1. Step 1 Step 2
Bond Quotes
Maturity Date Coupon Rate Ask price Price with accured interest Zero Coupon Bonds with Face Value $100
% x/32 Decimal Poly Derived Spot Rates
Maturity Date Price of Zero Time to Maturity Spot Rate
15.02.2013 4,625% 101 22 0,716372283 102,4038723
15.02.2013 0,875% 100 4 0,135529891 100,2605299 15.02.2013
15.08.2013 4,375% 103 20 0,677649457 104,3026495 15.08.2013
15.08.2013 1,750% 101 8 0,271059783 101,5210598 15.02.2014
15.02.2014 3,875% 105 18 0,600203804 106,1627038 15.08.2014
15.02.2014 1,375% 101 18 0,212975543 101,7754755 15.02.2015
15.08.2014 4,250% 107 16 0,658288043 108,158288 15.08.2015
15.08.2014 0,750% 100 17 0,116168478 100,6474185 15.02.2016
15.02.2015 4,000% 108 18 0,619565217 109,1820652 15.08.2016
15.02.2015 1,875% 103 12 0,290421196 103,6654212 15.02.2017
15.08.2015 4,250% 110 21 0,658288043 111,314538
15.08.2015 0,500% 100 1 0,077445652 100,1086957
15.02.2016 4,000% 111 15 0,619565217 112,0883152
15.02.2016 2,375% 106 9 0,367866848 106,6491168 -1,597673234
15.08.2016 4,250% 113 23 0,658288043 114,377038
15.08.2016 1,250% 102 19 0,19361413 102,7873641
15.02.2017 4,500% 115 13 0,69701087 116,1032609
15.02.2017 2,125% 105 9 0,329144022 105,610394
15.08.2012 Last coupon date
11.10.2012 Date of purchase
Step 5
1) Without short possitions
p 101.22 100.04 103,2 101,8 105,18 101,18 107,16 100,17 108,18 103,12 110,21 100,01 111,15 106,09 113,23 102,19 115,13 105,09
C 102.3125 100,4375 2,1875 0,875 1,9375 0,6875 2,125 0,375 2 0,9375 2,125 0,25 2 1,1875 2,125 0,625 2,25 1,0625
0 0 102,1875 100,875 1,9375 0,6875 2,125 0,375 2 0,9375 2,125 0,25 2 1,1875 2,125 0,625 2,25 1,0625
0 0 101,9375 100,6875 2,125 0,375 2 0,9375 2,125 0,25 2 1,1875 2,125 0,625 2,25 1,0625
0 0 102,125 100,375 2 0,9375 2,125 0,25 2 1,1875 2,125 0,625 2,25 1,0625
0 0 102 0,9375 2,125 0,25 2 1,1875 2,125 0,625 2,25 1,0625
0 0 102,125 100,25 2 1,1875 2,125 0,625 2,25 1,0625
0 0 102 101,1875 2,125 0,625 2,25 1,0625
0 0 102,125 100,625 2,25 1,0625
0 0 102,25 101,0625
y 10000 5000 40000 7000 80000 12000 50000 6000 15000 0 0
lb 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
MatLab results
x=
63.1554
0.0001
14.6158
0.0001
0.0002
364.8235
37.3317
0.0001
768.2368
0.0003
103.6018
0.0001
485.8033
0.0001
55.5194
0.0001
146.6991
0.0001
fval =
2.2051e+05
2) Short possitions are allowed
p 101.22 100.04 103,2 101,8 105,18 101,18 107,16 100,17 108,18 103,12 110,21 100,01 111,15 106,09 113,23 102,19 115,13 105,09

2. C 102.3125 100,4375 2,1875 0,875 1,9375 0,6875 2,125 0,375 2 0,9375 2,125 0,25 2 1,1875 2,125 0,625 2,25 1,0625
0 0 102,1875 100,875 1,9375 0,6875 2,125 0,375 2 0,9375 2,125 0,25 2 1,1875 2,125 0,625 2,25 1,0625
0 0 101,9375 100,6875 2,125 0,375 2 0,9375 2,125 0,25 2 1,1875 2,125 0,625 2,25 1,0625
0 0 102,125 100,375 2 0,9375 2,125 0,25 2 1,1875 2,125 0,625 2,25 1,0625
0 0 102 0,9375 2,125 0,25 2 1,1875 2,125 0,625 2,25 1,0625
0 0 102,125 100,25 2 1,1875 2,125 0,625 2,25 1,0625
0 0 102 101,1875 2,125 0,625 2,25 1,0625
0 0 102,125 100,625 2,25 1,0625
0 0 102,25 101,0625
y 10000 5000 40000 7000 80000 12000 50000 6000 15000 0 0
lb -1000 -1000 -1000 -1000 -1000 -1000 -1000 -1000 -1000 -1000 -1000 -1000 -1000 -1000 -1000 -1000 -1000 -1000
MatLab results
x=
1.0e+03 *
0.9716
-1.0000
0.9397
-1.0000
-1.0000
1.2986
0.9582
-1.0000
1.7076
-1.0000
1.0524
-1.0000
1.4523
-1.0000
1.0295
-1.0000
1.1351
-1.0000
fval =
2.1581e+05