ch 3 generic swaps
Post on 28-Feb-2018
222 Views
Preview:
TRANSCRIPT
-
7/25/2019 Ch 3 Generic Swaps
1/85
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
-
7/25/2019 Ch 3 Generic Swaps
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
-
7/25/2019 Ch 3 Generic Swaps
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 .$1"
2 '/0eb/2( .'""
2" '/0eb/33 .("
3 (/0eb/3( .(1"
against 3mo 6ibor
Deposit Futures
-
7/25/2019 Ch 3 Generic Swaps
4/85
Mar/( 1)/Mar/( )'.
7#n/( 1(/7#n/( )'.1
Sep/( 1'/Sep/( )'."2
Dec/( 1'/Dec/( )'.)"
Mar/) 1(/Mar/) )'.3)"
7#n/) 1'/7#n/) )'.22
Sep/) 1$/Sep/) )'.
Dec/) 1$/Dec/) )$.("
Mar/1 1'/Mar/1 )$.$$"
7#n/1 1$/7#n/1 )$.)"
Sep/1 1"/Sep/1 )$.3
Dec/1 1"/Dec/1 )$.2
Mar/11 1$/Mar/11 )$.$
7#n/11 1"/7#n/11 )".)3
Sep/11 21/Sep/11 )".(Dec/11 21/Dec/11 )".$'"
Mar/12 21/Mar/12 )"."$"
7#n/12 2/7#n/12 )"."
Sep/12 1)/Sep/12 )".33"
Dec/12 1)/Dec/12 )".22"
Mar/13 2/Mar/13 )".1
7#n/13 1)/7#n/13 )"."
Sep/13 1(/Sep/13 ).)""
Dec/13 1(/Dec/13 ).($
Mar/1 1)/Mar/1 ).'("7#n/1 1(/7#n/1 ).'1
Sep/1 1'/Sep/1 ).$"
Dec/1 1'/Dec/1 )."'
Mar/1" 1(/Mar/1" )."1"
7#n/1" 1'/7#n/1" ).$
Sep/1" 1$/Sep/1" ).1
Dec/1" 1$/Dec/1" ).3"
Mar/1$ 1$/Mar/1$ ).31"
7#n/1$ 1"/7#n/1$ ).2'"
Sep/1$ 21/Sep/1$ ).23"
Dec/1$ 21/Dec/1$ ).1("
Mar/1' 1"/Mar/1' ).1$"
7#n/1' 21/7#n/1' ).1"
Sep/1' 2/Sep/1' ).12
Dec/1' 2/Dec/1' ).(
-
7/25/2019 Ch 3 Generic Swaps
5/85
3.! Worksheet to "e#erate the $ash%lows o% a "e#eri$ &SD swap
+rade date- 4-Feb-08 +rade date- 4-Feb-08
Settlement date- $/0eb/( Settlement date- $/0eb/(
4otional principal- 1 million 4otional principal- 1 million
Mat#rity- ' years Mat#rity- ' years
+o receive fi!ed rate- 3.((" 448 ct3$ +o receive fi!ed rate 3.((" 448 ct3$
+o pay floating rate- 3 mo. 6ibor +o pay floating rate- 3 mo. 6ibor
0irst 6ibor fi!ing- 3.1" 0irst 6ibor fi!ing- 3.1"
3.((3)
Days 0i!ed 0loating 0i!ed 0loating 5ield/based
9ct3$: cashflows cashflows cashflows cashflows D0s$/0eb/( $/0eb/( /188 188 1
3 $/May/( .2" /'($82" $/May/( /'($82"
$ $/#g/( .2"$ /6ibor $/#g/( /6ibor
) $/4ov/( .2"$ /6ibor $/4ov/( /6ibor
12 $/0eb/) .2"$ 38))8'". /6ibor $/0eb/) 38))8'" /6ibor .)$22
1" $/May/) .2' /6ibor $/May/) /6ibor
1( $/#g/) .2"$ /6ibor $/#g/) /6ibor
21 $/4ov/) .2"$ /6ibor $/4ov/) /6ibor
2 (/0eb/1 .2$1 38)$8"1.$' /6ibor (/0eb/1 38)$8"2 /6ibor .)2"3"
2' $/May/1 .22 /6ibor $/May/1 /6ibor
3 $/#g/1 .2"$ /6ibor $/#g/1 /6ibor
33 (/4ov/1 .2$1 /6ibor (/4ov/1 /6ibor
3$ '/0eb/11 .2"3 38)2(81$$.$' /6ibor '/0eb/11 38)2(81$' /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: .'$2(()
1.311"
-
7/25/2019 Ch 3 Generic Swaps
6/85
3.3! Worksheet to demo#strate the dis$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.)') '(."$ .'""
