ch 3 generic swaps

7/25/2019 Ch 3 Generic Swaps

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Worksheet Title

3.1 Market data

3.2 Worksheet to generate the cashflows of a generic USD swap

3.3 Worksheet to demonstrate the discovery of a synthetic par bond

3. Worksheet to generate the fi!ed cashflows of a generic USD swap

3." Worksheet to calc#late a disco#nt c#rve #sing linear interpolation on

3.$ Details of %ermitian &nterpolation

3.' Worksheet to calc#late a disco#nt c#rve #sing %ermite interpolation3.( Worksheet to calc#late a disco#nt c#rve #sing an optimisation appro

3.) *#ilding a blended c#rve #sing optimisation


2/85

the swap c#rve and different methods on the disco#nt c#rve

on the swap c#rve and different methods on the disco#nt c#rvech


3/85

+oday,s date- 4-Feb-08

Cash rates

USD

on "/0eb/( 3.23'"

'/day 11/0eb/( 3.21'"

1/month /Mar/( 3.1(13

3/month /May/( 3.1"

$/month /#g/( 3.)'"

12/month /0eb/) 2.()$3

Swap rates (mid)

44

5ears $/0eb/( ct3$

1 $/0eb/) 2.')"

2 (/0eb/1 2.')"

3 '/0eb/11 3.3"

$/0eb/12 3.2'"

" $/0eb/13 3.""

$ $/0eb/1 3.'1"

' $/0eb/1" 3.(("( (/0eb/1$ .2"

) $/0eb/1' .1""

1 $/0eb/1( .2$"

12 $/0eb/2 .3"

1" $/0eb/23 .$1"

2 '/0eb/2( .'""

2" '/0eb/33 .("

3 (/0eb/3( .(1"

against 3mo 6ibor

Deposit Futures


4/85

Mar/( 1)/Mar/( )'.

7#n/( 1(/7#n/( )'.1

Sep/( 1'/Sep/( )'."2

Dec/( 1'/Dec/( )'.)"

Mar/) 1(/Mar/) )'.3)"

7#n/) 1'/7#n/) )'.22

Sep/) 1$/Sep/) )'.

Dec/) 1$/Dec/) )$.("

Mar/1 1'/Mar/1 )$.$$"

7#n/1 1$/7#n/1 )$.)"

Sep/1 1"/Sep/1 )$.3

Dec/1 1"/Dec/1 )$.2

Mar/11 1$/Mar/11 )$.$

7#n/11 1"/7#n/11 )".)3

Sep/11 21/Sep/11 )".(Dec/11 21/Dec/11 )".$'"

Mar/12 21/Mar/12 )"."$"

7#n/12 2/7#n/12 )"."

Sep/12 1)/Sep/12 )".33"

Dec/12 1)/Dec/12 )".22"

Mar/13 2/Mar/13 )".1

7#n/13 1)/7#n/13 )"."

Sep/13 1(/Sep/13 ).)""

Dec/13 1(/Dec/13 ).($

Mar/1 1)/Mar/1 ).'("7#n/1 1(/7#n/1 ).'1

Sep/1 1'/Sep/1 ).$"

Dec/1 1'/Dec/1 )."'

Mar/1" 1(/Mar/1" )."1"

7#n/1" 1'/7#n/1" ).$

Sep/1" 1$/Sep/1" ).1

Dec/1" 1$/Dec/1" ).3"

Mar/1$ 1$/Mar/1$ ).31"

7#n/1$ 1"/7#n/1$ ).2'"

Sep/1$ 21/Sep/1$ ).23"

Dec/1$ 21/Dec/1$ ).1("

Mar/1' 1"/Mar/1' ).1$"

7#n/1' 21/7#n/1' ).1"

Sep/1' 2/Sep/1' ).12

Dec/1' 2/Dec/1' ).(


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3.! Worksheet to "e#erate the $ash%lows o% a "e#eri$ &SD swap

+rade date- 4-Feb-08 +rade date- 4-Feb-08

Settlement date- $/0eb/( Settlement date- $/0eb/(

4otional principal- 1 million 4otional principal- 1 million

Mat#rity- ' years Mat#rity- ' years

+o receive fi!ed rate- 3.((" 448 ct3$ +o receive fi!ed rate 3.((" 448 ct3$

+o pay floating rate- 3 mo. 6ibor +o pay floating rate- 3 mo. 6ibor

0irst 6ibor fi!ing- 3.1" 0irst 6ibor fi!ing- 3.1"

3.((3)

Days 0i!ed 0loating 0i!ed 0loating 5ield/based

9ct3$: cashflows cashflows cashflows cashflows D0s$/0eb/( $/0eb/( /188 188 1

3 $/May/( .2" /'($82" $/May/( /'($82"

$ $/#g/( .2"$ /6ibor $/#g/( /6ibor

) $/4ov/( .2"$ /6ibor $/4ov/( /6ibor

12 $/0eb/) .2"$ 38))8'". /6ibor $/0eb/) 38))8'" /6ibor .)$22

1" $/May/) .2' /6ibor $/May/) /6ibor

1( $/#g/) .2"$ /6ibor $/#g/) /6ibor

21 $/4ov/) .2"$ /6ibor $/4ov/) /6ibor

2 (/0eb/1 .2$1 38)$8"1.$' /6ibor (/0eb/1 38)$8"2 /6ibor .)2"3"

2' $/May/1 .22 /6ibor $/May/1 /6ibor

3 $/#g/1 .2"$ /6ibor $/#g/1 /6ibor

33 (/4ov/1 .2$1 /6ibor (/4ov/1 /6ibor

3$ '/0eb/11 .2"3 38)2(81$$.$' /6ibor '/0eb/11 38)2(81$' /6ibor .()3''

3) $/May/11 .2 /6ibor $/May/11 /6ibor 2 (/#g/11 .2$1 /6ibor (/#g/11 /6ibor

" '/4ov/11 .2"3 /6ibor '/4ov/11 /6ibor

( $/0eb/12 .2"3 38)2(81$$.$' /6ibor $/0eb/12 38)2(81$' /6ibor .("$'2$

"1 '/May/12 .2"3 /6ibor '/May/12 /6ibor

" $/#g/12 .2"3 /6ibor $/#g/12 /6ibor

"' $/4ov/12 .2"$ /6ibor $/4ov/12 /6ibor

$ $/0eb/13 .2"$ 38))8'". /6ibor $/0eb/13 38))8'" /6ibor .(21'2

$3 $/May/13 .2' /6ibor $/May/13 /6ibor

$$ $/#g/13 .2"$ /6ibor $/#g/13 /6ibor

$) $/4ov/13 .2"$ /6ibor $/4ov/13 /6ibor

'2 $/0eb/1 .2"$ 38)3(8)"(.33 /6ibor $/0eb/1 38)3(8)"( /6ibor .')2)3)

'" $/May/1 .2' /6ibor $/May/1 /6ibor

'( $/#g/1 .2"$ /6ibor $/#g/1 /6ibor

(1 $/4ov/1 .2"$ /6ibor $/4ov/1 /6ibor

( $/0eb/1" .2"$ 38)3(8)"(.33 /6ibor $/0eb/1" 138)3(8)"( /96ibor;188: .'$2(()

1.311"


6/85

3.3! Worksheet to demo#strate the dis$o'er o% a s#theti$ par bo#d

Todas date! 4-Feb-08

US benchmark bonds

+ime to 5+M 5ield

mat#rity sa gradient spread ; spread

$/0eb/(

7an/1 1.)2 *.+4, .2 ('. 2.(1

7an/13 .)" ., .1) ($. 3."2

4ov/1' ).'(1 3.8, . '. .2(

May/3' 2).2) 4.34, (. .(2

/0eb/1" '. 3."1 (". 3.))

interpolated spread swap

yields 9bp: rates

$/0eb/(

2 (/0eb/1 2.( 1.)"$ (".(3 2.')"

