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QUESTION

Suppose that the holder of the call option of question 1 exercise
6 becomes bored with waiting for it to mature. She decides to sell
it after 7 months to someone else, when the asset price is \$45.
Calculate a fair price for the option at that time.


ANSWER

We use data as above but now the value of the option is at
$t=\frac{7}{12}=0.583$ with $S=\$45\ (D=0)$.

\begin{eqnarray*}
C\left(45,\frac{7}{12}\right)&=&45N(d_1)-50e^{-0.05(1-0.583)}N(d_2)\\
d_1&=&\frac{\log\left(\frac{45}{50}\right)+\left(0.05+\frac{0.03^2}{2}\right)
\left(\-\frac{7}{12}\right)}{0.3\left(1-\frac{7}{12}\right)^\frac{1}{2}}=-0.3397\\
d_2&=&\frac{\log\left(\frac{45}{50}\right)+\left(0.05-\frac{0.3^2}{2}\right)
\left(1-\frac{7}{12}\right)}{0.3\left(1-\frac{7}{12}\right)^\frac{1}{2}}=-0.5333\\
N(-0.3397)&=&0.3669\\ N(-0.5333)&=&0.2981\\
C\left(45,\frac{7}{12}\right)&=&45\times0.3669-50e^{-0.05(1-0.583)}\times0.2981\\
&=&1.9128
\end{eqnarray*}

So if holder sells they make $-2.2764+1.19128=-0.3636$.



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