Pricing Same-Day Options on Futures with European Models

# Binomial Tree Option Pricing Model. Lets talk dividends and futures


# Binomial Tree Option Pricing Model. Lets talk dividends and futures












I am writing an option pricing model for production use. Its not for arb or anything so it doesn't need to be 100% as accurate as possible. Just good enough for "what happens to my book if we jump 10 handles sorta thing."

I want to preface this with, I have to price most of my options same day expiry which kind of leaves out Quantlib or something of the sort unless I want to rewrite a lot of it and recompile it.

1.) I am pricing (futures options) on SPX, Nasdaq, Crude, NatGas 10year treasury note, long term treasury.

2.) What models should I be using? I realize for commodities I need to include cost of carry, but is there a model out there besides Binomial trees that I can use to price the commodities?

3.)As far as dividends, if Im pricing SPX Futures options is binomial tree the best way to do that? and do I really need to price in every discrete dividend into the BT model at the exact date and time it happens? Or will continuous/no dividend be accurate enough?

4.) Are there any additional caveats to pricing same day expiration options? - Currently I'm not sure what to divided the hours left in the day by for my time in the pricing model. I believe it would be from 6pm(open) to 4pm(settle) which is 22 hours if its under 24 hours to expiration. that would open some problems when pricing between 4-5pm say on a tuesday for wednesday expiration but that can be solved pretty easily.

Thanks

## Answer by Ezy (score 2, accepted)

https://quant.stackexchange.com/a/44110

1) First of all many future option contracts are European, so for those there's no modeling problem. Just use BS. Now certain contracts like quarterly ES option are american for historical reasons

2) Futures do not entitle the long holder to the dividends of the underlying. That's the difference with other type of derived instruments (like SPY or QQQ) and that's also the reason of the existence of the cash-future basis. So for the purpose of pricing american options on futures dividends play no role whatsoever.

3) The source of the early exercise opportunity for american options on futures lies in the possibility of positive cash flow through the margining account. This impacts both the call and the put. By contrast it is never optimal to early exercise an american call option on the forward contract.

4) for some reference on american options on futures you can look here

5) now I have not seen the result anywhere but I believe that it is never optimal to exercise the american option intraday. Therefore if you now restrict to same day expiry option i claim they are fairly priced as european options.

In conclusion for your specific purpose I think you would be good with simply pricing all these instruments as european options when they expire the same day.