Exercise 5. 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' lyr 2yr 3yr 4yr dyr Rate | 1.700% 2.000% 2.300% 2.700% 2.850% Table 1: LIBOR Rates (continuously compounded) Additionally, assume LIBOR is risk free, the Interest Rate Swap has a notional amount of $1MM 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) What is the value (today) of a 4% fixed coupon bond with annual coupons and maturing 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: e The value you get here should match what you got from (c)! e The forward rates you get using the formulas from class give you the continuously compounded lyr forward rates e You can convert the lyr forward rates to annual rates using the formula R = erxl _ 1) (e) Suppose the market rates just moved such that the 1lyr LIBOR increased by 1bp. That is, the new lyr LIBOR is 1.710%. What is the new price of your IRS? (f) Repeat the previous point 4 times for an increase of 1bp 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 1bp increase to each rate. (h) What are your conclusions from (g)