ch 7 mismatch swaps

7/25/2019 Ch 7 Mismatch Swaps

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Worksheet Title

7.1 Market data

7.2 Pricing an in-arrears swap

7.3 Creating a customised average-rate swap

7.4 Creating a compound swap

7.5 Pricing a Constant Maturity Swap - using sa.

7." Pricing a Constant Maturity Swap - using #u.

7.7 Pricing a Constant Maturity Swap - using sa. 7.$ Pricing a Participation Constant Maturity Swap

7.% &stimating t'e conve(ity e!!ect o! a )eneric *

7.1+ Pricing a Constant Maturity Swap, 'ow does it

7.11 to 7.2+ Modeing swaps wit' conve(ity e!!ects

7.21 to 7.2" 0)M simuation o! *S to estimate t'e C e!!


2/27

!erence ate

e!erence ate paying sa.

!erence ate paying #u.- using sa. e!erence ate

S using !orward rates

c'ange in aue !or a s'i!t in t'e /orward Curve

cts


3/27

7.1: Market data

odays date, 4-/e-+$

Settement 2

ay 6-c rates gradient

count

+ 3.21" +.++++ "-/e-+$

+.+1% 3.21" -+.++"4 "-May-+$ +.25+ 3.133

+.+$1 3.177 -+.++2" "-8ug-+$ +.5+" 3.+73

+.25+ 3.133 -+.++23 "-9ov-+$ +.7"1 2.%55

+.5+" 3.+73 -+.++4" "-/e-+% 1.+17 2.$54

+.7"1 2.%55 -+.++4+ "-May-+% 1.2"4 2.7$7

1.+17 2.$54 -+.++27 "-8ug-+% 1.51% 2.74$

1.2"4 2.7$7 -+.++1" "-9ov-+% 1.775 2.737

1.51% 2.74$ -+.+++4 $-/e-1+ 2.+3" 2.755

1.775 2.737 +.+++7 "-May-1+ 2.27$ 2.7%$

2.+3" 2.755 +.++1$ "-8ug-1+ 2.533 2.$"+

2.27$ 2.7%$ +.++24 $-9ov-1+ 2.7%4 2.%2%

2.533 2.$"+ +.++2" 7-/e-11 3.+47 2.%%5

2.7%4 2.%2% +.++2" "-May-11 3.2%2 3.+57

3.+47 2.%%5 +.++25 $-8ug-11 3.553 3.12+3.2%2 3.+57 +.++24 7-9ov-11 3.$+" 3.1$+

3.553 3.12+ +.++24 "-/e-12 4.+5$ 3.23%

3.$+" 3.1$+ +.++23 7-May-12 4.311 3.2%$

4.+5$ 3.23% +.++23 "-8ug-12 4.5"4 3.357

4.311 3.2%$ +.++23 "-9ov-12 4.$1% 3.417

4.5"4 3.357 +.++23 "-/e-13 5.+75 3.475

4.$1% 3.417 +.++23 "-May-13 5.322 3.531

5.+75 3.475 +.++23 "-8ug-13 5.57$ 3.5$$

5.322 3.531 +.++22 "-9ov-13 5.$33 3."435.57$ 3.5$$ +.++21 "-/e-14 ".+$% 3."%5

5.$33 3."43 +.++2+ "-May-14 ".33" 3.742

".+$% 3."%5 +.++1% "-8ug-14 ".5%2 3.7$%

".33" 3.742 +.++1$ "-9ov-14 ".$47 3.$33

".5%2 3.7$% +.++17 "-/e-15 7.1+3 3.$75

".$47 3.$33 +.++1" "-May-15 7.35+ 3.%13

7.1+3 3.$75 +.++15 "-8ug-15 7."+" 3.%51

7.35+ 3.%13 +.++15 "-9ov-15 7.$"1 3.%$7