-
7/25/2019 Ch 3 Generic Swaps
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"
-
7/25/2019 Ch 3 Generic Swaps
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
-
7/25/2019 Ch 3 Generic Swaps
9/85
-
7/25/2019 Ch 3 Generic Swaps
10/85
0.000 *.000 0.000 .000 30.000
e
maturit (rs)r
-
7/25/2019 Ch 3 Generic Swaps
11/85
-
7/25/2019 Ch 3 Generic Swaps
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(
.
-
7/25/2019 Ch 3 Generic Swaps
13/85
3.! Worksheet to $al$ulate a dis$ou#t $ur'e usi#" li#ear i#terpolatio# o# the s
Todas date! 4-Feb-08
=#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"
-
7/25/2019 Ch 3 Generic Swaps
14/85
-
7/25/2019 Ch 3 Generic Swaps
15/85
-
7/25/2019 Ch 3 Generic Swaps
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
-
7/25/2019 Ch 3 Generic Swaps
17/85
2( $/0eb/3$ .(11 1.1
2) $/0eb/3' .(13 1.1'
3 (/0eb/3( .(1" 1.1)
-
7/25/2019 Ch 3 Generic Swaps
18/85
-
7/25/2019 Ch 3 Generic Swaps
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)
-
7/25/2019 Ch 3 Generic Swaps
20/85
.2))" /.32"$ 2(.( .()2$$ /.2
.23'1'$ /.31$ 2).2" .()23 /.1)
.22"''$ 3. .(((2)
-
7/25/2019 Ch 3 Generic Swaps
21/85
-
7/25/2019 Ch 3 Generic Swaps
22/85
Forward rates %rom the bo
ln9D0: 0orward days
ln9D0: gradient dates ct3$
>'? >(?
/.()3$ $/0eb/(
/.' /.((1 3 $/May/( .2"
/.23(3 /.($( $ $/#g/( .2"$
/.'$"( /.''2) ) $/4ov/( .2"$/.1)2 /.'' 12 $/0eb/) .2"$
/.213'1 /.$)" 1" $/May/) .2'
/.2''23 /.''3( 1( $/#g/) .2"$
/."$123 /.)$$) 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$1
-
7/25/2019 Ch 3 Generic Swaps
23/85
/1.3())23 /.133)$ )) $/May/1$ .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
-
7/25/2019 Ch 3 Generic Swaps
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
-
7/25/2019 Ch 3 Generic Swaps
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') '.($1 3.)('11 .'3)3".'2111 ".2"' (.122 .2""" .'2111
-
7/25/2019 Ch 3 Generic Swaps
26/85
.'11))1 ".23)33 (.3$' .$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)")
-
7/25/2019 Ch 3 Generic Swaps
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$$ 2).2" .()23 .23'1'$
.2312 .''( 2).$'2 .(()'$ .233")
.231"" .(2)'2 2).)2( .(()2( .231(2
.22($)$ .()( 3.1(3 .(((') .22($2.22"''$ .)"332 3. .(((2) .22"''$
-
7/25/2019 Ch 3 Generic Swaps
28/85
lo"-li#ear i#terpolatio#
0orward 0orward
rates ln9D0: D0 rates
>13? >1? >1"? >1$?
1
3.113) /.'(12)$'1 .))221' 3.13'3
2.'(($" /.1)2)1 .)("1(' 2.')2"3
2."3'' /.213''((1 .)'(("$ 2."3''2.)3' /.2''23(' .)'2$"' 2.)3'
2.''2)2 /.3$1"""' .)$")(2 2.')"1
2.'('() /.1'2)(123 .)")12) 2.')"'
2.(2'( /.(()$) .)"232" 2.')"'
2.(1(" /."$123)2 .)"23 2.')")"
