Ch 8 LPI Inflation Swap

7/25/2019 Ch 8 LPI Inflation Swap

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Worksheet Title

8.38 Libor sheet for interpolation

8.39 RPI curve8.40 Sheet for simulating a fixe!floating LPI inflation s"ap


2/148

8.38 Libor#ile save as 3$$%8$&%'.xls

E Page $

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8.38: Libor sheet for interpolation

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E Page 3

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E Page 4

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8.39: RPI !r"e

Downloaded from Ch 8 Inflation swap

Spot + 4!#eb!08

Last inex ate + ec!0*

#or"ar

RPI curve

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6/148

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17/148

Sep!4* 8%3.**

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ct!48 88&.4%

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18/148

ov!%' 98*.94

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ec!%% ''40.43


19/148

8.#$: %heet for sim!latin& a fi'ed(floatin& LPI inflation swap

%pot ) #(*eb($8

*loatin& *i'ed

Constant Prinipal +,+8-,8/ +,+8-,8/m 56P

0ase inde'in& date (1t(2$$8 (1t(2$$8

%tart date (1t(2$$9 (1t(2$$9

at!rit4 date (1t(2$29 (1t(2$292rs

*re5!en4 of 6plift a a

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LPI onstraints Lower 6pper

+.$$ 3.$$ pa.

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%tati &rowth rate from RPI pa.

%im!lated &rowth rate from RPI pa.

%im!lated &rowth rate from LPI pa.

7d?!sted 0reak(e"en @rowth rate pa.

*loatin& side *i'ed side

ates Real an!al ates Real an!al

Prinipal Prinipal

%!/an!'0 %!/an!'0

%!1pr!'0 0 %!1pr!'0 0

%!/ul!'0 0 %!/ul!'0 0

%!ct!'0 0 %!ct!'0 0

%!/an!'' 0 %!/an!'' 0

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%!/ul!'' 0 %!/ul!'' 0%!ct!'' 0 %!ct!'' 0