7."+" 3.%51 +.++14 $-/e-1" $.122 4.+25

7.$"1 3.%$7 +.++14 "-May-1" $.3"7 4.+"+


4/27

$.122 4.+25 +.++14 $-8ug-1" $."2$ 4.+%$

$.3"7 4.+"+ +.++14 7-9ov-1" $.$$1 4.133

$."2$ 4.+%$ +.++14 "-/e-17 %.133 4.1"7

$.$$1 4.133 +.++14 $-May-17 %.3$" 4.2++

%.133 4.1"7 +.++13 7-8ug-17 %."3% 4.231%.3$" 4.2++ +.++12 "-9ov-17 %.$%2 4.2"1

%."3% 4.231 +.++12 "-/e-1$ 1+.147 4.2%+

%.$%2 4.2"1 +.++11 7-May-1$ 1+.3%7 4.317

1+.147 4.2%+ +.++11 "-8ug-1$ 1+."5+ 4.343

1+.3%7 4.317 +.++1+ "-9ov-1$ 1+.%+" 4.3"$

1+."5+ 4.343 +.++1+ "-/e-1% 11.1"1 4.3%3

1+.%+" 4.3"$ +.++1+ "-May-1% 11.4+$ 4.41"

11.1"1 4.3%3 +.+++% "-8ug-1% 11.""4 4.43%

11.4+$ 4.41" +.+++% "-9ov-1% 11.%1% 4.4"1

11.""4 4.43% +.+++% "-/e-2+ 12.175 4.4$311.%1% 4.4"1 +.+++$ "-May-2+ 12.425 4.5+3

12.175 4.4$3 +.+++$ "-8ug-2+ 12."$1 4.524

12.425 4.5+3 +.+++$ "-9ov-2+ 12.%3" 4.544

12."$1 4.524 +.+++$ $-/e-21 13.1%7 4.5"4

12.%3" 4.544 +.+++$ "-May-21 13.43% 4.5$2

13.1%7 4.5"4 +.+++7 "-8ug-21 13."%4 4."++

13.43% 4.5$2 +.+++7 $-9ov-21 13.%5" 4."1$

13."%4 4."++ +.+++7 7-/e-22 14.2+$ 4."34

13.%5" 4."1$ +.+++7 "-May-22 14.453 4."5+14.2+$ 4."34 +.+++" $-8ug-22 14.714 4."""

14.453 4."5+ +.+++" 7-9ov-22 14.%"7 4."$+

14.714 4.""" +.+++" "-/e-23 15.21% 4."%4

14.%"7 4."$+ +.+++5 $-May-23 15.472 4.7+7

15.21% 4."%4 +.+++5 7-8ug-23 15.725 4.71%

15.472 4.7+7 +.+++5 "-9ov-23 15.%7$ 4.73+

15.725 4.71% +.+++5 "-/e-24 1".233 4.741

15.%7$ 4.73+ +.+++4 "-May-24 1".4$3 4.752

1".233 4.741 +.+++4 "-8ug-24 1".73% 4.7"1

1".4$3 4.752 +.+++4 "-9ov-24 1".%%4 4.771

1".73% 4.7"1 +.+++4 "-/e-25 17.25+ 4.7$+

1".%%4 4.771 +.+++3 "-May-25 17.4%7 4.7$$

17.25+ 4.7$+ +.+++3 "-8ug-25 17.753 4.7%5

17.4%7 4.7$$ +.+++3 "-9ov-25 1$.++$ 4.$+3

17.753 4.7%5 +.+++3 "-/e-2" 1$.2"4 4.$1+

1$.++$ 4.$+3 +.+++3 "-May-2" 1$.511 4.$1"

1$.2"4 4.$1+ +.+++3 "-8ug-2" 1$.7"7 4.$23

1$.511 4.$1" +.+++2 "-9ov-2" 1%.+22 4.$2%

1$.7"7 4.$23 +.+++2 $-/e-27 1%.2$3 4.$341%.+22 4.$2% +.+++2 "-May-27 1%.525 4.$3%


5/27

1%.2$3 4.$34 +.+++2 "-8ug-27 1%.7$1 4.$44

1%.525 4.$3% +.+++2 $-9ov-27 2+.+42 4.$4%

1%.7$1 4.$44 +.+++2 7-/e-2$ 2+.2%4 4.$54

2+.+42 4.$4% +.+++2 $-May-2$ 2+.547 4.$5$

2+.2%4 4.$54 +.+++2 7-8ug-2$ 2+.$++ 4.$"22+.547 4.$5$ +.+++2 "-9ov-2$ 21.+53 4.$""

