Answer:
Check the explanation
Step-by-step explanation:
Zero coupon
K = N
Bond Price =∑ [(Annual Coupon)/(1 + YTM)^k] + Par value/(1 + YTM)^N
k=1
K =10
Bond Price =∑ [(0*1000/100)/(1 + 7.25/100)^k] + 1000/(1 + 7.25/100)^10
k=1
Bond Price = 496.62
Coupon bond
K = N
Bond Price =∑ [(Annual Coupon)/(1 + YTM)^k] + Par value/(1 + YTM)^N
k=1
K =30
Bond Price =∑ [(7.5*1000/100)/(1 + 7.25/100)^k] + 1000/(1 + 7.25/100)^30
k=1
Bond Price = 1030.26
a
Zero coupon bond
New bond price at YTM =8.25
K = N
Bond Price =∑ [(Annual Coupon)/(1 + YTM)^k] + Par value/(1 + YTM)^N
k=1
K =10
Bond Price =∑ [(0*1000/100)/(1 + 8.25/100)^k] + 1000/(1 + 8.25/100)^10
k=1
Bond Price = 452.61
Mod.duration prediction = -Mod. Duration*Yield_Change*Bond_Price
=-9.06*-0.01*496.62
=44.993772
Mod.duration prediction = -Mod. Duration*Yield_Change*Bond_Price
=-9.06*0.01*496.62
=-44.993772
New bond price at YTM =8.25 using duration and convexity
Convexity adjustment = 0.5*convexity*Yield_Change^2*Bond_Price
=0.5*157.5*0.01^2*496.62
=3.9108825
New bond price = bond price+Mod.duration pred.+convex. Adj.
=496.62+-44.99+3.91
=455.54
Coupon bond
New bond price at YTM =8.25
K = N
Bond Price =∑ [(Annual Coupon)/(1 + YTM)^k] + Par value/(1 + YTM)^N
k=1
K =30
Bond Price =∑ [(7.5*1000/100)/(1 + 8.25/100)^k] + 1000/(1 + 8.25/100)^30
k=1
Bond Price = 917.52
Mod.duration prediction = -Mod. Duration*Yield_Change*Bond_Price
=-9.04*0.01*1030.26
=-93.135504
New bond price at YTM =8.25 using duration and convexity
Convexity adjustment = 0.5*convexity*Yield_Change^2*Bond_Price
=0.5*251.6*0.01^2*1030.26
=12.9606708
New bond price = bond price+Mod.duration pred.+convex. Adj.
=1030.26+-93.14+12.96
=950.08
b
Zero coupon bond
New bond price at YTM =6.25
K = N
Bond Price =∑ [(Annual Coupon)/(1 + YTM)^k] + Par value/(1 + YTM)^N
k=1
K =10
Bond Price =∑ [(0*1000/100)/(1 + 6.25/100)^k] + 1000/(1 + 6.25/100)^10
k=1
Bond Price = 545.39
New bond price at YTM =6.25 using duration
Mod.duration prediction = -Mod. Duration*Yield_Change*Bond_Price
=-9.06*-0.01*496.62
=44.993772
New bond price at YTM =6.25 using duration and convexity
Convexity adjustment = 0.5*convexity*Yield_Change^2*Bond_Price
=0.5*157.5*-0.01^2*496.62
=3.9108825
New bond price = bond price+Mod.duration pred.+convex. Adj.
=496.62+44.99+-3.91
=545.52
Coupon bond
New bond price at YTM =6.25
K = N
Bond Price =∑ [(Annual Coupon)/(1 + YTM)^k] + Par value/(1 + YTM)^N
k=1
K =30
Bond Price =∑ [(7.5*1000/100)/(1 + 6.25/100)^k] + 1000/(1 + 6.25/100)^30
k=1
Bond Price = 1167.55
Mod.duration prediction = -Mod. Duration*Yield_Change*Bond_Price
=-9.04*-0.01*1030.26
=93.135504
New bond price at YTM =6.25 using duration and convexity
Convexity adjustment = 0.5*convexity*Yield_Change^2*Bond_Price
=0.5*251.6*-0.01^2*1030.26
=12.9606708
New bond price = bond price+Mod.duration pred.+convex. Adj.
=1030.26+93.14+-12.96
=1136.36