%!/an!'$ 0 %!/an!'$ 0

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%!/ul!'$ 0 %!/ul!'$ 0

%!ct!'$ 0 %!ct!'$ 0

*!/an!'3 0 *!/an!'3 0

%!1pr!'3 0 %!1pr!'3 0

%!/ul!'3 0 %!/ul!'3 0

*!ct!'3 0 *!ct!'3 0

&!/an!'4 0 &!/an!'4 0

*!1pr!'4 0 *!1pr!'4 0

*!/ul!'4 0 *!/ul!'4 0&!ct!'4 0 &!ct!'4 0


20/148

%!/an!'% 0 %!/an!'% 0

&!1pr!'% 0 &!1pr!'% 0

&!/ul!'% 0 &!/ul!'% 0

%!ct!'% 0 %!ct!'% 0

%!/an!'& 0 %!/an!'& 0

%!1pr!'& 0 %!1pr!'& 0

%!/ul!'& 0 %!/ul!'& 0

%!ct!'& 0 %!ct!'& 0

%!/an!'* 0 %!/an!'* 0

%!1pr!'* 0 %!1pr!'* 0

%!/ul!'* 0 %!/ul!'* 0

%!ct!'* 0 %!ct!'* 0

%!/an!'8 0 %!/an!'8 0

%!1pr!'8 0 %!1pr!'8 0

%!/ul!'8 0 %!/ul!'8 0

%!ct!'8 0 %!ct!'8 0

*!/an!'9 0 *!/an!'9 0

%!1pr!'9 0 %!1pr!'9 0%!/ul!'9 0 %!/ul!'9 0

*!ct!'9 0 *!ct!'9 0

&!/an!$0 0 &!/an!$0 0

&!1pr!$0 0 &!1pr!$0 0

&!/ul!$0 0 &!/ul!$0 0

%!ct!$0 0 %!ct!$0 0

%!/an!$' 0 %!/an!$' 0

%!1pr!$' 0 %!1pr!$' 0

%!/ul!$' 0 %!/ul!$' 0

%!ct!$' 0 %!ct!$' 0

%!/an!$$ 0 %!/an!$$ 0

%!1pr!$$ 0 %!1pr!$$ 0%!/ul!$$ 0 %!/ul!$$ 0

%!ct!$$ 0 %!ct!$$ 0

%!/an!$3 0 %!/an!$3 0

%!1pr!$3 0 %!1pr!$3 0

%!/ul!$3 0 %!/ul!$3 0

%!ct!$3 0 %!ct!$3 0

%!/an!$4 0 %!/an!$4 0

%!1pr!$4 0 %!1pr!$4 0

%!/ul!$4 0 %!/ul!$4 0

*!ct!$4 0 *!ct!$4 0

&!/an!$% 0 &!/an!$% 0

*!1pr!$% 0 *!1pr!$% 0

*!/ul!$% 0 *!/ul!$% 0

&!ct!$% 0 &!ct!$% 0

%!/an!$& 0 %!/an!$& 0

&!1pr!$& 0 &!1pr!$& 0

&!/ul!$& 0 &!/ul!$& 0

%!ct!$& 0 %!ct!$& 0

%!/an!$* 0 %!/an!$* 0

%!1pr!$* 0 %!1pr!$* 0

%!/ul!$* 0 %!/ul!$* 0

%!ct!$* 0 %!ct!$* 0

%!/an!$8 0 %!/an!$8 0%!1pr!$8 0 %!1pr!$8 0


21/148

%!/ul!$8 0 %!/ul!$8 0

%!ct!$8 0 %!ct!$8 0

%!/an!$9 0 %!/an!$9 0

%!1pr!$9 0 %!1pr!$9 0

%!/ul!$9 0 %!/ul!$9 0

%!ct!$9 0 %!ct!$9 0

0 0

0 0

0 0

0 0

0 0

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0 0

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0 0

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0 0

0 0

0 0

0 0

0 0

0 0

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0 00 0

0 0

0 0

0 0

0 0

0 0

0 0

0 0

0 0

0 0

0 0

0 0

0 0

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0 0

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0 0

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0 0

0 0

0 0

0 0

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22/148

0 0

0 0

0 0

0 0

0 0

0 0

0 0

0 0

0 0

0 0

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0 0

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0 0

0 0

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0 0

0 0

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0 0

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0 0

0 0

0 0

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0 0

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0 0

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0 0

0 0

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23/148

0 0

0 0

0 0

0 0

0 0

0 0

0 0

0 0

0 0

0 0

0 0

0 0

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0 0

0 0

0 0

0 00 0

0 0

0 0

0 0

0 0

0 0

0 0

0 0

0 0

0 0

0 0

0 00 0

0 0

0 0

0 0

0 0

0 0

0 0

0 0

0 0

0 0

0 0

0 0

0 0

0 0

0 0

0 0

0 0

0 0

0 0

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0 0

0 0

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24/148

0 0

0 0

0 0

0 0

0 0

0 0

0 0

0 0

0 0

0 0

0 0

0 0

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0 0

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0 0

0 00 0

0 0

0 0

0 0

0 0

0 0

0 0

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0 0

0 0

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0 0

0 0

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0 0

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25/148

0 0

0 0

0 0

0 0

0 0

0 0

0 0

0 0

0 0

0 0

0 0

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0 0

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0 0

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26/148

0 0

0 0

0 0

0 0

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0 0

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0 0

0 0

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27/148

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28/148


29/148

Aote: spread sheet will handle !pto #$$ ashflows

Last publishe inex ate ec!0*

#reuenc2 of plift '$ '$ months

#reuenc2 of :ashflo" 3 3 months

o. of Perios 80.0% 80.0%

o. of :#s 80 80

7n month $40 $407n ate %!ct!$9 %!ct!$9

T!rn sim!lation on B A 2

;olatilit4 for %im!lation +.+$$ pa.

anual

*loatin& side a2 count principal ;ime

6ase inexing ate

Start ate %!ct!09

plift ates

0 %!ct!09 %!ct!09 '.&&8 ct!09

3 %!/an!'0 %!/an!'0 0.$%$ 0 '.9$' 4.88'- 0.9'0%$$ ct!09

& %!1pr!'0 %!1pr!'0 0.$4* 0 $.'&* 4.8%3- 0.900'&% ct!09

9 %!/ul!'0 %!/ul!'0 0.$49 0 $.4'& 4.84*- 0.8894*4 ct!09

'$ %!ct!'0 %!ct!'0 0.$%$ 0 $.&&8 4.8%$- 0.8*8%&* ct!'0

'% %!/an!'' %!/an!'' 0.$%$ 0 $.9$' 4.8&0- 0.8&*&&4 ct!'0

'8 %!1pr!'' %!1pr!'' 0.$4* 0 3.'&* 4.8&9- 0.8%*098 ct!'0

$' %!/ul!'' %!/ul!'' 0.$49 0 3.4'& 4.8*&- 0.84&%4% ct!'0$4 %!ct!'' %!ct!'' 0.$%$ 0 3.&&8 4.883- 0.83%998 ct!''

$* %!/an!'$ %!/an!'$ 0.$%$ 0 3.9$' 4.889- 0.8$%%&* ct!''

30 %!1pr!'$ %!1pr!'$ 0.$49 0 4.'*0 4.89&- 0.8'%3%0 ct!''

33 %!/ul!'$ %!/ul!'$ 0.$49 0 4.4'9 4.90$- 0.80%$4$ ct!''

3& %!ct!'$ %!ct!'$ 0.$%$ 0 4.&*' 4.90*- 0.*9%'4% ct!'$

39 %!/an!'3 *!/an!'3 0.$%8 0 4.9$9 4.9'$- 0.*849&& ct!'$

4$ %!1pr!'3 %!1pr!'3 0.$4' 0 %.'*0 4.9'&- 0.**%%*& ct!'$

4% %!/ul!'3 %!/ul!'3 0.$49 0 %.4'9 4.9'9- 0.*&&00$ ct!'$

48 %!ct!'3 *!ct!'3 0.$%8 0 %.&** 4.9$$- 0.*%&$44 ct!'3

%' %!/an!'4 &!/an!'4 0.$49 0 %.9$& 4.9$4- 0.*4&9'* ct!'3

%4 %!1pr!'4 *!1pr!'4 0.$49 0 &.'*% 4.9$&- 0.*3*&93 ct!'3

%* %!/ul!'4 *!/ul!'4 0.$49 0 &.4$% 4.9$9- 0.*$8%&8 ct!'3&0 %!ct!'4 &!ct!'4 0.$49 0 &.&*4 4.93$- 0.*'9%34 ct!'4


