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I am trying to price a cash or nothing call option and I know know that the Cash or Nothing formula for a call option is $C(t,s)=Xe^{-r(T-t)}*N(d)$

If I have payoff X=100 r=0.03 T=2 $\sigma=0.3$

I would have $C(t,s)=100e^{-0.03(2-t)}N(d)$

but how would I find $N(d)$ and (T-t)as where $$ d=\dfrac{\ln(S/E)+(r-\sigma^2/2)(T-t)}{\sigma\sqrt{T-t}} $$

to calculate the price at time 0

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  • $\begingroup$ why not to replace $t$ by 0!!!! $\endgroup$ – Valometrics.com Feb 18 '20 at 1:34
  • $\begingroup$ Hi thank I managed to realise that one :) I should have been more specific wish my problem of actually calculating N(d) $\endgroup$ – Jacob Mitch Feb 18 '20 at 2:15
  • $\begingroup$ @JacobMitch where is the problem with calculating $N(d)$? $\endgroup$ – Kevin Feb 18 '20 at 6:38
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In your formula you have the following variables:

  • t= 0, T = the maturity of the call option which is known.
  • S is the spot value of the underlying asof t = 0 (today) which is known.
  • E is the strike of the option which is known
  • r and σ are known.

In other word all the variables are known and thus it's a straight forward formula to get N(d)

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