3.311( /.$"3"))) .)3'"3 3.)""1
3.31' /.'33""$" .)2)21 3.)$3$
3."""3" /.(2"1)3)2$ .)2') 3.)$'
3.$'(11 /.)131(1") .)12'2' 3.)$1)3.("( /.112()(3 .)3)' 3.))1)"
3.)2)( /.1111(3$ .()"') 3.))32'
."1 /.1213$') .(("$1 3.))2$1
.1'$(3 /.131(""13 .('$')2 3.))2$1
.2$'( /.12$"'" .($'"1 .2)
.3(3"' /.1"3(2("'' .("'1) .2)
."333 /.1$"122('3" .('') ."$
.$23"2 /.1'$1'1$)" .(3(2$( ."$
.$"22 /.1((2$'')'1 .(2(3)3 .(223
.'$"2 /.2"1'(( .(1(3' .(22))
.(''1 /.212'$')') .((3 .(22))
.)()11 /.22"1("'( .')("2 .(22))
.(('' /.23'2'3$ .'((''( .)($'
.)( /.2))3"$$)3 .''(("1 .)('"1
".31) /.2$2$)'$ .'$)) .)('"1
".123(2 /.2'"2$$2')) .'")3' .)('"1
.)((1 /.2('(33)3) .'))) ".1311
".$1 /.3'$31'3 .'2"3 ".12
".12 /.313'22(2' .'3'22 ".12".21($ /.32$)$2$' .'2111 ".1)2
.0
.
3.0
3.
4.0
4.
.0
.
.0
.
1.0
-
7/25/2019 Ch 3 Generic Swaps
29/85
".23( /.33))"22((3 .'11( ".3')
".312)( /.3"3(2"("$$ .'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)") ".')$2
-
7/25/2019 Ch 3 Generic Swaps
30/85
".""33 /.)3)"2' .3()2)( "."(113
"."'3( /.)"'"''(' .3(3(22 "."(32)
".")2)$ /.)'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
-
7/25/2019 Ch 3 Generic Swaps
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
-
7/25/2019 Ch 3 Generic Swaps
32/85
-
7/25/2019 Ch 3 Generic Swaps
33/85
-
7/25/2019 Ch 3 Generic Swaps
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#
-
7/25/2019 Ch 3 Generic Swaps
35/85
-
7/25/2019 Ch 3 Generic Swaps
36/85
-
7/25/2019 Ch 3 Generic Swaps
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
-
7/25/2019 Ch 3 Generic Swaps
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%
-
7/25/2019 Ch 3 Generic Swaps
39/85
10.000 15.000 20.000 25.000 30.000
-
7/25/2019 Ch 3 Generic Swaps
40/85
3.1! Worksheet to $al$ulate a dis$ou#t $ur'e usi#" 7ermite i#terpolatio# o# the
Todas date! 4-Feb-08
=#rrent USD market data
6ibor cash
ct3$
$/0eb/(
' day 11/0eb/( 3.21'"
1 mo /Mar/( 3.1(12"
3 mo /May/( 3.1"
0#t#res gradient
Mar/( 1)/Mar/( 3. /."
7#n/( 1(/7#n/( 2.") /.12
Sep/( 1'/Sep/( 2.( .3
Dec/( 1'/Dec/( 2."" .11
Mar/) 1(/Mar/) 2.$" .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""
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"
-
7/25/2019 Ch 3 Generic Swaps
41/85
-
7/25/2019 Ch 3 Generic Swaps
42/85
-
7/25/2019 Ch 3 Generic Swaps
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
-
7/25/2019 Ch 3 Generic Swaps
44/85
2( $/0eb/3$ .(1 1.1
2) $/0eb/3' .(1) 1.1'
3 (/0eb/3( .(1" 1.1)
-
7/25/2019 Ch 3 Generic Swaps
45/85
-
7/25/2019 Ch 3 Generic Swaps
46/85
/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'
.$'3 /.)) 1.1' .2)$ .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$1)1 /."(' 22.322 .((33$ .$$
.31)) /.313 23.33$ .()) .3)
.33'' /.)2 2.3" .()2 .31
.2(($)1 /.3($' 2".3$) .()'23 .1(
.2'$1" /.3$1' 2$.3(1 .()) /.1 .2$112 /.33) 2'.3) .()'"" /.3(
-
7/25/2019 Ch 3 Generic Swaps
47/85
.2)23 /.31)( 2(.( .()3$' /."
.23'31( /.32) 2).2" .(((21 /.$
.22$21 3. .((21
-
7/25/2019 Ch 3 Generic Swaps
48/85
-
7/25/2019 Ch 3 Generic Swaps
49/85
Forward rates %rom the bo
ln9D0: 0orward days
ln9D0: gradient dates ct3$
>'? >(?