30/148

&3 %!/an!'% %!/an!'% 0.$49 0 &.9$3 4.93%- 0.*'0%8* ct!'4

&& %!1pr!'% &!1pr!'% 0.$49 0 *.'*3 4.939- 0.*0'*'8 ct!'4

&9 %!/ul!'% &!/ul!'% 0.$49 0 *.4$$ 4.94$- 0.&9$949 ct!'4

*$ %!ct!'% %!ct!'% 0.$49 0 *.&*' 4.94%- 0.&84309 ct!'%

*% %!/an!'& %!/an!'& 0.$%$ 0 *.9$3 4.94*- 0.&*%*3' ct!'%

*8 %!1pr!'& %!1pr!'& 0.$49 0 8.'*3 4.94*- 0.&&*4$* ct!'%

8' %!/ul!'& %!/ul!'& 0.$49 0 8.4$$ 4.94*- 0.&%9$** ct!'%

84 %!ct!'& %!ct!'& 0.$%$ 0 8.&*4 4.94&- 0.&%''3* ct!'&

8* %!/an!'* %!/an!'* 0.$%$ 0 8.9$& 4.94*- 0.&4304% ct!'&

90 %!1pr!'* %!1pr!'* 0.$4* 0 9.'*3 4.949- 0.&3%'$9 ct!'&

93 %!/ul!'* %!/ul!'* 0.$49 0 9.4$$ 4.9%$- 0.&$*'4$ ct!'&

9& %!ct!'* %!ct!'* 0.$%$ 0 9.&*4 4.9%&- 0.&'9'%% ct!'*

99 %!/an!'8 %!/an!'8 0.$%$ 0 9.9$& 4.9%8- 0.&''3'0 ct!'*

'0$ %!1pr!'8 %!1pr!'8 0.$4* 0 '0.'*3 4.9%9- 0.&038$9 ct!'*

'0% %!/ul!'8 %!/ul!'8 0.$49 0 '0.4$$ 4.9%8- 0.%9&4*0 ct!'*

'08 %!ct!'8 %!ct!'8 0.$%$ 0 '0.&*4 4.9%&- 0.%89$'0 ct!'8

''' %!/an!'9 *!/an!'9 0.$%8 0 '0.93$ 4.9%$- 0.%8'9&0 ct!'8

''4 %!1pr!'9 %!1pr!'9 0.$4' 0 ''.'*3 4.948- 0.%*%3'0 ct!'8''* %!/ul!'9 %!/ul!'9 0.$49 0 ''.4$$ 4.944- 0.%&8%%& ct!'8

'$0 %!ct!'9 *!ct!'9 0.$%8 0 ''.&*9 4.939- 0.%&'&9' ct!'9

'$3 %!/an!$0 &!/an!$0 0.$49 0 ''.9$9 4.934- 0.%%%'38 ct!'9

'$& %!1pr!$0 &!1pr!$0 0.$49 0 '$.'*8 4.9$9- 0.%48&&' ct!'9

'$9 %!/ul!$0 &!/ul!$0 0.$49 0 '$.4$* 4.9$%- 0.%4$$%& ct!'9

'3$ %!ct!$0 %!ct!$0 0.$49 0 '$.&** 4.9$0- 0.%3%9$8 ct!$0

'3% %!/an!$' %!/an!$' 0.$%$ 0 '$.9$9 4.9'&- 0.%$9&'' ct!$0

'38 %!1pr!$' %!1pr!$' 0.$4* 0 '3.'*% 4.9'$- 0.%$3%'0 ct!$0

'4' %!/ul!$' %!/ul!$' 0.$49 0 '3.4$% 4.908- 0.%'*4$% ct!$0

'44 %!ct!$' %!ct!$' 0.$%$ 0 '3.&** 4.904- 0.%''3%9 ct!$'

'4* %!/an!$$ %!/an!$$ 0.$%$ 0 '3.9$9 4.899- 0.%0%383 ct!$'

'%0 %!1pr!$$ %!1pr!$$ 0.$4* 0.000 '4.'*% 4.89%- 0.499&$4 ct!$''%3 %!/ul!$$ %!/ul!$$ 0.$49 0.000 '4.4$% 4.89'- 0.49389$ ct!$'

