Question

You have a 2 year coupon bond with a coupon rate of 6 percent and a yield-to-maturity of 6.5 (continuously compounded). a. Compute the theoretical bond price. (Hint: Instead of using zero (spot) rate, use the yield to maturity) b. Compute the duration and convexity. c. Compute the new bond price when the yield to maturity moves up 10 basis points. d. Approximately compute the new bond price using only the obtained duration. (Hint: AP = -D · Ay)
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Answer 1

csa Dola given N-2 Coupon reate=6%. yield to matuotiry-650% Cocompoubled) As scemption: | As nothing is given I am assuming that it is an annual Cocepon paying Bond. * And the pan Vetue Of the Bond 10008 Bond price Calccelotions PV = 60 e 0.065 + 60+1000 0.065X2 = 60% 11.067 + 10607 /10138 2 56-23 + 930.78 987·018 Theoritical Bond Picíce = 987.01$

Page No. (6) Duration (Here I am cakeelating for movement of 10 basis point) LYTM 8-40% 65% 6.64 Bond Price 56-28 193264 987. 013 56.16 492892 (989.92 =985.08$] 10 basis point = 0.1% 1 (6:51) CAY=0.1% Effective Dorcation = 100 P2 - P1 - 988.92 - 985.08 2 x PoXmY 2 x987:01XO:1 = 1.99 yDurtation what is the movement in - Bond price for 1% Change in YTM for a 1% Change In YTM bond Price Changes by 1949. in opposite side. da olan effective Convexity : P2 tp, -2 Po - Pox QAY)² = -20.26 Teacher's Signature

Date Page No. c) As galcoilated in the previous Gloston new Bond price will be = 985-08 Osing D) ant Dautation ↑ Bond & 1.92%. So Bond price (new) - 987.01*(1-0.0194) = 9 67.86 $ of . R Intl TA) 1.94%. I so Bond prežce (New) =987.01 X (1+0.0194) =1006:15 $ E) costing EDC Duration) & convexity, Convexity ad Justment 1/2 x Ecx (ay) Ella (2020) X(0.001) ? -0.00l013% . Teacher's signature

Page No. УТМТ YTMI Bond price (1) Bomo Price 1 -1.940 -0.001013% -1.9410137 1.94% -0.001013% = 1.938910 New Bond Price New Bond Proce 987.01('1-0.01941013) 987 01 (1+0.81389) = 967 858 + 1006 148 Here we have celceclated for to Change Pal YTM what would be the valed of Bond. Similanly we can calculate for other peod % change in yTM. for example! of Change in yTM=0.84. then for 1%. Change in yTM Change - Change in Bond Price 1.94% fon 0.8% 9t would be 1.552%