/.()3$ $/0eb/(
/.' /.((1 3 $/May/( .2"
/.23(3 /.($( $ $/#g/( .2"$
/.'$"( /.''2) ) $/4ov/( .2"$/.1)2 /.'' 12 $/0eb/) .2"$
/.213'1 /.$)" 1" $/May/) .2'
/.2''23 /.''3( 1( $/#g/) .2"$
/."$123 /.)$$) 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$$ /.1(' 3$ '/0eb/11 .2"3/.32$)$ /.1'") 3) $/May/11 .2
/.3($(' /.1)') 2 (/#g/11 .2$1
/.3"3$2 /.1"' " '/4ov/11 .2"3
/.)3(1 /.1"1($ ( $/0eb/12 .2"3
/.""(1 /.1"3"( "1 '/May/12 .2"3
/.$232$ /.1"3($ " $/#g/12 .2"3
/.$"(331 /.1"11 "' $/4ov/12 .2"$
/.'12( /.1"2$$ $ $/0eb/13 .2"$
/.''1" /.1)) $3 $/May/13 .2'
/.(2($" /.1$)' $$ $/#g/13 .2"$
/.('(") /.1""( $) $/4ov/13 .2"$
/.)31)3( /.1")) '2 $/0eb/1 .2"$
/.)("') /.1"32 '" $/May/1 .2'
/1.3(121 /.123 '( $/#g/1 .2"$
/1.)'" /.13))" (1 $/4ov/1 .2"$
/1.111"' /.13($ ( $/0eb/1" .2"$
/1.1)1$)3 /.13(1$ (' $/May/1" .2'
/1.223)) /.13'32 ) $/#g/1" .2"$
/1.2)23( /.13)) )3 $/4ov/1" .2"$/1.31$"' /.1332 )$ (/0eb/1$ .2$1
-
7/25/2019 Ch 3 Generic Swaps
50/85
/1.3)211 /.131" )) $/May/1$ .2
/1.3(3"$ /.13'2 12 (/#g/1$ .2$1
/1.($33 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
-
7/25/2019 Ch 3 Generic Swaps
51/85
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
-
7/25/2019 Ch 3 Generic Swaps
52/85
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( '.$$ 3.))) .'"3$
.'3)) ".13') '.($1 3.)('11 .'3)3".'2111 ".2"' (.122 .2""" .'2111
-
7/25/2019 Ch 3 Generic Swaps
53/85
.'11))1 ".23)33 (.3$' .$2 .'11))2
.'22" ".312 (.$2( .)$(3 .'22"
.$)2(21 ".3(3 (.((1 .132' .$)2(1)
.$(33)1 "."($ ).133 .1$(11 .$(33)1
.$'32$ ".31(3 ).3($ .1)($1 .$'2)$.$$"2$1 ".3)(1 ).$3) .22)12 .$$"21(
.$"$1)" ".$"2) ).()2 .2")$2 .$"$1$2
.$'3 "."2' 1.1' .2)$ .$'3
.$3() ".3"" 1.3)' .31") .$3(3$
.$2)(" ".23) 1.$" .31$3 .$2)'(1
.$2112 "."1 1.)$ .3$'$ .$21$'
.$123)3 "."'("" 11.1$1 .3)3$" .$123)3
.$32 ".3()) 11.( .1"" .$2'3
.")$1) ".$3" 11.$$ .3')( .")")2"
."('$)" "."1' 11.)1) .$"1 ."('$2."')3'2 ".$213" 12.1'" .(3 ."')3'2
."'1"($ ".($' 12.2" ."2(" ."'1"'
."$3$2' "."2"$1 12.$(1 ."231 ."$3"1)
."""$$( ".$'" 12.)3$ ."33" .""""($
."'"3$ ".$(')) 13.1)' ."$ ."'"3$
.") "."''$ 13.3) ."($2 ."32"
."32('1 "."3)$ 13.$) .")(1$ ."32'"$
."2"1' ".$1$13 13.)"$ .$1$' ."2"(3
."1''1" ".$)' 1.2( .$332 ."1''1"."1((' ".$'3" 1."3 .$(11 ."1')(
."3")3 "."$"3 1.'1 .$$3( ."3'3
.)$"33 ".$2" 1.)$' .$'()) .)$2
.()'2 ".'$"" 1".21) .$)1( .()'2
.(2("( ".1(( 1".'2 .'$$$ .(2'$"
.'$2 ".)$ 1".'2" .'1)1 .'$12