3 '/0eb/11 3." 2.1)" (".() 3.3"

$/0eb/12 .3 2.3 (".) 3.2'"" $/0eb/13 "." 2.$'1 (".12 3.""

$ $/0eb/1 $." 2.($2 ('.1 3.'1"

' $/0eb/1" '." 3."2 (.() 3.(("

( (/0eb/1$ (.11 3.23 ').$( .2"

) $/0eb/1' ).( 3.33 '3.$2 .1""

1 $/0eb/1( 1.( 3."() $(.)$ .2$"

11 $/0eb/1) 11.( 3.$2(

12 $/0eb/2 12.( 3.$$' '(. .3"

13 (/0eb/21 13.1$ 3.'$

1 '/0eb/22 1.1 3.'"

1" $/0eb/23 1".11 3.'( (.1) .$1"

1$ $/0eb/2 1$.11 3.(23

1' $/0eb/2" 1'.1 3.($2

1( $/0eb/2$ 1(.1 3.)1

1) (/0eb/2' 1).1) 3.)

2 '/0eb/2( 2.1$ 3.)') '(."$ .'""


7/85

21 $/0eb/2) 21.1$ .1(

22 $/0eb/3 22.1$ ."'

23 $/0eb/31 23.1$ .)$

2 $/0eb/32 2.1$ .13"

2" '/0eb/33 2".22 .1' $.1 .("

2$ $/0eb/3 2$.1) .213

2' $/0eb/3" 2'.1) .2"2

2( $/0eb/3$ 2(.1) .2)

2) $/0eb/3' 2).22 .33

3 (/0eb/3( 3.2' .3 (.3' .(1"


8/85

=hange Swap

nn dayco#nt rates

2.(3 2.')1 2.')"

3.""1 3."2 3.""

.32$ .2$' .2$"

.('( .(11 .(1"

3.)3) 3.((" 3.(("

0.000 .000 *0.00,

*.00,

.00,

3.00,

4.00,

.00,

&S /e#$hmark /o#d $ur

4 Februar 008

ield

1


9/85


10/85

0.000 *.000 0.000 .000 30.000

e

maturit (rs)r


11/85


12/85

3.4! Worksheet to "e#erate the %i2ed $ash%lows o% a "e#eri$ &SD swap

+rade date- 4-Feb-08 +rade date- 4-Feb-08

Settlement date- $/0eb/( Settlement date- $/0eb/(

4otional principal- 1 million 4otional principal- 1 million

Mat#rity- 2 years Mat#rity- 12 years

+o receive fi!ed rate- 2.')" 448 ct3$ +o receive fi!ed rate- .3" 448 ct3$

+o pay floating rate- 3 mo. 6ibor +o pay floating rate- 3 mo. 6ibor

12 month D0 off f#t#res strip .)'2$"' 12 month D0 off f#t#res strip .)'2$"'

Days 0i!ed D0s Days 0i!ed D0s9ct3$: cashflows 9ct3$: cashflows

$/0eb/( /188. 1 $/0eb/( /188. 1

$/0eb/) 1.1' 28(18"(3.33 .)'2$"' $/0eb/) 1.1' 8"(8)1$.$' .)'2$"'

(/0eb/1 1.1) 128()83'.22 .)"23 (/0eb/1 1.1) 8"21823$.11 .)"23

'/0eb/11 1.11 8(82''.'( .)12'2'

$/0eb/12 1.11 8(82''.'( .('$')2

. $/0eb/13 1.1' 8"(8)1$.$' .(3(2$(

$/0eb/1 1.1 8)$8")'.22 .')("2

$/0eb/1" 1.1 8)$8")'.22 .'")3'

(/0eb/1$ 1.1) 8"21823$.11 .'2111

$/0eb/1' 1.11 8(82''.'( .$(33)1

$/0eb/1( 1.1 8)$8")'.22 .$'3

$/0eb/1) 1.1 8)$8")'.22 .$12)$2

$/0eb/2 1.1 18)$8")'.22 ."')3(

.


13/85

3.! Worksheet to $al$ulate a dis$ou#t $ur'e usi#" li#ear i#terpolatio# o# the s


=#rrent USD market data

6ibor cash

ct3$

$/0eb/(

' day 11/0eb/( 3.21'"

1 mo /Mar/( 3.1(12"

3 mo /May/( 3.1"

0#t#res gradient

Mar/( 1)/Mar/( 3. /."

7#n/( 1(/7#n/( 2.") /.12

Sep/( 1'/Sep/( 2.( .3

Dec/( 1'/Dec/( 2."" .11

Mar/) 1(/Mar/) 2.$" .1)

7#n/) 1'/7#n/) 2.'(

mid swap

44 ct3$

2 2 yr (/0eb/1 2.')" .'

3 3 yr '/0eb/11 3.3" .'

yr $/0eb/12 3.2'" .$

" " yr $/0eb/13 3."" .$

$ $ yr $/0eb/1 3.'1" ."

' ' yr $/0eb/1" 3.((" .

( ( yr (/0eb/1$ .2" .

) ) yr $/0eb/1' .1"" .3

1 1 yr $/0eb/1( .2$" .2

12 12 yr $/0eb/2 .3" .2

1" 1" yr $/0eb/23 .$1" .1

2 2 yr '/0eb/2( .'"" .

2" 2" yr '/0eb/33 .(" .

3 3 yr (/0eb/3( .(1"


14/85


15/85


16/85

ap $ur'e a#d di%%ere#t methods o# the dis$ou#t $ur'e

i#earl #terpolated market data

&nterpolated

=ash 0#t#res swap

rates rates rates days

>1?

$/0eb/(

11/0eb/( 3.21'" .1

/Mar/( 3.1(12" .'"

/May/( 3.1" .2$/#g/( 2.')2'" ."$

$/4ov/( 2."3'' .'$1

$/0eb/) 2.)3' 1.1'

2 (/0eb/1 2.')" 1.1)

3 '/0eb/11 3.3" 1.11

$/0eb/12 3.2'" 1.11

" $/0eb/13 3."" 1.1'

$ $/0eb/1 3.'1" 1.1

' $/0eb/1" 3.((" 1.1( (/0eb/1$ .2" 1.1)

) $/0eb/1' .1"" 1.11

1 $/0eb/1( .2$" 1.1

11 $/0eb/1) .3" 1.1

12 $/0eb/2 .3" 1.1

13 (/0eb/21 .)" 1.22

1 '/0eb/22 ."""2 1.11

1" $/0eb/23 .$1" 1.11

1$ $/0eb/2 .$3 1.1

1' $/0eb/2" .$'1 1.1'

1( $/0eb/2$ .$)) 1.1

1) (/0eb/2' .'2'1 1.1)

2 '/0eb/2( .'"" 1.11

21 $/0eb/2) .'$" 1.1

22 $/0eb/3 .''" 1.1

23 $/0eb/31 .'(" 1.1

2 $/0eb/32 .')" 1.1

2" '/0eb/33 .(" 1.1)

2$ $/0eb/3 .(' 1.112' $/0eb/3" .() 1.1


17/85

2( $/0eb/3$ .(11 1.1

2) $/0eb/3' .(13 1.1'

3 (/0eb/3( .(1" 1.1)


18/85


19/85

/ootstrappi#" a swap $ur'e

D0 @/c @/c @/c

D0,s gradient days rates gradient

>2? >3? >? >"? >$?