2+.$++ 4.$"2 +.+++1 "-/e-2% 21.3+$ 4.$"%

21.+53 4.$"" +.+++1 7-May-2% 21.55$ 4.$72

21.3+$ 4.$"% +.+++1 "-8ug-2% 21.$11 4.$75

21.55$ 4.$72 +.+++1 "-9ov-2% 22.+"7 4.$7$

21.$11 4.$75 +.+++1 "-/e-3+ 22.322 4.$$1

22.+"7 4.$7$ +.+++1 "-May-3+ 22.5"% 4.$$3

22.322 4.$$1 +.+++1 "-8ug-3+ 22.$25 4.$$"

22.5"% 4.$$3 +.+++1 "-9ov-3+ 23.+$1 4.$$$

22.$25 4.$$" +.+++1 "-/e-31 23.33" 4.$$%23.+$1 4.$$$ +.+++1 "-May-31 23.5$3 4.$%1

23.33" 4.$$% +.+++1 "-8ug-31 23.$3% 4.$%2

23.5$3 4.$%1 +.+++1 "-9ov-31 24.+%4 4.$%4

23.$3% 4.$%2 +.++++ "-/e-32 24.35+ 4.$%5

24.+%4 4.$%4 +.++++ "-May-32 24."++ 4.$%"

24.35+ 4.$%5 +.++++ "-8ug-32 24.$5" 4.$%"

24."++ 4.$%" +.++++ $-9ov-32 25.117 4.$%7

24.$5" 4.$%" +.++++ 7-/e-33 25.3"% 4.$%7

25.117 4.$%7 +.++++ "-May-33 25."14 4.$%725.3"% 4.$%7 +.++++ $-8ug-33 25.$75 4.$%7

25."14 4.$%7 +.++++ 7-9ov-33 2".12$ 4.$%7

25.$75 4.$%7 +.++++ "-/e-34 2".3$1 4.$%7

2".12$ 4.$%7 +.++++ $-May-34 2"."33 4.$%"

2".3$1 4.$%7 +.++++ 7-8ug-34 2".$$" 4.$%"

2"."33 4.$%" +.++++ "-9ov-34 27.13% 4.$%5

2".$$" 4.$%" +.++++ "-/e-35 27.3%4 4.$%4

27.13% 4.$%5 +.++++ 7-May-35 27."44 4.$%4

27.3%4 4.$%4 +.++++ "-8ug-35 27.$%7 4.$%3

27."44 4.$%4 +.++++ "-9ov-35 2$.153 4.$%2

27.$%7 4.$%3 +.++++ "-/e-3" 2$.4+$ 4.$%1

2$.153 4.$%2 +.++++ "-May-3" 2$."5$ 4.$%+

2$.4+$ 4.$%1 +.++++ "-8ug-3" 2$.%14 4.$$%

2$."5$ 4.$%+ +.++++ "-9ov-3" 2%.1"% 4.$$$

2$.%14 4.$$% +.++++ "-/e-37 2%.425 4.$$7

2%.1"% 4.$$$ +.++++ "-May-37 2%."72 4.$$"

2%.425 4.$$7 +.++++ "-8ug-37 2%.%2$ 4.$$5

2%."72 4.$$" +.++++ "-9ov-37 3+.1$3 4.$$4

2%.%2$ 4.$$5 +.++++ $-/e-3$ 3+.444 4.$$23+.1$3 4.$$4 +.++++


6/27

3+.444 4.$$2


7/27

1

+.%%21%%

+.%$45$2

+.%77757

+.%713%7

+.%"53$3

+.%5%112

+.%525$"

+.%4545$

+.%3$24%

+.%3+114

+.%21421

+.%127"4

+.%+4277

+.$%5+$++.$$"+33

+.$7"$3+

+.$"74"+

+.$57%3%

+.$4$1$1

+.$3$3+$

+.$2$"57

+.$1$"23

+.$+$572+.7%$542

+.7$$$%3

+.77$%$"

+.7"%15"

+.75%411

+.75++7+

+.74+47"

+.73+%14

+.72115+

+.711%$+


8/27

+.7+21%%

+."%2775

+."$3432

+."741%%

+.""5+77+."5"+""

+."47+7+

+."3$37$

+."2%"%7

+."21+2"

+."1245%

+."+42"2

+.5%5$$"

+.5$7"+2

+.57%4+%+.57147"

+.5"345%

+.555537

+.547547

+.54+244

+.532"27

+.524%57

+.517"41

+.51+"71+.5+334"