.$)$3 "."'13 1".)'( .'31$3 .$)"3'
.$2) ".$"1) 1$.233 .'2" .$2)
."$((2 ".3$' 1$.(3 .'"3) ."$'()
."$($ ".3')$$ 1$.'3) .'$2) .""$1
.) "."$" 1$.)) .''23( .3)$
.3(2) "."31'$ 1'.2" .'(1(3 .3(2)
.32'12 ".21')' 1'.)' .'(('2 .32$21
.2$)2 ".2(() 1'.'"3 .')"( .2$(1)
.211'2 ".3$) 1(.( .(2)$ .21')
.1"2 ".3"1 1(.2$ .(1) .1"2
.11$1 ".1$($ 1(."11 .(1"$1 .1'2
.'3 ".23'(3 1(.'$' .(2132 .$22
.3))32" ".3(() 1).22 .(2'3 .3))233.3)3') ".3(3"2 1).2(3 .(32(' .3)3')
-
7/25/2019 Ch 3 Generic Swaps
54/85
.3(()1) ".1(2$$ 1)."2" .(3') .3(((3"
.3(3'$( ".2"222 1).'(1 .(323 .3(3$"3
.3'("" ".32"2" 2.2 .(($' .3'(1)
.3'31 ".3)')1 2.2) .("3) .3'31
.3$($ ".1$1$' 2."' .("(2 .3$("1'.3$3')1 ".22)) 2.( .($2() .3$3$(
.3"()(2 ".2)))' 21."3 .($'3' .3"(()(
.3"11) ".3'2' 21.3( .('1) .3"11)
.3)$)) "."$) 21.""( .(''3 .3)$1)
.3"22) ".121)$ 21.(11 .(''"( .3"123
.3'1 ".1()() 22.$' .((' .3$3
.33$1)1 ".2")$" 22.322 .((33$ .33$1)1
.3321) .)'2' 22."$) .((" .3323
.32'(() ".3$$ 22.(2" .(($' .32''((
.323$$) ".11'2 23.(1 .(((3) .323")3.31)) ".1$)11 23.33$ .()) .31))
.31"$11 .)1)$" 23."(3 .()1" .31""3)
.311$3 .)(22) 23.(3) .()2 .311"$
.3'$'" ".$"" 2.) .()33 .3'$2
.33'' ".112( 2.3" .()2 .33''
.32 .))1 2.$ .()( .2)))""
.2)$2$ .)'1'( 2.("$ .()"$1 .2)$1$'
.2)21 ".3'1' 2".11' .()$3 .2)23"
.2(($)1 ".121 2".3$) .()'23 .2(($)1.2("2(( .(')$1 2".$1 .()'$$ .2("22
.2(1$"3 .)2"( 2".('" .()(11 .2(1"$$
.2'(13 "."12 2$.12( .()("$ .2'($)
.2'$1" ".$)2" 2$.3(1 .()) .2'$1"
.2'132 .'))"2 2$.$33 .()($ .2'12$2
.2$(32 .("($ 2$.(($ .()(2( .2$'))
.2$' .)1((' 2'.13) .()')2 .2$$'(
.2$112 .)(1) 2'.3) .()'"" .2$112
.2"(3"' .'2)'" 2'.$ .()$") .2"(2))
.2""2$( .'($)( 2'.()' .()"$3 .2""1)1
.2"21$ .($2$ 2(.1"3 .()$" .2"2('
.2)23 .)' 2(.( .()3$' .2)23
.2$1 .$''$ 2(.$"( .()233 .2$()
.2322 .'3 2(.)1 .())$ .2312(
.22$ .')22 2).1$) .(()"( .22"
.23'31( .("13 2).2" .(((21 .23'31(
.23$22 .$'"$ 2).$'2 .(($'3 .23"'
.231(3" .'32 2).)2( .(("2 .231'$"
.22)) .'$$" 3.1(3 .((3$' .22())".22$21 .(2"' 3. .((21 .22$21
-
7/25/2019 Ch 3 Generic Swaps
55/85
lo"-li#ear i#terpolatio#
0orward 0orward
rates ln9D0: D0 rates
>13? >1? >1"? >1$?
1
3.113) /.'(12)$'1 .))221' 3.13'3
2.'(($" /.1)2)1 .)("1(' 2.')2"3
2."3'' /.213''((1 .)'(("$ 2."3''2.)3' /.2''23(' .)'2$"' 2.)3'
2.''2)2 /.3$1"""' .)$")(2 2.')"1
2.'('() /.1'2)(123 .)")12) 2.')"'
2.(2'( /.(()$) .)"232" 2.')"'
2.(1(" /."$123)2 .)"23 2.')")"