1 /.()3

.)))""3 /.('() .1 3.21$'( /.$3

.))'$2 /.($" .'" 3.1''$ /.2$2$

.))23'1 /.'$3 .2 3.132)' /.$)3 .)("1(' /.$((1 ."$ 2.)"22 /."$2

.)'(("$ /.$'3( .'$1 2.('( /.31$'

.)'2$"' /.'21 1.1' 2.'2$) .2()

.)"23 /.()(2 2.3$ 2.'"$3) .23''

.)12'2' /.)('2 3.' 2.))$'' .2"

.('$')2 /.1"2$ ."( 3.23)() .232

.(3(2$( /.1()" ".'" 3.'$2 .21$3

.')("2 /.1'21 $.() 3.$)""" .1''"

.'")3' /.12" '.13 3.('"' .1'2 .'2111 /.13$2 (.122 .2""" .11

.$(33)1 /.))$2 ).133 .1$(11 .12'

.$'3 /.)33 1.1' .2)$ .)3$

.$12)$2 /.)2) 11.1$1 .3("3 .)$'

."')3( /.($ 12.1'" .(33( .$'

."(1 /.(211 13.1)' .""1) .$)'

."1("2$ /.() 1.2( .$223) .'23

.()3'2 /.$(3' 1".21) .$)""2 .2((

.$1" /.$")$ 1$.233 .'2' .3"

.2'2 /.$3$2 1'.2" .'""'2 .322

.1'"1 /.$131 1(.2$ .'((3) .33(

.3)") /.")) 1).2(3 .(22(( .3""

.3'31 /."" 2.2) .("(( .$'

.3"")3 /.( 21.3( .($"$3 .'(

.33$)2( /.$3 22.322 .('3"" .((

.321$ /.3$ 23.33$ .((2) .)(

.33(2$ /.2" 2.3" .()2 .1'

.2((2( /.3'( 2".3$) .)32( /.1

.2'$$ /.3"'$ 2$.3(1 .())13 /.3" .2$1""2 /.313 2'.3) .()"$ /.2)


20/85

.2))" /.32"$ 2(.( .()2$$ /.2

.23'1'$ /.31$ 2).2" .()23 /.1)

.22"''$ 3. .(((2)


21/85


22/85

Forward rates %rom the bo

ln9D0: 0orward days

ln9D0: gradient dates ct3$

>'? >(?

/.()3$ $/0eb/(

/.' /.((1 3 $/May/( .2"

/.23(3 /.($( $ $/#g/( .2"$

/.'$"( /.''2) ) $/4ov/( .2"$/.1)2 /.'' 12 $/0eb/) .2"$

/.213'1 /.$)" 1" $/May/) .2'

/.2''23 /.''3( 1( $/#g/) .2"$

/."$123 /.)$$) 21 $/4ov/) .2"$

/.)131( /.113" 2 (/0eb/1 .2$1

/.131($ /.122'$ 2' $/May/1 .22

/.1'$1' /.1331" 3 $/#g/1 .2"$

/.22"1( /.13'$' 33 (/4ov/1 .2$1

/.2'"2$$ /.1(' 3$ '/0eb/11 .2"3/.32$)$ /.1'") 3) $/May/11 .2

/.3($(' /.1)') 2 (/#g/11 .2$1

/.3"3$2 /.1(1) " '/4ov/11 .2"3

/.()"3 /.1""2 ( $/0eb/12 .2"3

/.""("2 /.1)11 "1 '/May/12 .2"3

/.$'2" /.1"3)$ " $/#g/12 .2"3

/.$"$'$" /.1"()( "' $/4ov/12 .2"$

/.'1$32 /.131 $ $/0eb/13 .2"$

/.'$$)'$ /.1"($ $3 $/May/13 .2'

/.(23$2 /.1(" $$ $/#g/13 .2"$

/.('"$ /.1"113 $) $/4ov/13 .2"$

/.)312 /.1" '2 $/0eb/1 .2"$

/.)($$$ /.13()" '" $/May/1 .2'

/1.3$'( /.1 '( $/#g/1 .2"$

/1.('((" /.11) (1 $/4ov/1 .2"$

/1.13)3( /.122 ( $/0eb/1" .2"$

/1.1)131 /.132 (' $/May/1" .2'

/1.23)3 /.1332 ) $/#g/1" .2"$

/1.2)21( /.133 )3 $/4ov/1" .2"$/1.31123 /.133' )$ (/0eb/1$ .2$1


23/85

/1.3())23 /.133)$ )) $/May/1$ .2

/1.3()"1 /.1323 12 (/#g/1$ .2$1

/1.((21 1" '/4ov/1$ .2"3

1( $/0eb/1' .2"3

111 (/May/1' .2"311 '/#g/1' .2"3

11' $/4ov/1' .2"3

12 $/0eb/1( .2"$

123 '/May/1( .2"

12$ $/#g/1( .2"3

12) $/4ov/1( .2"$

132 $/0eb/1) .2"$

13" $/May/1) .2'

13( $/#g/1) .2"$

11 $/4ov/1) .2"$1 $/0eb/2 .2"$

1' $/May/2 .2"

1" $/#g/2 .2"$

1"3 $/4ov/2 .2"$

1"$ (/0eb/21 .2$1

1") $/May/21 .22

1$2 $/#g/21 .2"$

1$" (/4ov/21 .2$1

1$( '/0eb/22 .2"31'1 $/May/22 .2

1' (/#g/22 .2$1

1'' '/4ov/22 .2"3

1( $/0eb/23 .2"3

1(3 (/May/23 .2"3

1($ '/#g/23 .2"3

1() $/4ov/23 .2"3

1)2 $/0eb/2 .2"$

1)" $/May/2 .2"

1)( $/#g/2 .2"$

21 $/4ov/2 .2"$

2 $/0eb/2" .2"$

2' $/May/2" .2'

21 $/#g/2" .2"$

213 $/4ov/2" .2"$

21$ $/0eb/2$ .2"$

21) $/May/2$ .2'

222 $/#g/2$ .2"$

22" $/4ov/2$ .2"$22( (/0eb/2' .2$1


24/85

231 $/May/2' .22

23 $/#g/2' .2"$

23' (/4ov/2' .2$1

2 '/0eb/2( .2"3

23 (/May/2( .2"32$ '/#g/2( .2"3

2) $/4ov/2( .2"3

2"2 $/0eb/2) .2"$

2"" '/May/2) .2"

2"( $/#g/2) .2"3

2$1 $/4ov/2) .2"$

2$ $/0eb/3 .2"$

2$' $/May/3 .2'

2' $/#g/3 .2"$

2'3 $/4ov/3 .2"$2'$ $/0eb/31 .2"$

2') $/May/31 .2'

2(2 $/#g/31 .2"$

2(" $/4ov/31 .2"$

2(( $/0eb/32 .2"$

2)1 $/May/32 .2"

2) $/#g/32 .2"$

2)' (/4ov/32 .2$1

3 '/0eb/33 .2"333 $/May/33 .2

3$ (/#g/33 .2$1

3) '/4ov/33 .2"3

312 $/0eb/3 .2"3

31" (/May/3 .2"3

31( '/#g/3 .2"3

321 $/4ov/3 .2"3

32 $/0eb/3" .2"$

32' '/May/3" .2"

33 $/#g/3" .2"3

333 $/4ov/3" .2"$

33$ $/0eb/3$ .2"$

33) $/May/3$ .2"

32 $/#g/3$ .2"$

3" $/4ov/3$ .2"$

3( $/0eb/3' .2"$

3"1 $/May/3' .2'

3" $/#g/3' .2"$

3"' $/4ov/3' .2"$3$ (/0eb/3( .2$1


25/85

tstrapped swap $ur'e

li#ear i#terpolatio# 5ero-$oupo# i#terpolatio#

0orward days interpolated

D0,s rates ct3$ @/c rates D0,s

>)? >1? >11? >12?

