I have an exercise where I need to replicate the following graph:
with my own parameters. To do this I use:
$\begin{align*} \text{Call option value} =SN(d_1)-Ee^{-r(T-t)}N(d_2) \end{align*}$
where $\begin{align*} d_1 = & \dfrac{log(S/E)+ \left(r+\frac{1}{2}\sigma^2\right)(T-t)}{\sigma\sqrt{T-t}} \end{align*}$, $\begin{align*} d_2 =& d_1 - \sigma\sqrt{T-t} \end{align*}$
and $N(x)$ is the cumulative distribution function for the standardized Normal distribution.
I set $E=110$, $r=8\%$, $T=1 year$, $t=0$ and $\sigma=0,4$ and calculate the call option value for different values of $S$. When I plot my results I get the following:
But I get negative option values, which I don't get and I can't see what I am doing wrong. I have checked everything but I cannot find the error?
Here is a screen shot of the values I get, I just used the formula to calculate the values in each column. Sorry about the screen shot, I don't know how to post an excel document on here.
I hope that some of you might find out what I have done wrong.
UPDATE!
I had another exercise where I had to varify that the call option value is 6,14. I had everything except for the option value, so this was pretty easy. I used the same excel document to calculate this and I get the correct result:
so it's not the formula. Is it my parameters then?