Hi guys,please help me understand the following as it's still not clear (mathematically and/or intuitively). A "cash-or-nothing" digital has payout of:notional * daycount* QN(d2) * e^-rt, where the payout Q = 7% (as an example), d2 = (log(F/K) - r*sigma^2 /t )/sigma*t^1/2.So allegedly, that should be equal to (or approximated by) the following cap spread (LONG cap with strike K - 10bps and SHORT cap with strike K + 10bps)notional* daycount * e^-rt * [ FN(d1a) - K-0.1%*N(d2a) - FN(d1b) - K + 0.1%N(d2b)] where d1a has log(F/K-0.1% etc..) and N(d1b) has log (F/K +0.1% etc..).Is that correct? Did I make a mistake?thnksF

Hi Fed,Theoritically for deep In the Money options, as N(d1) and N(d2) approach unity, you can have F*N(d1a) - F*N(d1b) cancel out and payoff = Short cap strike N(d2b) - Long cap strike N(d2a) where both N(d2) are 1.so if you need to keep digital payout Y BPs set long cap at K and short cap at K + Y BPs. But its applicable for Deep in the money caps.cheers