1 1

.))221( 3.13'21 .2" 3.12)12 .))22(

.)("1(' 2.')2'" ."$ 2.)"22 .)("1('

.)'(("$ 2."3'' .'$1 2.('( .)'(("$.)'2$"' 2.)3' 1.1' 2.'2$) .)'2$"'

.)$$"3 2.'$"3) 1.2$ 2.'3" .)$$3"

.)")22$ 2.'("' 1."1) 2.'1 .)")21

.)"23)( 2.("3 1.''" 2.'((3 .)"23')

.)"23 2.(2"'3 2.3$ 2.'"$3) .)"23

.)3'$( 3.(( 2.2'( 2.(13( .)3')1(

.)2)3 3.')$ 2."33 2.('$ .)2)'$"

.)2)1 3."113$ 2.') 2.)3$$' .)21213

.)12'2' 3."2(1 3.' 2.))$'' .)12'2'.) 3.)312) 3.2)2 3.""" .)31

.()'$ 3.)'2$ 3.""3 3.11(33 .()"12)

.(("''$ .123" 3.($ 3.1')11 .(($)

.('$')2 ."3$ ."( 3.23)() .('$')2

.($'21 .3$)2 .311 3.2)($ .($'1

.("'$3" .1(22 ."$ 3.3"' .("')3

.(')"2 .$($( .(1) 3.1$( .((1'3

.(3(2$( ."23 ".'" 3.'$2 .(3(2$(

.(2("'2 .'33$" ".322 3."2)$) .(2('33

.(1("( .')1$1 "."'( 3."()' .(1('$2

.(("2" .("11 ".(33 3.$2$ .(($(3

.')("2 .)11)1 $.() 3.$)""" .')("2

.'(()$ .()1)) $.33$ 3.'3)2 .'()3

.''))' .)"3)2 $.")2 3.'('' .'')2$

.'$)233 ".1' $.(' 3.(312 .'$)313

.'")3' ".(2$2 '.13 3.('"' .'")3'

.'")1 ".3' '.3" 3.)11(' .'"12

.'" ".$(2( '.$$ 3.))) .'"3$

.'3)) ".13') '.($1 3.)('11 .'3)3".'2111 ".2"' (.122 .2""" .'2111


26/85

.'11))1 ".23)33 (.3$' .$2 .'11))2

.'22" ".312 (.$2( .)$(3 .'22"

.$)2(21 ".3(3 (.((1 .132' .$)2(1)

.$(33)1 "."($ ).133 .1$(11 .$(33)1

.$'32$ ".31(3 ).3($ .1)($1 .$'2)$.$$"2$1 ".3)(1 ).$3) .22)12 .$$"21(

.$"$1)" ".$"2) ).()2 .2")$2 .$"$1$2

.$'3 "."2' 1.1' .2)$ .$'3

.$3($3 ".2$1"( 1.3)' .313(" .$3("'2

.$313$ ".332" 1.$" .33'"1 .$3"'

.$21") ".$1( 1.)$ .3$13 .$21()

.$12)$2 ".(1)1 11.1$1 .3("3 .$12)$2

.$'$" ".(21 11.( .)2" .$'1

.")$2)3 "."")) 11.$$ .33)$ .")$2

."('(2 ".$ 11.)1) ."($' ."(''"3."')3( ".'22"2 12.1'" .(33( ."')3(

."'1'(3 ".2)2' 12.2" ."1 ."'1$))

."$) ".3$"3 12.$(1 ."1'2' ."$3)3$

.""$31$ ".3)$2 12.)3$ ."3 .""$22)

."(1 "."1')) 13.1)' .""1) ."(1

."12'1 ".$1) 13.3) ."$('" ."11((

."33'1$ "."3(3) 13.$) ."($"' ."33$2

."2"))( ".$1)$" 13.)"$ .$'' ."2")12

."1("2$ ".'$3 1.2( .$223) ."1("2$."11'( ".$3'3 1."3 .$' ."113)2

."3)) ".'21"$ 1.'1 .$"()" ."3(31

.)$$$1 ".(""3 1.)$' .$''2 .)$"'2

.()3'2 ".()1)) 1".21) .$)""2 .()3'2

.(31" ".)$( 1".'2 .'2') .(3"

.'$)2( ".1$11" 1".'2" .'1' .'$(

.''$ ".22)3' 1".)'( .'1'3 .'$)

.$1" ".32 1$.233 .'2' .$1"

."('( ".1')$ 1$.(3 .'3233 ."(3("

."21 ".2)( 1$.'3) .'13 ."22(

.$31 ".32" 1$.)) .'')2 .$2'

.2'2 ".3)3') 1'.2" .'""'2 .2'2

.3$1 ".2$)' 1'.)' .'$3$) .3"2

.2('"' ".31$( 1'.'"3 .''1)2 .2($3"

.22) ".1"$1 1(.( .'(1$ .22(13

.1'"1 ".)1$1 1(.2$ .'((3) .1'"1

.11") ".3$2(2 1(."11 .')$'" .11"$

.")"3 ".3'3 1(.'$' .(" ."(33

.313 "."13)$ 1).22 .(1" .221.3)") ".")" 1).2(3 .(22(( .3)")


27/85

.3()( ".$2( 1)."2" .(31$ .3()32

.3(3)'2 "."3)(2 1).'(1 .(" .3(3("'

.3'(1( ".$2113 2.2 .()(2 .3'(331

.3'31 ".'21" 2.2) .("(( .3'31

.3$(2 .)3($ 2."' .($" .3$(3").3$3(3 ".() 2.( .($22 .3$3'32

.3")23 ".$)2 21."3 .($3)1 .3")1$

.3"")3 ".1313 21.3( .($"$3 .3"")3

.3"23( .)'" 21.""( .($'"( .3"1")

.3"(33 ".3'() 21.(11 .($)"$ .3"'2(

.313(1 ".13$ 22.$' .('1"" .3131

.33$)2( ".1'1 22.322 .('3"" .33$)2(

.332(" ".121( 22."$) .('"'3 .332'3

.32("2 ".''22 22.(2" .('')( .32(

.322') ".13)$ 23.(1 .((2 .3223.321$ ".212( 23.33$ .((2) .321$

.31$$( "."22 23."(3 .(()1 .31"))$

.311)(' ".11(2( 23.(3) .(('1 .311()

.3')' ".1($12 2.) .(())1 .3'(3

.33(2$ ".2""'' 2.3" .()2 .33(2$

.3$ ".)3) 2.$ .()"' .2)))3$

.2)$11 ".1$$$ 2.("$ .()'( .2)$$

.2)2111 ".2311" 2".11' .)"( .2)21

.2((2( ".312" 2".3$) .)32( .2((2(.2()" .'3)2 2".$1 .)22' .2((('

.2(12' .')2 2".('" .)12 .2(131

.2'(1$ .("31 2$.12( .)1' .2'')"2

.2'$$ .)132( 2$.3(1 .())13 .2'$$

.2'13"1 .') 2$.$33 .()(2" .2'12)

.2$()' .(2" 2$.(($ .()'3' .2$(1"

.2$(2 .($1"2 2'.13) .()$) .2$'(1

.2$1""2 .)22$( 2'.3) .()"$ .2$1""2

.2"(( .'"33$ 2'.$ .()(( .2"(22

.2""3' .(111' 2'.()' .()1 .2""2)$

.2"223 .('1$ 2(.1"3 .()3 .2"21'$

.2))" .)32$ 2(.( .()2$$ .2))"

.2$1$ .'$22 2(.$"( .()2$ .2$1(

.231$( .(2(( 2(.)1 .()1" .23)

.21'2 .((11 2).1$) .()( .211$

.23'1'$ .)2$$ 2).2" .()23 .23'1'$

.2312 .''( 2).$'2 .(()'$ .233")

.231"" .(2)'2 2).)2( .(()2( .231(2

.22($)$ .()( 3.1(3 .(((') .22($2.22"''$ .)"332 3. .(((2) .22"''$


28/85

lo"-li#ear i#terpolatio#

0orward 0orward

rates ln9D0: D0 rates

>13? >1? >1"? >1$?

