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( a ) Given the following information about the default - free, coupon paying yield curve, with face value of 1 0 0 0 ,

(a) Given the following information about the default-free, coupon paying yield curve,
with face value of 1000, derive the zero-coupon yield curve for years 1 through 4
using discrete compounding. Coupons are paid annually at the end of the year.
Solution The candidate should apply the bootstrap methodology:
F(1+c1)1+y1=PV1=F(1+c1)1+r1=>r1=y1=0.03
F*C21+y2+F(1+C2)(1+y2)2=PV2=FC21+r1+F(1+C2)(1+r2)2=>r2=0.0402
and similarly r3=0.0506 and r4=0.0614.
(b) You have 1,000,000 at the beginning of year 2. Using the information from the
table above, and assume that all the bonds are selling at par (ignore the column
of YTM for this part), what transaction should you undertake today to lock in the
forward rate from year 2 to year 3, using the coupon paying bonds provided above?
What is the forward rate?
Solution Solving the following system of equations:
1000x+1000y+1000z=0
1020x+30y+40z=0
1030y+40z=-1,000,000
yields x=-10.3,y=-1010.5,z=1020.8. The payoff in year 3 is given by
1040z=1,061,632 implying a forward rate from period 2 to 3 of 6.16%. I do not understand how to slove question b in the solution Could youpl ease explain to me in detailed how does it works Thanks
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