# Cash-or-Nothing Call Option

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

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

## 1 Answer

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)