1

3.113) /.'(12)$'1 .))221' 3.13'3

2.'(($" /.1)2)1 .)("1(' 2.')2"3

2."3'' /.213''((1 .)'(("$ 2."3''2.)3' /.2''23(' .)'2$"' 2.)3'

2.''2)2 /.3$1"""' .)$")(2 2.')"1

2.'('() /.1'2)(123 .)")12) 2.')"'

2.(2'( /.(()$) .)"232" 2.')"'

2.(1(" /."$123)2 .)"23 2.')")"

3.311( /.$"3"))) .)3'"3 3.)""1

3.31' /.'33""$" .)2)21 3.)$3$

3."""3" /.(2"1)3)2$ .)2') 3.)$'

3.$'(11 /.)131(1") .)12'2' 3.)$1)3.("( /.112()(3 .)3)' 3.))1)"

3.)2)( /.1111(3$ .()"') 3.))32'

."1 /.1213$') .(("$1 3.))2$1

.1'$(3 /.131(""13 .('$')2 3.))2$1

.2$'( /.12$"'" .($'"1 .2)

.3(3"' /.1"3(2("'' .("'1) .2)

."333 /.1$"122('3" .('') ."$

.$23"2 /.1'$1'1$)" .(3(2$( ."$

.$"22 /.1((2$'')'1 .(2(3)3 .(223

.'$"2 /.2"1'(( .(1(3' .(22))

.(''1 /.212'$')') .((3 .(22))

.)()11 /.22"1("'( .')("2 .(22))

.(('' /.23'2'3$ .'((''( .)($'

.)( /.2))3"$$)3 .''(("1 .)('"1

".31) /.2$2$)'$ .'$)) .)('"1

".123(2 /.2'"2$$2')) .'")3' .)('"1

.)((1 /.2('(33)3) .'))) ".1311

".$1 /.3'$31'3 .'2"3 ".12

".12 /.313'22(2' .'3'22 ".12".21($ /.32$)$2$' .'2111 ".1)2

.0

.

3.0

3.

4.0

4.

.0

.

.0

.

1.0


29/85

".23( /.33))"22((3 .'11( ".3')

".312)( /.3"3(2"("$$ .'1))' ".3"31

".3("2" /.3$'2"$$"13 .$)2$32 ".3)12

"."'" /.3($('$1 .$(33)1 ".3)12

".33$3) /.3)31($3'( .$'13) ".2)(".3)(22 /.'))(2) .$$"12 ".2)(

".$$ /.21"(121 .$"$) ".2)(

"."22$( /.3"3$2$ .$'3 ".2)()

".2)(2( /.($))(1 .$3("( ".3''3

".3$3$ /.$21("1"1 .$2))$ ".3'113

".3))( /.'"(1)13 .$213'$ ".3'1"2

".3' /.()"2('$( .$12)$2 ".3'1"2

"."2")3 /."32"1'2 .$") ".$1)

"."'$"1 /."1'2'12) .")$"$ ".$23)

".$2$$ /."31$3$($ ."('$3 ".$23)".$'$'( /.""("213 ."')3( ".$23)

".3"1' /."")2'2"$ ."'1$2" ".1$

".3($(" /."'2))22)$ ."$3(3' ".)'

".21"( /."($'(2) .""$1"" ".)'

"."'"2 /.$'2')'3 ."(1 "."'(

"."2"32 /.$111()133 ."111' "."')$(

"."$2"( /.$2(2(2($1 ."33"' "."(1(3

".")))( /.$2'"$)$ ."2"(2 "."(2$)

".$3"1 /.$"$'$"'1 ."1("2$ "."(1".''1" /.$''")2) ."11323 ".'$33(

".'$)' /.$("$)(2)(' ."3'3( ".'$$1

".'(331 /.'1$"1'" .)$"3 ".'$'$

".(21 /.'1$32"3 .()3'2 ".'$'$

".1'3 /.'2'$(21)3 .(32' ".1)$"3

".1()( /.''3233$" .'$'$" ".1)$"3

".23(2 /.'"3'(2')$ .'"(3 ".1)$"3

".21)2 /.'$$)'$3( .$1" ".1)$)

".2$21 /.'(13'$' ."(3"( ".2("'1

".2'(1 /.')3"2323$ ."22) ".2($)

".2)22 /.($)2$)2 .$22 ".2($)

".313 /.(23$21"'( .2'2 ".2($)

".3"$1 /.(33"'1$" .3) ".3')$3

".3'222 /.('231(31 .2($ ".3((

".3(()1 /.($((((1)' .22'($ ".3((

"."$1 /.('"$1"$3 .1'"1 ".3((

"."1$ /.(('))$)('" .11') ".''"

".$)" /.)1)121'$ ."')' ".'(')

".('( /.)1"("'$ .1) ".'(')".""$ /.)311)3" .3)") ".')$2


30/85

".""33 /.)3)"2' .3()2)( "."(113

"."'3( /.)"'"''(' .3(3(22 "."(32)

".")2)$ /.)'2"2$3'( .3'(3$ "."(1"

".$11' /.)($$$22" .3'31 "."(2("

".2((( /.))('1)311 .3$(3" ".3'".3233 /1.113""$")' .3$3'2$ ".3'

".3"'( /1.23((3 .3")1"" ".3'

".3)") /1.3$'($)) .3"")3 ".32

".$"() /1.)3(1)2 .3"1"3 ".'1)3

".'22 /1.$212311( .3"'21 ".'22)

".'$ /1.'"3( .312)$ ".'2$"

".'($" /1.('((""'( .33$)2( ".'2$"

".1") /1.11))$) .332'2 ".111

".111' /1.11322'2$ .32(33 ".112"2

".11'3 /1.12$33 .321)' ".112"2".11)3 /1.13)3(1$') .321$ ".112"2

".1"( /1.1"2323 .31")) ".1"3'

".1"1"$ /1.1$"12)22) .311((2 ".1"1'

".1"$$2 /1.1'(21("$ .3'(2( ".1"1'

".1$1$( /1.1)13"((3 .33(2$ ".1"1'

".1((11 /1.22')) .2)))2) ".1)$3

".1)32 /1.21'2231) .2)"))( ".1)'1'

".2$" /1.23((33" .2)23" ".1)')2

".2"( /1.23)31223 .2((2( ".1)$(.(2$"3 /1.2""$"""$"$ .2((() .(233"

.(2$3$ /1.2$(1'$1)(2 .2(13 .(2"2(

.(232' /1.2(2)'23$2 .2'')"" .(231

.(211' /1.2)21(2'1 .2'$$ .(231

.(3"' /1.3"$113'2 .2'12)2 .(33"

