I would like to price a digital option on equity (cash or nothing) with just one day to expiry (actually, I price it today and check the payoff tomorrow).My question is: since the returns are far from normal in a so short time, which model can I use to price this option?Can I use something like the Gram-Charlier model to account for both skewness and kurtosis estimated on a daily basis? Is it better another model?Can I use the Gram-Charlier model to extract implied moments from option prices with longer maturity and convert the estimated moments in a daily basis?All suggestions are welcome.Thanks.Pier

I think its super dangerous to rely on a model for such an option

I agree with you but you always need a model to compare.

I concur with DaveAngel on this one. Regardless of the type of option in question, most pricing models break down as expiration approaches. With one day to go, most models will be practically useless unless you are only looking for ballpark estimates. I can't tell you how much time I've spent struggling with my models in order to get a somewhat useful calculation of gamma, etc on expiration day. Those situations have taught me that over-reliance on models can be a very dangerous, and expensive, thing.

I think it is priced against a book, to which it may fit and you do not have a pretty formula (as that already numerically might be to false) neither you can expect a fair price (nor the usual assumed continuous trading)

i traded lots of one day one touchs , touchs, no touchs, european digitals etc...most banks do not want to give quotes to those options and you can be very sure that bid/offer spreads are very wide...rather than the model the most important thing is what vol will you assign as one day implied-historical vol spread change can be very dangerous...you make your delta only for one day and come back tomorrow to see where you are..hard to hedge short term digitals for a book runner