'%& %!ct!$$ %!ct!$$ 0.$%$ 0.000 '4.&** 4.88&- 0.488'90 ct!$$

'%9 %!/an!$3 %!/an!$3 0.$%$ 0.000 '4.9$9 4.88'- 0.48$%8% ct!$$

'&$ %!1pr!$3 %!1pr!$3 0.$4* 0.000 '%.'*% 4.8*%- 0.4**'9$ ct!$$

'&% %!/ul!$3 %!/ul!$3 0.$49 0.000 '%.4$% 4.8*0- 0.4*'834 ct!$$

'&8 %!ct!$3 %!ct!$3 0.$%$ 0.000 '%.&** 4.8&4- 0.4&&%08 ct!$3

'*' %!/an!$4 %!/an!$4 0.$%$ 0.000 '%.9$9 4.8%8- 0.4&'$&9 ct!$3

'*4 %!1pr!$4 %!1pr!$4 0.$49 0.000 '&.'*8 4.8%$- 0.4%&'*' ct!$3

'** %!/ul!$4 %!/ul!$4 0.$49 0.000 '&.4$* 4.84%- 0.4%''%3 ct!$3

'80 %!ct!$4 *!ct!$4 0.$%8 0.000 '&.&8% 4.839- 0.44&0%' ct!$4

'83 %!/an!$% &!/an!$% 0.$49 0.000 '&.934 4.83$- 0.44''88 ct!$4

'8& %!1pr!$% *!1pr!$% 0.$49 0.000 '*.'84 4.8$&- 0.43&398 ct!$4

'89 %!/ul!$% *!/ul!$% 0.$49 0.000 '*.433 4.8'9- 0.43'&** ct!$4

'9$ %!ct!$% &!ct!$% 0.$49 0.000 '*.&8$ 4.8'$- 0.4$*0$4 ct!$%

'9% %!/an!$& %!/an!$& 0.$49 0.000 '*.93$ 4.80&- 0.4$$43& ct!$%

'98 %!1pr!$& &!1pr!$& 0.$49 0.000 '8.'8' 4.*99- 0.4'*9'0 ct!$%

$0' %!/ul!$& &!/ul!$& 0.$49 0.000 '8.430 4.*9$- 0.4'344% ct!$%

$04 %!ct!$& %!ct!$& 0.$49 0.000 '8.&*9 4.*8&- 0.409040 ct!$&

$0* %!/an!$* %!/an!$* 0.$%$ 0.000 '8.93$ 4.**9- 0.404&43 ct!$&

$'0 %!1pr!$* %!1pr!$* 0.$4* 0.000 '9.'*8 4.**3- 0.40039& ct!$&

$'3 %!/ul!$* %!/ul!$* 0.$49 0.000 '9.4$* 4.*&&- 0.39&'%% ct!$&

$'& %!ct!$* %!ct!$* 0.$%$ 0.000 '9.&*9 4.*&0- 0.39'9$0 ct!$*

$'9 %!/an!$8 %!/an!$8 0.$%$ 0.000 '9.93$ 4.*%3- 0.38**3% ct!$*$$$ %!1pr!$8 %!1pr!$8 0.$49 0.000 $0.'8' 4.*4*- 0.383&44 ct!$*