.(33)" /1.31$'3 .2$(1' .(33"

.(321' /1.32(($($3 .2$'(2 .(33"

.(3' /1.311231$" .2$1""2 .(333(

.( /1.3"31""('(3 .2"(23 .(21$

.(32" /1.3$"3222() .2""2)( .(2(

.(2( /1.3''$223)$" .2"21'' .(2(1

.("( /1.3())22"3) .2))" .(2(1

.("3"2 /1.1)'('23 .2$1) .("1$'

.("2)$ /1.132("2" .23)" .("233

.("1'2 /1.2$$2$)(( .211' .("233

.(") /1.3()"111' .23'1'$ .("233

.($2'( /1."()'$(( .233$ .($13

.($2( /1.$32$)3'( .231(3 .($22(

.($1(1 /1.'"")$1)( .22($2 .($22(.($1' /1.((213)13) .22"''$ .($2)3


31/85

0.000 .000 *0.000 *.000000,

000,

000,

000,

000,

000,

000,

000,

000,

000,

000,

/ootstrappi#" a swap

with li#ear i#terpola


32/85


33/85


34/85

0.000 .000 30.000

$ur'e

tio#

6-C i#terpolatio# o% DF $ur'e

i#ear i#terpolatio#

o"-li#ear i#terpolatio#


35/85


36/85


37/85

3.6: Details of Hermitian Interpolation

t(i) r(i) r'(i) g(i) c(i) t(i+1) r(i+1) t m(i,t)

2.01 2.7950% 0.2407% 0.0000% ### 3.005 3.0350%

3.01 3.0350% 0.2463% 0.0056% 0.0000% 4.003 3.2750%

4.00 3.2750% 0.2350% 0.0057% 0.0041% 5.005 3.5050% 2.008 0.000

5.01 3.5050% 0.2197% 0.0097% 0.0103% 6.005 3.7150% 3.005 0.000

6.01 3.7150% 0.1900% 0.0200% ### 7.005 3 .8850% 4.003 0.000

7.01 3.8850% 0.1547% 0.0155% ### 8.011 4 .0250% 5.005 0.000

8.01 4.0250% 0.1348% 0.0044% 0.0057% 9.008 4.1550% 6.005 0.000

9.01 4.1550% 0.1202% 0.0102% ### 10.008 4.2650% 7.005 0.000

10.01 4.2650% 0.1017% 0.0333% ### 12.008 4.4350% 8.011 0.000

12.01 4.4350% 0.0750% 0.0452% ### 15.011 4.6150% 9.008 0.000

15.01 4.6150% 0.0480% 0.1000% ### 20.016 4.7550% ### 0 .000

20.02 4.7550% 0.0190% 0.0450% ### 25.022 4.8050% 11.008 0.500

25.02 4.8050% 0.0060% 0.0200% ### 30.027 4.8150% ### 0 .00030.03 4.8150% ### 0.336

### 0.668

15.011 0.000

16.011 0.200

### 0.400

### 0.600

### 0.801

### 0.000

### 0.200

### 0.400

### 0.599

### 0.799### 0.000

### 0.199

### 0.399

### 0.599

### 0.799

### 0.000


38/85

r(i) r(i+1) g(i) c(i) r(t)

2.7950% 3.0350% 0.0000% -0.0056% 2.7950%

3.0350% 3.2750% 0.0056% 0.0000% 3.0350%

3.2750% 3.5050% 0.0057% 0.0041% 3.2750%

3.5050% 3.7150% 0.0097% 0.0103% 3.5050%

3.7150% 3.8850% 0.0200% -0.0047% 3.7150%

3.8850% 4.0250% 0.0155% -0.0110% 3.8850%

4.0250% 4.1550% 0.0044% 0.0057% 4.0250%

4.1550% 4.2650% 0.0102% -0.0019% 4.1550%

4.2650% 4.4350% 0.0333% -0.0133% 4.2650%

4.2650% 4.4350% 0.0333% -0.0133% 4.3567%

4.4350% 4.6150% 0.0452% -0.0092% 4.4350%4.4350% 4.6150% 0.0452% -0.0092% 4.5048%

4.4350% 4.6150% 0.0452% -0.0092% 4.5639%

4.6150% 4.7550% 0.1000% -0.0550% 4.6150%

4.6150% 4.7550% 0.1000% -0.0550% 4.6572%

4.6150% 4.7550% 0.1000% -0.0550% 4.6897%

4.6150% 4.7550% 0.1000% -0.0550% 4.7151%

4.6150% 4.7550% 0.1000% -0.0550% 4.7360%

4.7550% 4.8050% 0.0450% -0.0250% 4.7550%

4.7550% 4.8050% 0.0450% -0.0250% 4.7714%

4.7550% 4.8050% 0.0450% -0.0250% 4.7834%

4.7550% 4.8050% 0.0450% -0.0250% 4.7922%

4.7550% 4.8050% 0.0450% -0.0250% 4.7990%4.8050% 4.8150% 0.0200% -0.0100% 4.8050%

4.8050% 4.8150% 0.0200% -0.0100% 4.8099%

4.8050% 4.8150% 0.0200% -0.0100% 4.8128%

4.8050% 4.8150% 0.0200% -0.0100% 4.8144%

4.8050% 4.8150% 0.0200% -0.0100% 4.8149%

4.8150% 4.8150%

0.000 5.000

0.0000%

1.0000%

2.0000%

3.0000%

4.0000%

5.0000%

6.0000%


39/85

10.000 15.000 20.000 25.000 30.000


40/85

3.1! Worksheet to $al$ulate a dis$ou#t $ur'e usi#" 7ermite i#terpolatio# o# the



6ibor cash

ct3$

$/0eb/(

' day 11/0eb/( 3.21'"

1 mo /Mar/( 3.1(12"

3 mo /May/( 3.1"

0#t#res gradient

Mar/( 1)/Mar/( 3. /."

7#n/( 1(/7#n/( 2.") /.12

Sep/( 1'/Sep/( 2.( .3

Dec/( 1'/Dec/( 2."" .11

Mar/) 1(/Mar/) 2.$" .1)

7#n/) 1'/7#n/) 2.'(

mid swap

44 ct3$

2 2 yr (/0eb/1 2.')"

3 3 yr '/0eb/11 3.3"

yr $/0eb/12 3.2'"

" " yr $/0eb/13 3.""

$ $ yr $/0eb/1 3.'1"

' ' yr $/0eb/1" 3.(("

( ( yr (/0eb/1$ .2"

) ) yr $/0eb/1' .1""

1 1 yr $/0eb/1( .2$"

12 12 yr $/0eb/2 .3"

1" 1" yr $/0eb/23 .$1"

2 2 yr '/0eb/2( .'""

2" 2" yr '/0eb/33 .("

3 3 yr (/0eb/3( .(1"


41/85


42/85


43/85

swap $ur'e a#d di%%ere#t methods o# the dis$ou#t $ur'e

7ermite i#terpolated market data

&nterpolated

=ash 0#t#res swap

rates rates rates days

>1?

$/0eb/(

11/0eb/( 3.21'" .1

/Mar/( 3.1(12" .'"

