# How to find the upper bound of a digital option given some market data?

Given the price of a call equals to 5 with Strike 100, please find the upper bound (sup) of the digital option with strike 105.

I am not sure about the solution, but I write the condition like this,

$S\mathcal{N}(d_1)-Ke^{-rT}\mathcal{N}(d_2) = 5$

what's the $\sup{N(d_1+\frac{\ln(\frac{100}{105})}{\sigma\sqrt{T}})}$?

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 $\mathcal{N}(\cdot)$ is a cumulative distribution function. Hence, the image of $\mathcal{N}$ is clearly $[0,1]$. – SRKX♦ May 27 '12 at 9:54 Is this a homework assignment? I notice you posted some questions on Math.SE and were called-out there too for posting school work with no effort. – chrisaycock♦ May 27 '12 at 13:49 Hi chrisaycock, it's not a homework. To SRKK, it's obvious $\mathcal{N}\in[0,1]$ but it doesn't help on solving the sup, any idea on it? – pidig May 27 '12 at 15:26