3.311( /.$"3"))) .)3'"3 3.)""1
3.31' /.'33""$" .)2)21 3.)$3$
3."""3" /.(2"1)3)2$ .)2') 3.)$'
3.$'(11 /.)131(1") .)12'2' 3.)$1)3.("( /.112()(3 .)3)' 3.))1)"
3.)2)( /.1111(3$ .()"') 3.))32'
."1 /.1213$') .(("$1 3.))2$1
.1'$(3 /.131(""13 .('$')2 3.))2$1
.2$'( /.12$"'" .($'"1 .2)
.3(3"' /.1"3(2("'' .("'1) .2)
."333 /.1$"122('3" .('') ."$
.$23"2 /.1'$1'1$)" .(3(2$( ."$
.$"22 /.1((2$'')'1 .(2(3)3 .(223
.'$"2 /.2"1'(( .(1(3' .(22))
.(''1 /.212'$')') .((3 .(22))
.)()11 /.22"1("'( .')("2 .(22))
.(('' /.23'2'3$ .'((''( .)($'
.)( /.2))3"$$)3 .''(("1 .)('"1
".31) /.2$2$)'$ .'$)) .)('"1
".123(2 /.2'"2$$2')) .'")3' .)('"1
.)((1 /.2('(33)3) .'))) ".1311
".$1 /.3'$31'3 .'2"3 ".12
".12 /.313'22(2' .'3'22 ".12".21($ /.32$)$2$' .'2111 ".1)2
-
7/25/2019 Ch 3 Generic Swaps
56/85
".23( /.33))"22((3 .'11( ".3')
".312)( /.3"3(2"("$$ .'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)(
".$$ /.21"(121 .$"$) ".2)(
"."22$( /.3"3$2$ .$'3 ".2)()
".3($$ /.()2(23 .$3(312 ".$3'
".3$) /.$2$"21($ .$2)$1$ ".$3((
".()(1 /.'$"12)2() .$2)" ".$3
"."2"' /.)3($3)2 .$123)3 ".$3
".3"$ /."3()$2$3( .$1'2 "."11
".(1'' /."1'($''11 .")"') ".""3$
"."2'' /."31(3($'(" ."('"2 ".""3$"."'31$ /.""()((") ."')3'2 ".""3$
".""12 /."")$31(2' ."'11) "."$'1$
"."$") /."'3'$)1'( ."$33 "."$(2
"."('$$ /."('()1( .""")( "."$(2
".$3' /.$232$2"(1 ."'"3$ "."$(((
"."22' /.$1"'12(3) ."2"$ "."'$2
"."")1 /.$2)($'211 ."32$$3 "."'(3"
".")$23 /.$33"$ ."2"1 "."')21
".$3$) /.$"(331322" ."1''1" "."'')2"."3)( /.$'1()3$ ."1'1 "."("''
"."'2 /.$($3')$13 ."33)" "."((3$
".$2' /.'3"3' .)$3(" "."(''
".$332( /.'12'$1 .()'2 "."(''
".)$1 /.'2(32$2 .(2'1) "."32"
"."21" /.'2212122 .'$$ "."32"
"."$'' /.'"$1(1(3 .$))2 "."32"
"."'2$$ /.''1)(((1 .$2) "."3$'
".3()$ /.'(3$'' ."$'"' ".1(1(
".)2 /.')'3"')1$$ .""1( ".1())
".2(3$ /.(111112"$ .3$ ".1())
".'"1 /.(2($)3" .3(2) ".1())
".33 /.(3')"2''2 .32")( ".32"$(
".31) /.("1$$"33 .2$'() ".32$($
".333( /.($)(''(3 .21"' ".32$($
".3(2( /.('(")3$" .1"2 ".32$($
".2"'$ /.()1$")2' .1" ".2'"(
".2'13 /.)(")"1'2 .")) ".2'$23
".2(1'1 /.)1(2"3131' .3))21$ ".2'$23".2)1( /.)31)3')11( .3)3') ".2''
-
7/25/2019 Ch 3 Generic Swaps
57/85
".2'3 /.)$3)322' .3(((2 ".2()2(
".2("$ /.)"('$))( .3(3$32 ".2)121
".2)'1" /.)'1')$33 .3'( ".2)1))
".3$( /.)("')'2 .3'31 ".2)(2
".2"2") /.))(33") .3$(" ".2$$2"".2$1$' /1.11"2'$3' .3$3$$3 ".2$$2"
".2'' /1.2'"1'2(" .3"((($ ".2$$2"
".2(2$ /1.3(12112 .3"11) ".2$$$
".1(2 /1.")31$") .3)$12 ".1"'1'
".1""" /1.$3(("1"( .3"113 ".1"'"
".1$' /1.'$)')'11 .3$23 ".1"')1
".1$$") /1.)')$) .33$1)1 ".1"')1
".$"' /1.12"3($( .3323 ".$)'2
".$)1 /1.11"")1'$ .32''(2 ".'')