+.4%"37+

+.4$%511

+.4$277+

+.47"145

+.4"%"32

+.4"315%

+.45"%33

+.45+"75

+.444521

+.43$4"%

+.4327+$

+.42"$5+

+.421+$7

+.41541$

+.41++1$

+.4+4525

+.3%%12+

+.3%3"$4+.3$$72%


9/27

+.3$357+

+.37$3$1

+.373434

+.3"$5"2

+.3"37"3+.35%+37

+.354332

+.34%7%%

+.3452$"

+.34+7%4

+.33"371

+.33215$

+.327$7+

+.323"5+

+.31%4%"+.31553$

+.311512

+.3+754%

+.3+3"4%

+.2%%$%3

+.2%"114

+.2%231"

+.2$$"%7

+.2$5251+.2$1"2%

+.27$17"

+.27477"

+.27142"

+.2"$12"

+.2"4$73

+.2"1"32

+.25$5+"

+.2553$%

+.2522$1

+.24%21"

+.24"25"

+.243271

+.24+325

+.237417

+.234"3%

+.231$+3

+.22%++2

+.22"17"


10/27


11/27

7.2: Pricing an in-arrears swap

Today's date: 4-Feb-08

Swap structure

Maturity 5 years

Principa 1++ m :S

To receive 3m ;ior in-arrears

To pay 3m ;ior < 7.2 in advance

Swap ay *0= *mpied Swap Swap

dates count d!s /orward cas'!ows cas'!ows

>8ct?3"+@ rates receive side pay side

>miions@ >miions@

A1B A2B A3B

"-/e-+$ 1

"-May-+$ +.25+ +.%%21%$$37 3.145 +.75"$ -+.$+51"-8ug-+$ +.25" +.%$45$1$5$ 3.+27 +."%$+ -+.7%2%

"-9ov-+$ +.25" +.%77757275 2.731 +."54$ -+.7172

"-/e-+% +.25" +.%713%7+13 2.5"2 +."43% -+."74+

"-May-+% +.247 +.%"53$3272 2.52+ +."325 -+."415

"-8ug-+% +.25" +.%5%11224 2.55$ +."$52 -+."731

"-9ov-+% +.25" +.%525$5575 2."$1 +.737% -+.7+44

$-/e-1+ +.2"1 +.%4545757" 2.$$7 +.$3+1 -+.773"

"-May-1+ +.242 +.%3$24$$"7 3.17% +.$27+ -+.7$"5

"-8ug-1+ +.25" +.%3+114445 3.422 +.%234 -+.$%3$

$-9ov-1+ +.2"1 +.%2142+734 3."13 +.%7%7 -+.%"32

7-/e-11 +.253 +.%127"3%5$ 3.752 +.%7+5 -+.%"74

"-May-11 +.244 +.%+427714 3.$3% +.%"1% -+.%5"%

$-8ug-11 +.2"1 +.$%5+$+33" 3.%35 1.+547 -1.+471

7-9ov-11 +.253 +.$$"+33334 4.+3% 1.+4%" -1.+4+1

"-/e-12 +.253 +.$7"$3+2%5 4.152 1.+$+2 -1.+"$"

7-May-12 +.253 +.$"745%744 4.273 1.1+%7 -1.+%%2

"-8ug-12 +.253 +.$57%3%2% 4.3%+ 1.137% -1.12$7

"-9ov-12 +.25" +.$4$1$135% 4.5+2 1.177$ -1.1"%7

"-/e-13 +.25" +.$3$3+7$+$ 4."+% 1.2+3% -1.1%7+

"-May-13 +.247 +.$2$"5"$34 4.711

Present aue D

Spread etween !irst and ast rates 7.8!


