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Consider a $($payer$)$ Interest Rate Swap that exchanges a $4\%$ annual fixed rate for a floating rate every year. The floating rate is LIBOR, which at the time you are examining this IRS is

Period $1$yr $2$yr $3$yr $4$yr $5$yr Rate $1\mathrm{.}700\%2\mathrm{.}000\%2\mathrm{.}300\%2\mathrm{.}700\%2\mathrm{.}850\%$

Table $1$: LIBOR Rates $($continuously compounded$)$

Additionally, assume LIBOR is risk free, the Interest Rate Swap has a notional amount of $$1$MM and expires exactly in $5$ years, today$$s cashflows were already settled, and there is no credit risk from the Interest Rate Swap.

$($a$)$ What is the value $($today$)$ of a floating rate bond indexed on LIBOR and maturing in $5$ years?

$($b$)$ Whatisthevalue$($today$)$ofa$4\%$fixedcouponbondwithannualcouponsandmaturing in $5$ years?

$($c$)$ What is the value of the $($receiver$)$ Interest Rate Swap you have? Use the results from $($a$)$ and $($b$)$ to solve this question.

$($d$)$ Use the fact that an IRS can be expressed as multiple FRAs to compute the value of the Interest Rate Swap from this question. Hints:

$$ The value you get here should match what you got from $($c$)!$

$$ The forward rates you get using the formulas from class give you the continuously

compounded $1$yr forward rates

$$ You can convert the $1$yr forward rates to annual rates using the formula R $=$

er$\backslash$times $11)$

$($e$)$ Suppose the market rates just moved such that the $1$yr LIBOR increased by $1$bp$.$ That

is$,$ the new $1$yr LIBOR is $1\mathrm{.}710\%.$ What is the new price of your IRS?

$($f$)$ Repeat the previous point $4$ times for an increase of $1$bp for each rate, respectively.

$($g$)$ Plot a graph with the results from $($e$)$ and $($f$).$ The xx axis should be the periods $1,...,5$ years $$ and the yy axis the dollar difference from a $1$bp increase to each rate.

$($h$)$ What are your conclusions from $($g$)?$

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