".'2" /1.12(2(13(" .323"() ".'')".'"(( /1.111"$'') .31)) ".'')
".1222 /1.1"3')2)$ .31""3' ".1"23
".1"23 /1.1$$21'1')2 .311"3 ".1$2'
".1'2 /1.1'()""$2 .3'$ ".1$2'
".1)2 /1.1)1$)2)( .33'' ".1$2'
".2( /1.212'$3)" .2)))" ".)3
".'( /1.21$(3($$( .2)$1$" "."$2
".'12 /1.22)(2$($ .2)233 ".$32
".''2 /1.223)(($$$ .2(($)1 "."2(.)'22 /1.2"(32""" .2("223 .)'3$
.)'"1) /1.2$'3)1"( .2(1"$" .)'"$$
.)'"( /1.2')((')3$' .2'($( .)'$3
.)'")( /1.2)23(2)3 .2'$1" .)'$3
.()(" /1.3$$('11" .2'12$2 .(()'
.()11 /1.31$)"312)' .2$')" .(()'
.(()3( /1.32)23'"') .2$$') .(()'
.((()' /1.31$"$)")$ .2$112 .()'
.(2$1 /1.3"3$2)13 .2"(31 .(1'$$
.(1()) /1.3$"'33"32 .2""1)3 .(1')(
.(1'3 /1.3'')'2"($ .2"2() .(1(3
.(1"3$ /1.3)21(1)" .2)23 .(1(3
.'$'() /1.2)''2( .2$)2 .'$3'2
.'$"'' /1.11"1(1 .23132 .'$3"
.'$2)) /1.2$2"3(""1 .22' .'$3"
.'$21 /1.3(3""()$2 .23'31( .'$3"
.'3(2 /1.))()(331 .23"'3 .'333
.'3")1 /1.$21")2"2 .231'$) .'32'
.'32(1 /1.'21'3 .22())( .'32'.'32) /1.($32)"$2 .22$21 .'3()
-
7/25/2019 Ch 3 Generic Swaps
58/85
Difference between
6inear and %ermite
interpolated forwardc#rves
verage /.$3
Minim#m /3.33
Ma!im#m 3".3$
.
.
..
.
.
.
.
.
.
.
..
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
..
.000
.00
3.000
3.00
4.000
4.00
.000
.00
.000
.00
1.000
-
7/25/2019 Ch 3 Generic Swaps
59/85
.
.
.
.
..
.
.
(.$
).$
).(
).)1
/).3
/).'
/).)2/1.3$
1".3
1".)'
1$.$1
1'.2$
/.2$
/.32
/.3(
/.3/1$.(1
/1'."
/1(.(
/1(.'1
32.1(
33.2
3.3
3".3$
12.'
13.(
13.1
13.'"
/".$
/".2(
/"."1
/".'3
/1).3"
/1).)
/2."/21.1"
-
7/25/2019 Ch 3 Generic Swaps
60/85
/2(.
/2(.(
/2)."(
/3.33
22.3'22.)3
23."
2.'
(.2"
(.3
(.$1
(.')
/.
/.12
/.23/.3
/13.33
/13.$3
/13.)
/1.2
/1(."$
/1(.)"
/1).3"
/1).'1."'
1.((
1".1(
1".(
"."1
".$2
".'2
".(3
/2.3(
/2.3
/2.'
/2."2
/(."$
/(.'2
/(.('
/).3
/12.(
/12.$)
/12.)/13.12
-
7/25/2019 Ch 3 Generic Swaps
61/85
0.000 .000 *0.000 *.0000,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
/ootstrappi#" a sw
with 6-C i#terpolatio# o
Cubi$ 7ermit
i#ear i#terpo
-
7/25/2019 Ch 3 Generic Swaps
62/85
-
7/25/2019 Ch 3 Generic Swaps
63/85
-
7/25/2019 Ch 3 Generic Swaps
64/85
0.000 .000 30.000
p $ur'e
the DF $ur'e
i#terpolatio# o% swap $ur'e
latio# o% swap $ur'e
-
7/25/2019 Ch 3 Generic Swaps
65/85
-
7/25/2019 Ch 3 Generic Swaps
66/85
-
7/25/2019 Ch 3 Generic Swaps
67/85
3.8! Worksheet to $al$ulate a dis$ou#t $ur'e usi#" a# optimisatio# approa$h
Todas date! 4-Feb-08
=#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
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$ Aal#e
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" .