12/27

7.!: "reating a c#sto$ised a%erage-rate swap


Structure of Debt

Next payment Margin Last fixing Last fixing

Date Principal >p@ date Weights

2+-/e-+$ 1++ 25 E9?8 3.325+ 2$.57

7-Mar-+$ 5+ 35 E9?8 3.315+ 14.2%

21-Mar-+$ 75 3+ E9?8 3.2%75 21.43

3-8pr-+$ 1++ 25 E9?8 3.2725 2$.57

17-8pr-+$ 25 5+ E9?8 3.225+ 7.14

Debt ) Debt , Debt

ates ay /s *mpied ates ay /s *mpied ates ay

count 3mo. count 3mo. count

>8ct?3"+@ /orward >8ct?3"+@ /orward >8ct?3"+@

rates rates

E9?8 E9?8 E9?8

A1B A2B A3B A4B A5B A"B A7B

"-/e-+$ 1 "-/e-+$ 1 "-/e-+$

2+-/e-+$ E9?8 +.%%$755 3.325++ 7-Mar-+$ E9?8 +.%%735" 3.315++ 21-Mar-+$ E9?8

3 2+-May-+$ +.25+ +.%%1+17 3.123 %-Gun-+$ +.2"1 +.%$%342 3.1+2 23-Gun-+$ +.2"1

" 2+-8ug-+$ +.25" +.%$35+2 2.%%+ $-Sep-+$ +.253 +.%$2+"+ 2.%33 22-Sep-+$ +.253

% 2+-9ov-+$ +.25" +.%7"754 2.7+3 $-ec-+$ +.253 +.%754$3 2.""7 22-ec-+$ +.253

12 2+-/e-+% +.25" +.%7+427 2.551 %-Mar-+% +.253 +.%"%2"2 2.53% 23-Mar-+% +.253

15 2+-May-+% +.247 +.%"4414 2.522 $-Gun-+% +.253 +.%"31+7 2.52$ 22-Gun-+% +.253

1$ 2+-8ug-+% +.25" +.%5$113 2.573 7-Sep-+% +.253 +.%5"$31 2.5%5 21-Sep-+% +.253

21 2+-9ov-+% +.25" +.%5152" 2.7+% 7-ec-+% +.253 +.%5+23% 2.744 21-ec-+% +.253

24 22-/e-1+ +.2"1 +.%443+7 2.%2$ $-Mar-1+ +.253 +.%43153 2.%72 22-Mar-1+ +.253

27 2+-May-1+ +.242 +.%37+25 3.21" 7-Gun-1+ +.253 +.%35445 3.2"+ 21-Gun-1+ +.253

3+ 2+-8ug-1+ +.25" +.%2$$3" 3.45+ 7-Sep-1+ +.25" +.%271$3 3.4$7 21-Sep-1+ +.25"

33 22-9ov-1+ +.2"1 +.%2+1+4 3."34 7-ec-1+ +.253 +.%1$"$7 3."5% 21-ec-1+ +.253


13/27

7.4: "reating a co$po#nd swap


Maturity 5 yrs

Principal roercoaster

#loating mo. ;ior < ,* bp

#ixed (-!)+ ann 8ct?3"+ .ompound margin

#ixed rate

ates ay /s 9otiona *mpied /oating /i(ed 9et Compounded

count Principa 3mo. Pay eceive C/s /oating

>8ct?3"+@ /orward side side Pay

rates side

"-/e-+$ 1 "-/e-+$

"-May-+$ +.25+ +.%%21%% 5+ 3.145 -+.4244 -+.4244 "-May-+$ -+.4244

"-8ug-+$ +.25" +.%$45$2 5+ 3.+27 -+.41$$ -+.41$$ "-8ug-+$ -+.$4"1

"-9ov-+$ +.25" +.%77757 5+ 2.731 -+.3$+% -+.3$+% "-9ov-+$ -1.2324

"-/e-+% +.25" +.%713%7 5+ 2.5"2 -+.35%3 1.%+15 1.5422 "-/e-+% -1.5%%+ 1

"-May-+% +.247 +.%"53$3 75 2.52+ -+.513" -+.513" "-May-+% -+.513"

"-8ug-+% +.25" +.%5%112 75 2.55$ -+.53$3 -+.53$3 "-8ug-+% -1.+54%

"-9ov-+% +.25" +.%525$" 75 2."$1 -+.5"1$ -+.5"1$ "-9ov-+% -1."232$-/e-1+ +.2"1 +.%4545$ 75 2.$$7 -+."144 2.$"++ 2.245" $-/e-1+ -2.24$$ 2

