Instructions

Round $up$ critical values $d1$ and $d2to$ four decimal places.

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

$Nd1$ 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 $ofan$ interest rate call option using the Black model. The interest rate call

option $is$ based $ona90-$day underlying rate has $an$ exercise rate $of7\mathrm{.}5\%$ and expires $in180$ days.

The forward rate $is7\mathrm{.}25\%,$ and the volatility $is0\mathrm{.}04.$ The continuously compounded risk$-$free rate

$is5\%.$

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

put option based $ona90-$day underlying rate has $an$ exercise rate $of7\mathrm{.}5\%$ and expires $in180$

days. The forward rate $is7\mathrm{.}25\%,$ and the volatility $is0\mathrm{.}04.$ The continuously compounded risk$-$

free rate $is5\%.$

$1\mathrm{.}3.$ Does the corresponding put$-$call parity for the options $in1\mathrm{.}1$ 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 $d1$ and $d2to$ four decimal places.

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

$Nd1$ 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 $ofan$ interest rate call option using the Black model. The interest rate call

option $is$ based $ona90-$day underlying rate has $an$ exercise rate $of7\mathrm{.}5\%$ and expires $in180$ days.

The forward rate $is7\mathrm{.}25\%,$ and the volatility $is0\mathrm{.}04.$ The continuously compounded risk$-$free rate

$is5\%.$

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

put option based $ona90-$day underlying rate has $an$ exercise rate $of7\mathrm{.}5\%$ and expires $in180$

days. The forward rate $is7\mathrm{.}25\%,$ and the volatility $is0\mathrm{.}04.$ The continuously compounded risk$-$

free rate $is5\%.$

$1\mathrm{.}3.$ Does the corresponding put$-$call parity for the options $in1\mathrm{.}1$ and $1\mathrm{.}2$ hold? $If$ yes show $it,if$

not show $it$ and also explain why $it$ does not hold.$$Fill in the given values you have, and we'll solve for the missing variable.$=\frac{v}{f}$

$$	$=$	$\text{wavelength}$
$v$	$=$	$\text{velocity}$
$f$	$=$	$\text{frequency}$