Instructions

Round up critical values d$1$ and d$2$ to four decimal places.

Use Excel, Matlab or any package of your choice to compute the Normal probabilities

$N(d1)$ and $)$ accurately, and round up their values to four decimal places.

Round up your final answer to two decimal places.

Submit one handwritten scan pdf document on Moodle before the cut$-$off time.

Question $1$

$1\mathrm{.}1.$ Calculate the price of an interest rate call option using the Black model. The interest rate call

option is based on a $90-$day underlying rate has an exercise rate of $7\mathrm{.}5\%$ and expires in $180$ days.

The forward rate is $7\mathrm{.}25\%,$ and the volatility is $0\mathrm{.}04.$ The continuously compounded risk$-$free rate

is $5\%.$

$1\mathrm{.}2.$ Calculate the price of the interest rate put option using the Black model. The interest rate

put option based on a $90-$day underlying rate has an exercise rate of $7\mathrm{.}5\%$ and expires in $180$

days. The forward rate is $7\mathrm{.}25\%,$ and the volatility is $0\mathrm{.}04.$ The continuously compounded risk$-$

free rate is $5\%.$

$1\mathrm{.}3.$ Does the corresponding put$-$call parity for the options in $1\mathrm{.}1$ and $1\mathrm{.}2$ hold? If yes show it$,$ if

not show it and also explain why it does not hold.

Instructions

Round up critical values d$1$ and d$2$ to four decimal places.

Use Excel, Matlab or any package of your choice to compute the Normal probabilities

$N(d1)$ and $)$ accurately, and round up their values to four decimal places.

Round up your final answer to two decimal places.

Submit one handwritten scan pdf document on Moodle before the cut$-$off time.

Question $1$

$1\mathrm{.}1.$ Calculate the price of an interest rate call option using the Black model. The interest rate call

option is based on a $90-$day underlying rate has an exercise rate of $7\mathrm{.}5\%$ and expires in $180$ days.

The forward rate is $7\mathrm{.}25\%,$ and the volatility is $0\mathrm{.}04.$ The continuously compounded risk$-$free rate

is $5\%.$

$1\mathrm{.}2.$ Calculate the price of the interest rate put option using the Black model. The interest rate

put option based on a $90-$day underlying rate has an exercise rate of $7\mathrm{.}5\%$ and expires in $180$

days. The forward rate is $7\mathrm{.}25\%,$ and the volatility is $0\mathrm{.}04.$ The continuously compounded risk$-$

free rate is $5\%.$

$1\mathrm{.}3.$ Does the corresponding put$-$call parity for the options in $1\mathrm{.}1$ and $1\mathrm{.}2$ hold? If yes show it$,$ if

not show it and also explain why it does not hold.