"-May-1+ +.242 +.%3$24% 1++ 3.17% -+.$2$7 -+.$2$7 "-May-1+ -+.$2$7

"-8ug-1+ +.25" +.%3+114 1++ 3.422 -+.%3$5 -+.%3$5 "-8ug-1+ -1.773%

$-9ov-1+ +.2"1 +.%21421 1++ 3."13 -1.++$$ -1.++$$ $-9ov-1+ -2.7%$3

7-/e-11 +.253 +.%127"4 1++ 3.752 -1.+11" 3.7$22 2.77+" 7-/e-11 -3.$34" 3

"-May-11 +.244 +.%+4277 75 3.$3% -+.74%7 -+.74%7 "-May-11 -+.74%7

$-8ug-11 +.2"1 +.$%5+$+ 75 3.%35 -+.$1%" -+.$1%" $-8ug-11 -1.57"5

7-9ov-11 +.253 +.$$"+33 75 4.+3% -+.$132 -+.$132 7-9ov-11 -2.4+4$

"-/e-12 +.253 +.$7"$3+ 75 4.152 -+.$34" 2.$3"" 2.++21 "-/e-12 -3.2"31 2

7-May-12 +.253 +.$"74"+ 5+ 4.273 -+.5717 -+.5717 7-May-12 -+.5717

"-8ug-12 +.253 +.$57%3% 5+ 4.3%+ -+.5$"4 -+.5$"4 "-8ug-12 -1.1"41

"-9ov-12 +.25" +.$4$1$1 5+ 4.5+2 -+."+72 -+."+72 "-9ov-12 -1.7$4+

"-/e-13 +.25" +.$3$3+$ 5+ 4."+% -+."2+$ 1.%+15 1.2$+" "-/e-13 -2.4247 1

P +.++++ P


14/27

-(* Pricing a .onstant Maturity S/ap " using sa( 0eference 0ate

Today's date !"#eb"$%

Maturity ! year swap

Principa, )$$ miion :S

o pay, 1 mo ;ior

o receive, * year CMS pus "2)($% p margin

Swap day ;ior H *mpied ;ior *mpied CMSates count /s ;ior cas'!ows CMS Cas'!ow

>act?3"+@ discounted

A1B A2B A3B A4B A5B A"B A7

"-/e-+$ 1 + I I

"-8ug-+$ +.5+" +.%$45$2 +.4%77"1 I 3.+%7 -1J5"5J%5$.33 I 3.474 1J75"J245.75 -4

"-/e-+% +.511 +.%713%7 +.%%4253 I 2."5" -1J357J3+7.5$ I 3."33 1J$5"J77".31 -4

"-8ug-+% +.5+3 +.%5%112 1.47"473 I 2.54$ -1J2$+J$4$.2$ I 3.$5$ 1J%3%J%12.2% -4

$-/e-1+ +.517 +.%4545$ 1.%"4%5% I 2.7%5 -1J444J23$.71 I 4.1+37 2J12+J225.2% -4

"-8ug-1+ +.4%7 +.%3+114 2.427433 I 3.31$ -1J"4%J5%".+5 I 4.33$ 2J15"J$+3.+5 -4

7-/e-11 +.514 +.%127"4 2.$%"4%2 I 3."%% -1J%++J$73.41 I 4.51" 2J32+J%25.5+ -4

$-8ug-11 +.5+" +.$%5+$+ 3.34%++5 I 3.%+$ -1J%75J"4".33 I 4."71 2J3"1J324.5$ -4

"-/e-12 +.5+" +.$7"$3+ 3.7%22%1 I 4.117 -2J+$1J3"5.2" I 4.$1" 2J434J$23.17 -4

"-8ug-12 +.5+" +.$57%3% 4.22"+27 I I"-/e-13 +.511 +.$3$3+$ 4."544%" I I

"-8ug-13 +.5+3 +.$1$"23 5.+""+$1 I I

"-/e-14 +.511 +.7%$542 5.474225 I I

"-8ug-14 +.5+3 +.77$%$" 5.$"5$$2 I I

"-/e-15 +.511 +.75%411 ".254+25 I I

"-8ug-15 +.5+3 +.74+47" "."2"32+ I I

$-/e-1" +.517 +.72115+ ".%%$%14 I I

$-8ug-1" +.5+" +.7+21%% 7.353%14 I I

"-/e-17 +.5+" +."$3432 7."%%427 I I

7-8ug-17 +.5+" +.""5+77 $.+35""+ I I

"-/e-1$ +.5+$ +."47+7+ $.3"45$7 I I

I I

P -12J31"J%7+.53 15J771J+44.+7 -3J4

/air vaue

8verage !i(ings 3.2"7 4.17"

i!!erence 2$(2$ p


15/27

-(1 Pricing a .onstant Maturity S/ap " using 3u( 0eference 0ate paying sa(




o pay, 1 mo ;ior

o receive, * year CMS pus "%%(%1 p margin

;ior H

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17/27

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18/27

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"-May-+% +.247 2.52+ +.%"53$3