-
7/25/2019 Ch 3 Generic Swaps
68/85
-
7/25/2019 Ch 3 Generic Swaps
69/85
-
7/25/2019 Ch 3 Generic Swaps
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' $/0eb/3" )$
-
7/25/2019 Ch 3 Generic Swaps
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(
-
7/25/2019 Ch 3 Generic Swaps
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$
-
7/25/2019 Ch 3 Generic Swaps
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 .)$$$(
$/#g/) .2"$ 2.7010% .22 .)")(3
$/4ov/) .2"$ 2.8500% .32 .)"2)2
(/0eb/1 .2$1 3.0296% . .)"23 1.1)
$/May/1 .22 3.2404% .3" .)3(''
$/#g/1 .2"$ 3.4264% .2" .)2))3
(/4ov/1 .2$1 3.5860% .1( .)213(
'/0eb/11 .2"3 3.7188% .11 .)12'2( 1.11$/May/11 .2 3.8254% .12 .)2'2
(/#g/11 .2$1 3.9346% .12 .()"'$
'/4ov/11 .2"3 4.0464% .13 .(($1
$/0eb/12 .2"3 4.1605% .1 .('$')3 1.11
'/May/12 .2"3 4.2772% .13 .($'1
$/#g/12 .2"3 4.3905% .12 .("'()3
$/4ov/12 .2"$ 4.5005% .11 .((13)
$/0eb/13 .2"$ 4.6072% .11 .(3(2$) 1.1'
$/May/13 .2' 4.7105% .' .(2($1)
$/#g/13 .2"$ 4.7966% ." .(1("("
$/4ov/13 .2"$ 4.8649% .3 .(("33
$/0eb/1 .2"$ 4.9154% .1 .')("2 1.1
$/May/1 .2' 4.9481% .1 .'((("3
$/#g/1 .2"$ 4.9768% .1 .''()$
$/4ov/1 .2"$ 5.0013% . .'$)11"
$/0eb/1" .2"$ 5.0216% . .'")3' 1.1
$/May/1" .2' 5.0376% .1 .'"3
$/#g/1" .2"$ 5.0700% .2 .'3$
$/4ov/1" .2"$ 5.1193% . .'3('(/0eb/1$ .2$1 5.1857% .' .'2111 1.1)
-
7/25/2019 Ch 3 Generic Swaps
74/85
$/May/1$ .2 5.2693% . .'11)
(/#g/1$ .2$1 5.3349% .2 .'21")
'/4ov/1$ .2"3 5.3813% .1 .$)2'3$
$/0eb/1' .2"3 5.4089% . .$(33)2 1.11
(/May/1' .2"3 5.4179% . .$'1")'/#g/1' .2"3 5.4262% . .$$"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)
-
7/25/2019 Ch 3 Generic Swaps
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)
-
7/25/2019 Ch 3 Generic Swaps
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,
-
7/25/2019 Ch 3 Generic Swaps
77/85
'.$1))
(.2'")
(.()$)
).(3
1.
1."$'3
11.$22
11."31(
11.)''"
12.3)('
12.(
0.000 .000.00000,
.0000,
3.00000,
-
7/25/2019 Ch 3 Generic Swaps
78/85
13.1''$
13."3$(
13.(''(
1.21'
1.")$
1.(3)
1".(1'
1".3$)
1"."))$
1".()
1$.'1"
-
7/25/2019 Ch 3 Generic Swaps
79/85
/ootstrappi#" a swap $ur'e
Cubi$ 7ermite i#terpolatio# o% swap $ur'e
ptimisatio#
-
7/25/2019 Ch 3 Generic Swaps
80/85
*0.000 *.000 0.000 .
-
7/25/2019 Ch 3 Generic Swaps
81/85
-
7/25/2019 Ch 3 Generic Swaps
82/85
-
7/25/2019 Ch 3 Generic Swaps
83/85
000 30.000
-
7/25/2019 Ch 3 Generic Swaps
84/85
-
7/25/2019 Ch 3 Generic Swaps
85/85
top related