/May/( 3.1" .2$/#g/( 2.')2'" ."$

$/4ov/( 2."3'' .'$1

$/0eb/) 2.)3' 1.1'

2 (/0eb/1 2.')" 1.1)

3 '/0eb/11 3.3" 1.11

$/0eb/12 3.2'" 1.11

" $/0eb/13 3."" 1.1'

$ $/0eb/1 3.'1" 1.1

' $/0eb/1" 3.((" 1.1( (/0eb/1$ .2" 1.1)

) $/0eb/1' .1"" 1.11

1 $/0eb/1( .2$" 1.1

11 $/0eb/1) .3"$' 1.1

12 $/0eb/2 .3" 1.1

13 (/0eb/21 ."( 1.22

1 '/0eb/22 ."$3) 1.11

1" $/0eb/23 .$1" 1.11

1$ $/0eb/2 .$"'2 1.1

1' $/0eb/2" .$()' 1.1'

1( $/0eb/2$ .'1"1 1.1

1) (/0eb/2' .'3$ 1.1)

2 '/0eb/2( .'"" 1.11

21 $/0eb/2) .''1 1.1

22 $/0eb/3 .'(3 1.1

23 $/0eb/31 .')22 1.1

2 $/0eb/32 .')) 1.1

2" '/0eb/33 .(" 1.1)

2$ $/0eb/3 .()) 1.112' $/0eb/3" .(12( 1.1


44/85

2( $/0eb/3$ .(1 1.1

2) $/0eb/3' .(1) 1.1'

3 (/0eb/3( .(1" 1.1)


45/85


46/85


D0 @/c @/c @/c

D0,s gradient days rates gradient

>2? >3? >? >"? >$?

1 /.()3

.)))""3 /.('() .1 3.21$'( /.$3

.))'$2 /.($" .'" 3.1''$ /.2$2$

.))23'1 /.'$3 .2 3.132)' /.$)3 .)("1(' /.$((1 ."$ 2.)"22 /."$2

.)'(("$ /.$'3( .'$1 2.('( /.31$'

.)'2$"' /.'21 1.1' 2.'2$) .2()

.)"23 /.()(2 2.3$ 2.'"$3) .23''

.)12'2' /.)('2 3.' 2.))$'' .2"

.('$')2 /.1"2$ ."( 3.23)() .232

.(3(2$( /.1()" ".'" 3.'$2 .21$3

.')("2 /.1'21 $.() 3.$)""" .1''"

.'")3' /.12" '.13 3.('"' .1'2 .'2111 /.13$2 (.122 .2""" .11

.$(33)1 /.))$2 ).133 .1$(11 .12'

.$'3 /.)) 1.1' .2)$ .11(

.$123)3 /.)' 11.1$1 .3)3$" .((2

."')3'2 /.($"1 12.1'" .(3 .')2

."'"3$ /.(1)3 13.1)' ."$ .$($

."1''1" /.''") 1.2( .$332 .$1

.()'2 /.'2$( 1".21) .$)1( .)

.$2) /.$'3" 1$.233 .'2" .3'

.3(2) /.$2'2 1'.2" .'(1(3 .2')

.1"2 /."(() 1(.2$ .(1) .223

.3)3') /."")) 1).2(3 .(32(' .2(

.3'31 /."2(" 2.2) .("3) .1''

.3"11) /.)12 21.3( .('1) .113

.33$1)1 /."(' 22.322 .((33$ .$$

.31)) /.313 23.33$ .()) .3)

.33'' /.)2 2.3" .()2 .31

.2(($)1 /.3($' 2".3$) .()'23 .1(

.2'$1" /.3$1' 2$.3(1 .()) /.1 .2$112 /.33) 2'.3) .()'"" /.3(


47/85

.2)23 /.31)( 2(.( .()3$' /."

.23'31( /.32) 2).2" .(((21 /.$

.22$21 3. .((21


48/85


49/85

Forward rates %rom the bo

ln9D0: 0orward days

ln9D0: gradient dates ct3$

>'? >(?

/.()3$ $/0eb/(

/.' /.((1 3 $/May/( .2"

/.23(3 /.($( $ $/#g/( .2"$

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50/85

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51/85

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52/85

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53/85

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54/85

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55/85

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56/85

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57/85

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58/85

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59/85

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60/85

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65/85


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3 3 yr '/0eb/11 3.3" .

yr $/0eb/12 3.2'" .

" " yr $/0eb/13 3."" .

$ $ yr $/0eb/1 3.'1" .

' ' yr $/0eb/1" 3.((" .

( ( yr (/0eb/1$ .2" .

) ) yr $/0eb/1' .1"" .

1 1 yr $/0eb/1( .2$" .

12 12 yr $/0eb/2 .3" .

1" 1" yr $/0eb/23 .$1" .

2 2 yr '/0eb/2( .'"" .

2" 2" yr '/0eb/33 .(" .

3 3 yr (/0eb/3( .(1" .


68/85


69/85


70/85

&nterpolated

=ash 0#t#res

rates rates

$/0eb/(

11/0eb/( 3.21'" 3

/Mar/( 3.1(12" $

/May/( 3.1" )$/#g/( 2.')2'" 12

$/4ov/( 2."3'' 1"

$/0eb/) 2.)3' 1(

2 (/0eb/1 21

3 '/0eb/11 2

$/0eb/12 2'

" $/0eb/13 3

$ $/0eb/1 33

' $/0eb/1" 3$( (/0eb/1$ 3)

) $/0eb/1' 2

1 $/0eb/1( "

11 $/0eb/1) (

12 $/0eb/2 "1

13 (/0eb/21 "

1 '/0eb/22 "'

1" $/0eb/23 $

1$ $/0eb/2 $3

1' $/0eb/2" $$

1( $/0eb/2$ $)

1) (/0eb/2' '2

2 '/0eb/2( '"

21 $/0eb/2) '(

22 $/0eb/3 (1

23 $/0eb/31 (

2 $/0eb/32 ('

2" '/0eb/33 )

2$ $/0eb/3 )32' $/0eb/3" )$


71/85

2( $/0eb/3$ ))

2) $/0eb/3' 12

3 (/0eb/3( 1"

1(

11111

11'

12

123

12$

12)

132

13"

13(

111

1'

1"

1"3

1"$

1")

1$2

1$"

1$(1'1

1'

1''

1(

1(3

1($

1()

1)2

1)"

1)(

21

2

2'

21

213

21$

21)

222

22"22(


72/85

231

23

23'

2

232$

2)

2"2

2""

2"(

2$1

2$

2$'

2'

2'32'$

2')

2(2

2("

2((

2)1

2)

2)'

333

3$

3)

312

31"

31(

321

32

32'

33

333

33$

33)

32

3"

3(

3"1

3"

3"'3$


73/85

Forward rates %rom the bootstrapped swap $ur'e

0orward days 0orward Smoothing D0,s days

dates ct3$ rates ct3$

3$.1"2)(1'

>1? >2? >3?

