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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
Consider a payer Interest Rate Swap that exchanges a 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 yr yr yr yr yr Rate
Table : LIBOR Rates continuously compounded
Additionally, assume LIBOR is risk free, the Interest Rate Swap has a notional amount of $MM and expires exactly in years, todays 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 years?
b Whatisthevaluetodayofafixedcouponbondwithannualcouponsandmaturing in 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 yr forward rates
You can convert the yr forward rates to annual rates using the formula R
ertimes
e Suppose the market rates just moved such that the yr LIBOR increased by bp That
is the new yr LIBOR is What is the new price of your IRS?
f Repeat the previous point times for an increase of bp for each rate, respectively.
g Plot a graph with the results from e and f The xx axis should be the periods years and the yy axis the dollar difference from a bp increase to each rate.
h What are your conclusions from g
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