31/148

$$% %!/ul!$8 %!/ul!$8 0.$49 0.000 $0.430 4.*4'- 0.3*9&0' ct!$*

$$8 %!ct!$8 %!ct!$8 0.$%$ 0.000 $0.&8$ 4.*3%- 0.3*%%&$ ct!$8

$3' %!/an!$9 %!/an!$9 0.$%$ 0.000 $0.934 4.*$9- 0.3*'%*$ ct!$8

$34 %!1pr!$9 %!1pr!$9 0.$4* 0.000 $'.'8' 4.*$3- 0.3&**'* ct!$8

$3* %!/ul!$9 %!/ul!$9 0.$49 0.000 $'.430 4.*'8- 0.3&38&* ct!$8

$40 %!ct!$9 %!ct!$9 0.$%$ 0.000 $'.&8$ 4.*'$- 0.3&00$% ct!$9

$43 0.000

$4& 0.000

$49 0.000

$%$ 0.000

$%% 0.000

$%8 0.000

$&' 0.000

$&4 0.000

$&* 0.000

$*0 0.000

$*3 0.000

$*& 0.000$*9 0.000

$8$ 0.000

$8% 0.000

$88 0.000

$9' 0.000

$94 0.000

$9* 0.000

300 0.000

303 0.000

30& 0.000

309 0.000

3'$ 0.0003'% 0.000

3'8 0.000

3$' 0.000

3$4 0.000

3$* 0.000

330 0.000

333 0.000

33& 0.000

339 0.000

34$ 0.000

34% 0.000

348 0.000

3%' 0.000

3%4 0.000

3%* 0.000

3&0 0.000

3&3 0.000

3&& 0.000

3&9 0.000

3*$ 0.000

3*% 0.000

3*8 0.000

38' 0.000384 0.000


32/148

38* 0.000

390 0.000

393 0.000

39& 0.000

399 0.000

40$ 0.000

40% 0.000

408 0.000

4'' 0.000

4'4 0.000

4'* 0.000

4$0 0.000

4$3 0.000

4$& 0.000

4$9 0.000

43$ 0.000

43% 0.000

438 0.00044' 0.000

444 0.000

44* 0.000

4%0 0.000

4%3 0.000

4%& 0.000

4%9 0.000

4&$ 0.000

4&% 0.000

4&8 0.000

4*' 0.000

4*4 0.0004** 0.000

480 0.000

483 0.000

48& 0.000

489 0.000

49$ 0.000

49% 0.000

498 0.000

%0' 0.000

%04 0.000

%0* 0.000

%'0 0.000

%'3 0.000

%'& 0.000

%'9 0.000

%$$ 0.000

%$% 0.000

%$8 0.000

%3' 0.000

%34 0.000

%3* 0.000

%40 0.000

%43 0.000%4& 0.000


33/148

%49 0.000

%%$ 0.000

%%% 0.000

%%8 0.000

%&' 0.000

%&4 0.000

%&* 0.000

%*0 0.000

%*3 0.000

%*& 0.000

%*9 0.000

%8$ 0.000

%8% 0.000

%88 0.000

%9' 0.000

%94 0.000

%9* 0.000

&00 0.000&03 0.000

&0& 0.000

&09 0.000

&'$ 0.000

&'% 0.000

&'8 0.000

&$' 0.000

&$4 0.000

&$* 0.000

&30 0.000

&33 0.000

&3& 0.000&39 0.000

&4$ 0.000

&4% 0.000

&48 0.000

&%' 0.000

&%4 0.000

&%* 0.000

&&0 0.000

&&3 0.000

&&& 0.000

&&9 0.000

&*$ 0.000

&*% 0.000

&*8 0.000

&8' 0.000

&84 0.000

&8* 0.000

&90 0.000

&93 0.000

&9& 0.000

&99 0.000

*0$ 0.000

*0% 0.000*08 0.000


34/148

*'' 0.000

*'4 0.000

*'* 0.000

*$0 0.000

*$3 0.000

*$& 0.000

*$9 0.000

*3$ 0.000

*3% 0.000

*38 0.000

*4' 0.000

*44 0.000

*4* 0.000

*%0 0.000

*%3 0.000

*%& 0.000

*%9 0.000

*&$ 0.000*&% 0.000

*&8 0.000

**' 0.000

**4 0.000

*** 0.000

*80 0.000

*83 0.000

*8& 0.000

*89 0.000

*9$ 0.000

*9% 0.000

*98 0.00080' 0.000

804 0.000

80* 0.000

8'0 0.000

8'3 0.000

8'& 0.000

8'9 0.000

8$$ 0.000

8$% 0.000

8$8 0.000

83' 0.000

834 0.000

83* 0.000

840 0.000

843 0.000

84& 0.000

849 0.000

8%$ 0.000

8%% 0.000

8%8 0.000

8&' 0.000

8&4 0.000

8&* 0.0008*0 0.000


35/148

8*3 0.000

8*& 0.000

8*9 0.000

88$ 0.000

88% 0.000

888 0.000

89' 0.000

894 0.000

89* 0.000

900 0.000

903 0.000

90& 0.000

909 0.000

9'$ 0.000

9'% 0.000

9'8 0.000

9$' 0.000

9$4 0.0009$* 0.000

930 0.000

933 0.000

93& 0.000

939 0.000

94$ 0.000

94% 0.000

948 0.000

9%' 0.000

9%4 0.000

9%* 0.000

9&0 0.0009&3 0.000

9&& 0.000

9&9 0.000

9*$ 0.000

9*% 0.000

9*8 0.000

98' 0.000

984 0.000

98* 0.000

990 0.000

993 0.000

99& 0.000

999 0.000

'00$ 0.000

'00% 0.000

'008 0.000

'0'' 0.000

'0'4 0.000

'0'* 0.000

'0$0 0.000

'0$3 0.000

'0$& 0.000

'0$9 0.000'03$ 0.000


36/148

'03% 0.000

'038 0.000

'04' 0.000

'044 0.000

'04* 0.000

'0%0 0.000

'0%3 0.000

'0%& 0.000

'0%9 0.000

'0&$ 0.000

'0&% 0.000

'0&8 0.000

'0*' 0.000

'0*4 0.000

'0** 0.000

'080 0.000

'083 0.000

'08& 0.000'089 0.000

'09$ 0.000

'09% 0.000

'098 0.000

''0' 0.000

''04 0.000

''0* 0.000

'''0 0.000

'''3 0.000

'''& 0.000

'''9 0.000

''$$ 0.000''$% 0.000

''$8 0.000

''3' 0.000

''34 0.000

''3* 0.000

''40 0.000

''43 0.000

''4& 0.000

''49 0.000

''%$ 0.000

''%% 0.000

''%8 0.000

''&' 0.000

''&4 0.000

''&* 0.000

''*0 0.000

''*3 0.000

''*& 0.000

''*9 0.000

''8$ 0.000

''8% 0.000

''88 0.000

''9' 0.000''94 0.000


37/148

''9* 0.000

'$00 0.000


38/148


39/148

*re5!en4 table

'

= 3 This "ersion al!lates the &rowth rate !si

S &

1 '$ This "ersion a"era&es the res!lts of normal

7t this point, it r!ns two sim!lations sim!l

%tati RPI str!t!re ((((E Implie

1verage

1ccumulative :# 5ro"th

Reference Inex Inex (/-,/9,+8# rate pa. >olatilit2 pa.