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7-May-12 +.253 4.273 +.$"74"+

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"-8ug-15 +.25" 5.+7+ +.74+47"


19/27

"-9ov-15 +.25" 5.11% +.73+%14

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7-9ov-22 +.253 5.5"+ +.4%"37+

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20/27

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21/27

ard rates

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23/27

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".+2" +.23$$12 13.14537 4.+2" +.3$"321

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5.%%3 +.23172$ 3.%%3 +.37$"23

5.%77 +.22$1"$ 3.%77 +.374732

5.%5% +.2247$1 13.37453 3.%5% +.371+1%

5.%42 +.2215"3 3.%42 +.3"747$

5.%2" +.21$1$7 3.%2" +.3"374%

5.%1+ +.214%7" 3.%1+ +.3"+1$%

5.$%" +.211$1% 13.5$$7 3.$%" +.35""77

5.$$2 +.2+$71" 3.$$2 +.353211

5.$7+ +.2+5""4 3.$7+ +.34%7$%

5.$5$ +.2+2""3 3.$5$ +.34"411

5.$47 +.1%%"$+ 13.7%115 3.$47 +.343+3%

5.$37 +.1%"$+7 3.$37 +.33%77%

5.$2$ +.1%3%5+ 3.$2$ +.33"522

5.$2+ +.1%11+7 3.$2+ +.3332"%5.$13 +.1$$31+ 13.%$2+$ 3.$13 +.33++52

5.$+7 +.1$5"15 3.$+7 +.32"%41

5.$+1 +.1$2%+4 3.$+1 +.3237%5

5.7%7 +.1$+234 3.7%7 +.32+"$4

5.7%3 +.177"+4 14.1"2"4 3.7%3 +.317"+5

5.7%+ +.175+%$ 3.7%+ +.314"57

5.7$$ +.17254" 3.7$$ +.311"41

5.7$" +.17++32 3.7$" +.3+$"54

5.7$5 +.1"75+2 14.3334 3.7$5 +.3+5"33


24/27

Conve(ity e!!ect !or di!!erent maturities

*mpact o! 1++p parae s'i!t

Maturity :S :S per yr p pa.

2 451 225 +.+2

5 2J413 4$3 +.+5

1+ 7J%5% 7%" +.+$

15 14J$74 %%2 +.1+

2+ 22J2"2 1J113 +.11

25 2%J"%1 1J1$$ +.12

3+ 3"J%54 1J232 +.12

+

+.%%7"1$

&(tract !rom :S curve, 15 /eruary 2++$

Midpoints

1.%$1171 2+ 5.+$$ 5.+5$ 5.+73

25 5.143 5.113 5.12$

3+ 5.1"3 5.133 5.14$

4+ 5.1"$ 5.13$ 5.153

2.%3244% 5+ 5.15$ 5.12$ 5.143

3.$554$2

4.7517$%

5."11$2$

".437%"2


25/27

7.2347"1

7.%%1231

$.71""4%

%.41+174

1+.+72$$

1+.71+"%

11.313+%

11.$$$4$

12.43%$$

12.%"$"

13.4731$

13.%5$$5


26/27

14.42+3"

14.$"3$$

15.2$%17

15."%71%

1".+$$$7

1".4"711

1".$2775

17.17555

17.51+1%

17.$33+$

1$.144""


27/27

-()$ Pricing a .onstant Maturity S/ap ho/ does it change in 8alue for a shift in the #or/ard .ur5e


&(ampe, 4 year swap

o pay, " mo ;ior

o receive, 5 year CMS pus -%1.+$p margin Ne/ 8alue after shift 9per bp: "$*(!21

Shift in Libor & )$$ bp

;ior I I

Swap day d!s I *mpied I ;ior new new ;ior CMS CM

ates count intpoated I /8 I up / H cas'!ows yied Cas'!ow

>act?3"+@ I I discounted

I I -%1.+

"-/e-+$ 1 I I 1

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I I

P -157J4+1.53 157J+%".+

ch 7 mismatch swaps

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