Hi,I'm trying to replicate Haug's BSM formula adjusted for delayed settlement (pg234 2nd ed). The fustrating thing is I can get very close, but not exactly quite, using simple arguments like 'a delay of 3 days in paying the strike is like paying Xe^{-r * 3 days}'. I'm guessing I'm either missing something or putting something extra in, but can't quite pin it down.Could anyone give a hint toward the solution - or even a text book where this is elucidated (cool word, huh!). Cheers,qUosh.

I re-read my post and realized it doesn't really explain what I'd like to know and looks like I haven't bothered to think for myself, plus I like talking to myself and replying to my own posts:Beginning from the generalized BSM formula (the one with r's and b's):Supposing T2 is the time until we receive the premium (which is longer than the time to expiry) replace all e^{r T} with e^{r T2} as we are discounting the payoff over a longer time to expiry.Now, suppose we don't pay the premuim for t1 years. The entire option value needs to be adjusted by the factor e^{r t1} (ie what the option is worth when we pay the premium).The above gives the formula as presented by The Collector.What I MEANT to ask, in the above, why don't we modify the terms involving b? More importantly (for me), if we are doing options on indicies and let b = r-q things get messy trying to work out what we are changing and why (again, for me - I'm hoping someone else can make this oh-so-easy).Cheers!qUosh.

Do you mean deferred settlement of the premium or deferred settlement of the payoff? The premium is a fixed known cashflow, so usually excluded from option pricing formulas (I only have the first edition so can't see Haug's formula).If you mean deferred settlement of the option payoff, it shoudl be straight forward to see that the payoff value (whether zero in the case of non exercise or non-zero) is reduced by a factor of a year's discount value. If every payoff is reduced by a deterministic factor of e^{-r t1}, then the current value will be reduced by a deterministic factor of e^{-r t1}.(this doesn't necessarily hold in the case of stochastic interest rates, but if that's the case you shouldn't be using this formula anyway).

Deferred settlement of both.What you say about the delayed settlement makes sense - and matches Haug's formula.With the delayed payment of the premium, I think that is like asking 'What is the fair amount to pay tomorrow'. So it affects the amount you'd agree to pay, but not really today's fair value in the way the delayed settlement does.I think I've got my head around this now - so simple I don't know what the confusion was all about!As for stochasitic rates - if I'm using a constant single volatility interest rates are the least of my worries!