ct!08 $'%.$$

ov!09 $$'.%* $.&*8- '.'00-

Reference Inex

ov!09 $$'.%* '0$.9%-

ov!09 $$'.%* '0$.9%- !'?$$'?840

ov!09 $$'.%* '0$.9%- !'?$$'?840

ov!09 $$'.%* '0$.9%- !'?$$'?840

ov!'0 $$8.$$ '0&.04- !'?$$'?840 $.9%8- '.'00-

ov!'0 $$8.$$ '0&.04- !'?$%8?%$0

ov!'0 $$8.$$ '0&.04- !'?$%8?%$0

ov!'0 $$8.$$ '0&.04- !'?$%8?%$0ov!'' $3%.33 '09.34- !'?$%8?%$0 3.0&8- '.'00-

ov!'' $3%.33 '09.34- !'?$9*?*$3

ov!'' $3%.33 '09.34- !'?$9*?*$3

ov!'' $3%.33 '09.34- !'?$9*?*$3

ov!'$ $43.'$ ''$.9&- !'?$9*?*$3 3.$48- '.'00-

ov!'$ $43.'$ ''$.9&- !'?340?&83

ov!'$ $43.'$ ''$.9&- !'?340?&83

ov!'$ $43.'$ ''$.9&- !'?340?&83

ov!'3 $%'.3* ''&.80- !'?340?&83 3.3$'- '.'00-

ov!'3 $%'.3* ''&.80- !'?38&?$03

ov!'3 $%'.3* ''&.80- !'?38&?$03

ov!'3 $%'.3* ''&.80- !'?38&?$03ov!'4 $&0.'' '$0.8&- !'?38&?$03 3.4$*- '.'00-


40/148

ov!'4 $&0.'' '$0.8&- !'?434?40$

ov!'4 $&0.'' '$0.8&- !'?434?40$

ov!'4 $&0.'' '$0.8&- !'?434?40$

ov!'% $&9.'8 '$%.0*- !'?434?40$ 3.43%- '.'00-

ov!'% $&9.'8 '$%.0*- !'?484?39&

ov!'% $&9.'8 '$%.0*- !'?484?39&

ov!'% $&9.'8 '$%.0*- !'?484?39&

ov!'& $*8.9* '$9.&$- !'?484?39& 3.%&3- '.'00-

ov!'& $*8.9* '$9.&$- !'?%38?38%

ov!'& $*8.9* '$9.&$- !'?%38?38%

ov!'& $*8.9* '$9.&$- !'?%38?38%

ov!'* $89.$4 '34.39- !'?%38?38% 3.&'%- '.'00-

ov!'* $89.$4 '34.39- !'?%9%?0'8

ov!'* $89.$4 '34.39- !'?%9%?0'8

ov!'* $89.$4 '34.39- !'?%9%?0'8

ov!'8 300.0& '39.4$- !'?%9%?0'8 3.&*$- '.'00-

ov!'8 300.0& '39.4$- !'?&%4?&**

ov!'8 300.0& '39.4$- !'?&%4?&**ov!'8 300.0& '39.4$- !'?&%4?&**

ov!'9 3''.%% '44.*&- !'?&%4?&** 3.*38- '.'00-

ov!'9 3''.%% '44.*&- !'?*'8?04%

ov!'9 3''.%% '44.*&- !'?*'8?04%

ov!'9 3''.%% '44.*&- !'?*'8?04%

ov!$0 3$3.40 '%0.$&- !'?*'8?04% 3.*43- '.'00-

ov!$0 3$3.40 '%0.$&- !'?*83?383

ov!$0 3$3.40 '%0.$&- !'?*83?383

ov!$0 3$3.40 '%0.$&- !'?*83?383

ov!$' 33%.8& '%&.0%- !'?*83?383 3.*80- '.'00-

ov!$' 33%.8& '%&.0%- !'?8%$?084

ov!$' 33%.8& '%&.0%- !'?8%$?084ov!$' 33%.8& '%&.0%- !'?8%$?084

ov!$$ 349.03 '&$.'*- !'?8%$?084 3.848- '.'00-

ov!$$ 349.03 '&$.'*- !'?9$4?*3&

ov!$$ 349.03 '&$.'*- !'?9$4?*3&

ov!$$ 349.03 '&$.'*- !'?9$4?*3&

ov!$3 3&$.40 '&8.38- !'?9$4?*3& 3.*%8- '.'00-

ov!$3 3&$.40 '&8.38- !'?998?444

ov!$3 3&$.40 '&8.38- !'?998?444

ov!$3 3&$.40 '&8.38- !'?998?444

ov!$4 3*&.44 '*4.9'- !'?998?444 3.**'- '.'00-

ov!$4 3*&.44 '*4.9'- !$?0*%?8*8

ov!$4 3*&.44 '*4.9'- !$?0*%?8*8

ov!$4 3*&.44 '*4.9'- !$?0*%?8*8

ov!$% 39'.'& '8'.*%- !$?0*%?8*8 3.848- '.'00-

ov!$% 39'.'& '8'.*%- !$?'%*?08*

ov!$% 39'.'& '8'.*%- !$?'%*?08*

ov!$% 39'.'& '8'.*%- !$?'%*?08*

ov!$& 40&.&& '88.9%- !$?'%*?08* 3.894- '.'00-

ov!$& 40&.&& '88.9%- !$?$4$?%'0

ov!$& 40&.&& '88.9%- !$?$4$?%'0

ov!$& 40&.&& '88.9%- !$?$4$?%'0

ov!$* 4$$.9% '9&.%$- !$?$4$?%'0 3.930- '.'00-

ov!$* 4$$.9% '9&.%$- !$?33$?394ov!$* 4$$.9% '9&.%$- !$?33$?394


41/148

ov!$* 4$$.9% '9&.%$- !$?33$?394

ov!$8 439.40 $04.'&- !$?33$?394 3.804- '.'00-

ov!$8 439.40 $04.'&- !$?4$3?0*0

ov!$8 439.40 $04.'&- !$?4$3?0*0

ov!$8 439.40 $04.'&- !$?4$3?0*0

ov!$9 4%&.%0 $'$.'0- !$?4$3?0*0 3.8'*- '.'00-


42/148


43/148


44/148


45/148


46/148


47/148


48/148


49/148

& ontin!o!s ompo!ndin&

and antitheti sim!lations, and then estimates fi'ed rate

aneo!sl4 on the LPI 7AD the RPI str!t!res

*orward sim!lation (((E

6nbo!nded RPI str!t!re ((((E 0o!nded LPI

rv Simulate Simulate 1ccumulate Simulate

;ime gro"th Inex Inex :# Inex

@2earsA (/,898,$82

$'%.$$ $'%.$$

'.08 '0&.*- 4.'$'- $$4.$8 $$4.$8

$$4.$8 '04.$'-

$$4.$8 '04.$'- !'?$3&?*9'

$$4.$8 '04.$'- !'?$3&?*9'

$$4.$8 '04.$'- !'?$3&?*9'

'.00 !3'- $.&'3- $30.$$ '0&.9*- !'?$3&?*9' $$8.''