$/0eb/( 1

$/May/( .2" 3.1" .))21))

$/#g/( .2"$ 2.')2'" .)("1$(

$/4ov/( .2"$ 2."3'' .)'((3'$/0eb/) .2"$ 2.)3' .( .)'2$3) 1.1'

$/May/) .2' 2.5826% .1 .)$$$(

$/#g/) .2"$ 2.7010% .22 .)")(3

$/4ov/) .2"$ 2.8500% .32 .)"2)2

(/0eb/1 .2$1 3.0296% . .)"23 1.1)

$/May/1 .22 3.2404% .3" .)3(''

$/#g/1 .2"$ 3.4264% .2" .)2))3

(/4ov/1 .2$1 3.5860% .1( .)213(

'/0eb/11 .2"3 3.7188% .11 .)12'2( 1.11$/May/11 .2 3.8254% .12 .)2'2

(/#g/11 .2$1 3.9346% .12 .()"'$

'/4ov/11 .2"3 4.0464% .13 .(($1

$/0eb/12 .2"3 4.1605% .1 .('$')3 1.11

'/May/12 .2"3 4.2772% .13 .($'1

$/#g/12 .2"3 4.3905% .12 .("'()3

$/4ov/12 .2"$ 4.5005% .11 .((13)

$/0eb/13 .2"$ 4.6072% .11 .(3(2$) 1.1'

$/May/13 .2' 4.7105% .' .(2($1)

$/#g/13 .2"$ 4.7966% ." .(1("("

$/4ov/13 .2"$ 4.8649% .3 .(("33

$/0eb/1 .2"$ 4.9154% .1 .')("2 1.1

$/May/1 .2' 4.9481% .1 .'((("3

$/#g/1 .2"$ 4.9768% .1 .''()$

$/4ov/1 .2"$ 5.0013% . .'$)11"

$/0eb/1" .2"$ 5.0216% . .'")3' 1.1

$/May/1" .2' 5.0376% .1 .'"3

$/#g/1" .2"$ 5.0700% .2 .'3$

$/4ov/1" .2"$ 5.1193% . .'3('(/0eb/1$ .2$1 5.1857% .' .'2111 1.1)


74/85

$/May/1$ .2 5.2693% . .'11)

(/#g/1$ .2$1 5.3349% .2 .'21")

'/4ov/1$ .2"3 5.3813% .1 .$)2'3$

$/0eb/1' .2"3 5.4089% . .$(33)2 1.11

(/May/1' .2"3 5.4179% . .$'1")'/#g/1' .2"3 5.4262% . .$$"3(

$/4ov/1' .2"3 5.4337% . .$"$2'

$/0eb/1( .2"$ 5.4404% . .$'31 1.1

'/May/1( .2" 5.4465% . .$3(33)

$/#g/1( .2"3 5.4541% . .$2)$"(

$/4ov/1( .2"$ 5.4634% . .$2)((

$/0eb/1) .2"$ 5.4742% . .$1221 1.1

$/May/1) .2' 5.4868% . .$22

$/#g/1) .2"$ 5.5008% . .")"((

$/4ov/1) .2"$ 5.5165% . ."('"$"$/0eb/2 .2"$ 5.5337% . ."')3'2 1.1

$/May/2 .2" 5.5524% . ."'1

$/#g/2 .2"$ 5.5679% . ."$323

$/4ov/2 .2"$ 5.5800% . .""""1

(/0eb/21 .2$1 5.5888% . ."'"11 1.22

$/May/21 .22 5.5941% . ."2(

$/#g/21 .2"$ 5.5963% . ."32")1

(/4ov/21 .2$1 5.5954% . ."2)22

'/0eb/22 .2"3 5.5912% . ."1'$' 1.11$/May/22 .2 5.5838% . ."1$3'

(/#g/22 .2$1 5.5735% . ."3312

'/4ov/22 .2"3 5.5600% . .)$33$

$/0eb/23 .2"3 5.5435% . .()'( 1.11

(/May/23 .2"3 5.5240% . .(2'3'

'/#g/23 .2"3 5.5050% . .'$112

$/4ov/23 .2"3 5.4864% . .$)"))

$/0eb/2 .2"$ 5.4684% . .$312' 1.1

$/May/2 .2" 5.4509% . ."$)1

$/#g/2 .2"$ 5.4338% . ."$3

$/4ov/2 .2"$ 5.4172% . .()

$/0eb/2" .2"$ 5.4010% . .3(3( 1.1'

$/May/2" .2' 5.3853% . .32$''

$/#g/2" .2"$ 5.3701% . .2$(2

$/4ov/2" .2"$ 5.3552% . .21"'

$/0eb/2$ .2"$ 5.3408% . .1"3(( 1.1

$/May/2$ .2' 5.3268% . .))()

$/#g/2$ .2"$ 5.3133% . .)$

$/4ov/2$ .2"$ 5.3002% . .3)))1(/0eb/2' .2$1 5.2874% . .3)3$"$ 1.1)


75/85

$/May/2' .22 5.2752% . .3(('

$/#g/2' .2"$ 5.2633% . .3(3"2

(/4ov/2' .2$1 5.2518% . .3'(3"3

'/0eb/2( .2"3 5.2407% . .3'3' 1.11

(/May/2( .2"3 5.2300% . .3$("3'/#g/2( .2"3 5.2189% . .3$3'3$

$/4ov/2( .2"3 5.2075% . .3")1

$/0eb/2) .2"$ 5.1957% . .3"3$ 1.1

'/May/2) .2" 5.1835% . .3)''3

$/#g/2) .2"3 5.1709% . .3"2$

$/4ov/2) .2"$ 5.1580% . .3'$(

$/0eb/3 .2"$ 5.1447% . .33$3$ 1.1

$/May/3 .2' 5.1310% . .332133

$/#g/3 .2"$ 5.1170% . .32'($

$/4ov/3 .2"$ 5.1027% . .323$2$$/0eb/31 .2"$ 5.0880% . .31)'2 1.1

$/May/31 .2' 5.0730% . .31""1"

$/#g/31 .2"$ 5.0577% . .311()

$/4ov/31 .2"$ 5.0421% . .3'"2$

$/0eb/32 .2"$ 5.0261% . .33$2$ 1.1

$/May/32 .2" 5.0099% . .2))('

$/#g/32 .2"$ 4.9934% . .2)$)2

(/4ov/32 .2$1 4.9766% . .2)22)

'/0eb/33 .2"3 4.9595% . .2(($'" 1.1)$/May/33 .2 4.9421% . .2("22)

(/#g/33 .2$1 4.9257% . .2(1$'

'/4ov/33 .2"3 4.9102% . .2'(1""

$/0eb/3 .2"3 4.8957% . .2''"" 1.11

(/May/3 .2"3 4.8822% . .2'1"

'/#g/3 .2"3 4.8696% . .2$(1"

$/4ov/3 .2"3 4.8580% . .2$("3

$/0eb/3" .2"$ 4.8472% . .2$1$12 1.1

'/May/3" .2" 4.8374% . .2"(($

$/#g/3" .2"3 4.8285% . .2""3$)

$/4ov/3" .2"$ 4.8204% . .2"22$2

$/0eb/3$ .2"$ 4.8132% . .2)1)$ 1.1

$/May/3$ .2" 4.8069% . .2$23'

$/#g/3$ .2"$ 4.8014% . .232"2

$/4ov/3$ .2"$ 4.7967% . .23'

$/0eb/3' .2"$ 4.7928% . .23'3)) 1.1'

$/May/3' .2' 4.7898% . .23$21

$/#g/3' .2"$ 4.7875% . .231'("

$/4ov/3' .2"$ 4.7860% . .22()((/0eb/3( .2$1 4.7852% .22$1"( 1.1)


76/85

B

>?

.)(((

1.)"2'

2.('""

3.'$21

.$13

".23)

$.1)3(

$.)2()

3.0000,

4.00000,

4.0000,

.00000,

.0000,

.00000,

.0000,

1.00000,


77/85

'.$1))

(.2'")

(.()$)

).(3

1.

1."$'3

11.$22

11."31(

11.)''"

12.3)('

12.(

0.000 .000.00000,

.0000,

3.00000,


78/85

13.1''$

13."3$(

13.(''(

1.21'

1.")$

1.(3)

1".(1'

1".3$)

1"."))$

1".()

1$.'1"


79/85


Cubi$ 7ermite i#terpolatio# o% swap $ur'e

ptimisatio#


80/85

*0.000 *.000 0.000 .


81/85


82/85


83/85

000 30.000


84/85


85/85

ch 3 generic swaps

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