if not, I'd not do it or make it crazy costly. For my analysis, I would take the recent year or two of divs - again, if there is no div history, it makes it a no-go or much more expensive. * If I am a net seller of divs, I'd apply some div growth, usually the max of historical growth and the SPX div growth. * As a net buyer of divs, I'd look at fixed divs (dollar) and proportional divs (div yield). Depending on the stock (the higher the yield, the sooner I assume proportional), I'd blend the proportional dividends with fixed divs in such a way that I am assuming fully proportional dividends 2.5-3 years out.
Thank you Secret Santa. Just two more points. - You discount the whole premium using OIS (?), and which carry cost would you use ? (what would you put in it, based on what ?) - Using proportional divs, you wont care about ex-div dates interval frequency ?
* I'd probably grow the stock at Libor+ (internal stock funding) and discount at OIS. * At 4 years, it really is not that sensitive to the dividend dates though I'd still make sure the client is not trying to pin the date (e.g. make an expiration date pinning an expected ex-date as I would). This obviously assumes a dealer-side setup. On the buyside, if I was pricing this as a layoff it is a bit more complex since you have an internal ROC requirement and internal funding to account for. I'd also figure out ways of hedging a partial forward risk via combos and try to price that roll cost in.
As I said, things have changed since I've been involved in that kind of stuff. Maybe, American style made the whole things look different.