$30.$$ '0&.9*- !'?$&9?%3%

$30.$$ '0&.9*- !'?$&9?%3%

$30.$$ '0&.9*- !'?$&9?%3%'.00 '$'- 4.39%- $40.%& '''.**- !'?$&9?%3% $38.3&

$40.%& '''.**- !'?3$&?%**

$40.%& '''.**- !'?3$&?%**

$40.%& '''.**- !'?3$&?%**

'.00 !9%- $.$0&- $4%.93 ''4.$*- !'?3$&?%** $40.$0

$4%.93 ''4.$*- !'?3%&?'*$

$4%.93 ''4.$*- !'?3%&?'*$

$4%.93 ''4.$*- !'?3%&?'*$

'.0' '0*- 4.%''- $%*.$8 ''9.%4- !'?3%&?'*$ $%'.$8

$%*.$8 ''9.%4- !'?4'8?*%&

$%*.$8 ''9.%4- !'?4'8?*%&

$%*.$8 ''9.%4- !'?4'8?*%&'.00 ''4- 4.&%9- $&9.%% '$%.$4- !'?4'8?*%& $%9.$0


50/148

$&9.%% '$%.$4- !'?48&?4$0

$&9.%% '$%.$4- !'?48&?4$0

$&9.%% '$%.$4- !'?48&?4$0

'.00 !$&'- 0.%%8- $*'.0% '$%.94- !'?48&?4$0 $%&.$%

$*'.0% '$%.94- !'?494?*30

$*'.0% '$%.94- !'?494?*30

$*'.0% '$%.94- !'?494?*30

'.00 !'&4- '.*&'- $*%.8* '$8.'8- !'?494?*30 $&'.9%

$*%.8* '$8.'8- !'?%$'?$90

$*%.8* '$8.'8- !'?%$'?$90

$*%.8* '$8.'8- !'?%$'?$90

'.00 '%- 3.**&- $8&.49 '33.''- !'?%$'?$90 $*$.03

$8&.49 '33.''- !'?%*9?83&

$8&.49 '33.''- !'?%*9?83&

$8&.49 '33.''- !'?%*9?83&

'.00 !$*- 3.3*'- $9&.3' '3*.&*- !'?%*9?83& $*9.0&

$9&.3' '3*.&*- !'?&34?003

$9&.3' '3*.&*- !'?&34?003$9&.3' '3*.&*- !'?&34?003

'.0' !9'- $.*%'- 304.%* '4'.%'- !'?&34?003 $8%.&%

304.%* '4'.%'- !'?&*9?%*$

304.%* '4'.%'- !'?&*9?%*$

304.%* '4'.%'- !'?&*9?%*$

'.00 0- 3.*3$- 3'&.'% '4&.89- !'?&*9?%*$ $9&.%'

3'&.'% '4&.89- !'?*43?43'

3'&.'% '4&.89- !'?*43?43'

3'&.'% '4&.89- !'?*43?43'

'.00 !$0$- '.%%$- 3$'.'0 '49.'9- !'?*43?43' $98.8$

3$'.'0 '49.'9- !'?**0?*03

3$'.'0 '49.'9- !'?**0?*033$'.'0 '49.'9- !'?**0?*03

'.00 !%'- 3.$83- 33'.8$ '%4.'*- !'?**0?*03 308.80

33'.8$ '%4.'*- !'?8$9?803

33'.8$ '%4.'*- !'?8$9?803

33'.8$ '%4.'*- !'?8$9?803

'.00 *0- 4.%$*- 34*.'8 '&'.3'- !'?8$9?803 3$$.04

34*.'8 '&'.3'- !'?9'4?%39

34*.'8 '&'.3'- !'?9'4?%39

34*.'8 '&'.3'- !'?9'4?%39

'.0' !'3$- $.340- 3%%.40 '&%.'3- !'?9'4?%39 3$4.%3

3%%.40 '&%.'3- !'?9%9?8*3

3%%.40 '&%.'3- !'?9%9?8*3

3%%.40 '&%.'3- !'?9%9?8*3

'.00 '%8- %.%*$- 3*%.** '*4.%9- !'?9%9?8*3 343.'$

3*%.** '*4.%9- !$?0*$?'&9

3*%.** '*4.%9- !$?0*$?'&9

3*%.** '*4.%9- !$?0*$?'&9

'.00 38- 4.$90- 39$.$4 '8$.$%- !$?0*$?'&9 348.9'

39$.$4 '8$.$%- !$?'&$?99%

39$.$4 '8$.$%- !$?'&$?99%

39$.$4 '8$.$%- !$?'&$?99%

'.00 '3'- %.3&%- 4'3.8& '9$.$9- !$?'&$?99% 3&3.$*

4'3.8& '9$.$9- !$?$8$?$'*4'3.8& '9$.$9- !$?$8$?$'*


51/148

4'3.8& '9$.$9- !$?$8$?$'*

'.00 34- 4.'8&- 43'.%% $00.%'- !$?$8$?$'* 3&9.*8

43'.%% $00.%'- !$?3*9?*88

43'.%% $00.%'- !$?3*9?*88

43'.%% $00.%'- !$?3*9?*88

'.00 &3- 4.%00- 4%'.4' $09.*4- !$?3*9?*88 38$.0*


52/148


53/148


54/148


55/148


56/148


57/148


58/148


59/148

7ntitheti

str!t!re ((((E

Lo"er pper 6oune 6oune 1ccumulate antithetic

boun boun uplift Inex Inex :# rv

(/$,9/9,#+-

$'%.$$

'.08- 3.$%- '03.3- $$$.$3 !'0&.*-

'.00- 3.00- $$$.$3 '03.$%- $0499'0.8&

'.00- 3.00- $$$.$3 '03.$%- !'?$$%?48* $0499'0.8&

'.00- 3.00- $$$.$3 '03.$%- !'?$$%?48* $0499'0.8&

'.00- 3.00- $$$.$3 '03.$%- !'?$$%?48* $0499'0.8&

'.00- 3.00- '0$.&- $$8.'' '0%.99- !'?$$%?48* $'04'8'.&3* 3'-

'.00- 3.00- $$8.'' '0%.99- !'?$%*?93' $'04'8'.&3*

'.00- 3.00- $$8.'' '0%.99- !'?$%*?93' $'04'8'.&3*

'.00- 3.00- $$8.'' '0%.99- !'?$%*?93' $'04'8'.&3*'.00- 3.00- '03.0- $34.9& '09.'*- !'?$%*?93' %&04*8*.&08 !'$'-

