When the non-dividend paying stock price is $20,the strike price is $20,the risk-free rate is 5%,the volatility is 20% and the time to maturity is 3 months which of the following is the price of a European put option on the stock
A)19.7N(-0.1)-20N(-0.2)
B)20N(-0.1)-20N(-0.2)
C)19.7N(-0.2)-20N(-0.1)
D)20N(-0.2)-20N(-0.1)

Question

Quizplus · Accepted Answer

The formula for the option price is
$\begin{array} { l } 
K e ^ { - r T } N \left( - d _ { 2 } \right) - S _ { 0 } N \left( - d _ { 1 } \right) \
d _ { 1 } = \frac { \ln \left( S _ { 0 } / K \right) + \left( r + \sigma ^ { 2 } / 2 \right) T } { \sigma \sqrt { T } } \quad \text { and } \quad d _ { 2 } = d _ { 1 } - \sigma \sqrt { T }
\end{array}$
In this case $S _ { 0 } = K = 20 , r = 0.06 , \sigma = 0.2$, and $T = 0.25$ so that $K e ^ { - r T } = 20 \mathrm { e } ^ { - 0.06 \times 0.25 } = 19.7$. Also $d _ { 1 } = [ \ln ( 1 ) + ( 0.06 + 0.04 / 2 ) \times 0.25 ] / ( 0.2 \times 0.5 ) = 0.2$ and $d _ { 2 } = 0.2 - 0.2 \times 0.5 = 0.1$
$\mathrm { A }$ is therefore the correct answer.

When the Non-Dividend Paying Stock Price Is $20,the Strike Price