Imagine the following binary option modification: if the stock price at t = 0,5 is greater that 100 roubles, the owner of the option receives 1 rouble at t = 1. Otherwise, he gets 0 roubles.So this is just a binary call option, but with the payment being made not at the expiry date, but some time later.Analytical formulae for valuing standard binary options are available. The question is: how to value those a bit altered binary options?I have come to the following solution and would like to make sure that I didn't make any mistakes.First, we calculate the PV of the cash flow "+ 1 rouble at t = 1" at t = 0,5. We can do that if we assume that the percent rate is constant. Let's assume that the PV of this cash flow is 0,95 roubles.We then use the standard binary option value formula and use 0,95 as the binary option cash flow. The idea is that the holder of the option gets 0,95 roubles, invests them at the risk-free rate and gets 1 rouble at t = 1, which is the same as buying our binary option with delayed payment.So the value of our binary option with delayed payment is as follows: StandardBinaryCallValue (Strike = 100, Years to expiry = 1, Volatility = ..., Risk-free rate = ..., Cash Flow = PV (1)).Is this logic correct?

Assuming deterministic interest rates (or at least uncorrelated with the equity performance), which is a reasonably standard assumption, that is exactly what I'd do.

I am not sure if this delayed payment or contigent ? The contract as described seems to indicate that the buyer of the option pays nothing if the stock price is below R100 ?

My reading of it was that it is the payment to the option buyer that is deferred; that the premium was paid by the buyer at the time of purchase as per normal.

Gjlipman, thank you for your answer.Yes, absolutely - the premium is paid immediately after the contract is signed, as usual. And the payoff is either 0 or 1 rouble at t = 1, whereas the base asset price is monitored is t = 0,5 to see if it it below or above R100.Could anyone else please confirm that the pricing solution presented in my first post is correct?

Your logic seems correct, but I would use the forward rate from t = 0.5 to t = 1 to discount the 1 payoff back to time t = 0.5, and as you state price a normal binary the usual way with the discounted value of 1 as the binary payoff

I agree Vegawizard's way of discounting is better than assuming a constant rate.