'.00- 3.00- $34.9& '09.'*- !'?$9%?&&9 %&04*8*.&08

'.00- 3.00- $34.9& '09.'*- !'?$9%?&&9 %&04*8*.&08

'.00- 3.00- $34.9& '09.'*- !'?$9%?&&9 %&04*8*.&08

'.00- 3.00- '0$.$- $40.$0 '''.&0- !'?$9%?&&9 %*$98$9.403 9%-

'.00- 3.00- $40.$0 '''.&0- !'?3$4?%*% %*$98$9.403

'.00- 3.00- $40.$0 '''.&0- !'?3$4?%*% %*$98$9.403

'.00- 3.00- $40.$0 '''.&0- !'?3$4?%*% %*$98$9.403

'.00- 3.00- '03.0- $4*.40 ''4.9%- !'?3$4?%*% 98*$*4*.*04 !'0*-

'.00- 3.00- $4*.40 ''4.9%- !'?3&4?3'$ 98*$*4*.*04

'.00- 3.00- $4*.40 ''4.9%- !'?3&4?3'$ 98*$*4*.*04

'.00- 3.00- $4*.40 ''4.9%- !'?3&4?3'$ 98*$*4*.*04'.00- 3.00- '03.0- $%4.83 ''8.40- !'?3&4?3'$ '4*$0*38.$9 !''4-


60/148

'.00- 3.00- $%4.83 ''8.40- !'?40%?$4$ '4*$0*38.$9

'.00- 3.00- $%4.83 ''8.40- !'?40%?$4$ '4*$0*38.$9

'.00- 3.00- $%4.83 ''8.40- !'?40%?$4$ '4*$0*38.$9

'.00- 3.00- '0'.0- $%*.3* ''9.%8- !'?40%?$4$ '3&*9493.$8 $&'-

'.00- 3.00- $%*.3* ''9.%8- !'?4'9?$94 '3&*9493.$8

'.00- 3.00- $%*.3* ''9.%8- !'?4'9?$94 '3&*9493.$8

'.00- 3.00- $%*.3* ''9.%8- !'?4'9?$94 '3&*9493.$8

'.00- 3.00- '0'.8- $&'.9% '$'.*'- !'?4'9?$94 '39$$%&3.88 '&4-

'.00- 3.00- $&'.9% '$'.*'- !'?444?%'4 '39$$%&3.88

'.00- 3.00- $&'.9% '$'.*'- !'?444?%'4 '39$$%&3.88

'.00- 3.00- $&'.9% '$'.*'- !'?444?%'4 '39$$%&3.88

'.00- 3.00- '03.0- $&9.8' '$%.3&- !'?444?%'4 '&&8090'.39 !'%-

'.00- 3.00- $&9.8' '$%.3&- !'?48*?849 '&&8090'.39

'.00- 3.00- $&9.8' '$%.3&- !'?48*?849 '&&8090'.39

'.00- 3.00- $&9.8' '$%.3&- !'?48*?849 '&&8090'.39

'.00- 3.00- '03.0- $**.90 '$9.'$- !'?48*?849 '8409$9&.$9 $*-

'.00- 3.00- $**.90 '$9.'$- !'?%3$?48% '8409$9&.$9

'.00- 3.00- $**.90 '$9.'$- !'?%3$?48% '8409$9&.$9'.00- 3.00- $**.90 '$9.'$- !'?%3$?48% '8409$9&.$9

'.00- 3.00- '0$.8- $8%.&% '3$.*$- !'?%3$?48% '89$$&9*.%* 9'-

'.00- 3.00- $8%.&% '3$.*$- !'?%*%?$$3 '89$$&9*.%*

'.00- 3.00- $8%.&% '3$.*$- !'?%*%?$$3 '89$$&9*.%*

'.00- 3.00- $8%.&% '3$.*$- !'?%*%?$$3 '89$$&9*.%*

'.00- 3.00- '03.0- $94.$$ '3&.*0- !'?%*%?$$3 $'933$99.3* 0-

'.00- 3.00- $94.$$ '3&.*0- !'?&$$?4*9 $'933$99.3*

'.00- 3.00- $94.$$ '3&.*0- !'?&$$?4*9 $'933$99.3*

'.00- 3.00- $94.$$ '3&.*0- !'?&$$?4*9 $'933$99.3*

'.00- 3.00- '0'.&- $98.8$ '38.84- !'?&$$?4*9 $$$*&400.** $0$-

'.00- 3.00- $98.8$ '38.84- !'?&4*?8&0 $$$*&400.**

'.00- 3.00- $98.8$ '38.84- !'?&4*?8&0 $$$*&400.**'.00- 3.00- $98.8$ '38.84- !'?&4*?8&0 $$$*&400.**

'.00- 3.00- '03.0- 30*.*9 '43.0'- !'?&4*?8&0 $40$8*88.83 %'-

'.00- 3.00- 30*.*9 '43.0'- !'?&9*?$9& $40$8*88.83

'.00- 3.00- 30*.*9 '43.0'- !'?&9*?$9& $40$8*88.83

'.00- 3.00- 30*.*9 '43.0'- !'?&9*?$9& $40$8*88.83

'.00- 3.00- '03.0- 3'*.0$ '4*.30- !'?&9*?$9& 30'&'$&'.39 !*0-

'.00- 3.00- 3'*.0$ '4*.30- !'?*48?$'4 30'&'$&'.39

'.00- 3.00- 3'*.0$ '4*.30- !'?*48?$'4 30'&'$&'.39

'.00- 3.00- 3'*.0$ '4*.30- !'?*48?$'4 30'&'$&'.39

'.00- 3.00- '0$.4- 3$4.%3 '%0.*9- !'?*48?$'4 308*%438.%3 '3$-

'.00- 3.00- 3$4.%3 '%0.*9- !'?*89?&'0 308*%438.%3

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