ch 11.67 bdt with a smile

7/25/2019 Ch 11.67 BDT With a Smile

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Worksheet Title

11.64 This worksheet demonstrates the basic principles of incorporating a smile11.65 Market data

11.66 Floorlet with no smile

11.67 Floorlet with smile


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within a numerical tree


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11.64: This worksheet demonstrates the basic principles of incorporating a s

Some artificial data Step length 0.25

Volatilities

ATM

-3% -2% -1% 0% 1% 2%

1 18.0%

2 18.5% 1.0% 18.0%

3 1.5% 1.0% 1!.0% 1!.5% 1.0%

" 1!.5% 1!.0% 15.5% 15.0% 15.5% 1!.0%

0 1 2 3 " 5

3 2.10%

2 1.33% 1."0%

1 0.!2% 0.!% 0.0%

ATM 0 0.0% 0.0% 0.0% 0.0%

-1 -0.!2% -0.!% -0.0%

-2 -1.33% -1."0%

-3 -2.10%

1 18.00% 1.!2% 1!.!% 1!.05%

2 18.00% 1.00% 1!.00% 15.35%

3 1.#3% 1!.00% 15.00%

" 1.1% 15.35%

5 1!.05%

!

0 1 2 3 "

$orards 5% !% % 8% #%

ATM Vol 18% 1% 1!% 15%

0.#8!5" 0.#3058 0.#5!323 0.#351 0.#1!#"0

&rice of disco'nt (ond 0.#3058 0.#5!323 0.#351 0.#1!#"0

)rror 0.000000 0.000000 0.000000 0.000000

Appro* Step length 0.!2% 0.!% 0.0%Act'al rate 5.#!5% !.#531% .#30!% 8.#011%


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0 1 2 3 "

0.00 0.25 0.50 0.5 1.00

1 5% !.53#3% 8.2#2#% 10.1831% 12.20!%

2 5."!21% !.#531% 8.5#12% 10.3#%

3 5.811% .320#% 8.#011%

" !.1303% .!3"5%

5 !."5!#%

!

8


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ile within a numerical tree

+ears

3% -3% -2% -1% 0% 1% 2%

0.00%

-150.00% 100.00%

-50.00% -100.00% 50.00% 50.00%

1!.5% -50.00% -50.00% -50.00% 50.00% 50.00% 50.00%

!

0 -1 -2 -3 -" -5

0 0 0 -1 -2 -3

1 0 0 0 -1

2 1 0 0

3 2 1

" 3

5


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0 1 2 3 " 0 1

0.#8!5" 0.#83#15 0.##!8# 0.#51" 0.#023 1.0000 0."#38

0.#8!52# 0.#82#1" 0.#8#" 0.#"11 0."#38

0.#85!# 0.#8202 0.#8232

0.#8"#0! 0.#8121

0.#8"11"


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&ricing a caplet

Time " periods

3% Time 1 +ears

$orard #.00%

Stri,e 10%

istance from ATM 1.00%

Smile ol 15.50%

d1 -0.!022"5

d2 -0.52"5

&rice of /aplet ".#518 (ps

ifference 0.3!#3 (ps

5.3""" #.2# 1.5!21 31.3""5

1.0#28 2.215" ".50#

0.0000 0.0000

0.0000


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2 3 " 5

0.2"2# 0.11#0 0.0580 0.0281

0."8!5 0.3581 0.2333 0.1"1#

0.2"3! 0.35#2 0.351! 0.285

0.1200 0.2355 0.285

0.05#1 0.1""!

0.02#1


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55.05"

#.20#5

0.0000

0.0000

0.0000


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Market data (from ICAP screen) - par cap vols

Tenor 0.25+ears ass'med constant thro'gho'

T ATM strike ATM Vol .5 .!51 3.!"% 10.""% 33."0% 32.10%

1.5 3.1% 12.2% 30.!0% 28.30%

2 3.5% 13.53% 30."0% 2.0%

3 3.8% 1".8% 2.#0% 25."0%

" 3.#1% 15.2% 2!.0% 2".30%

5 3.#"% 15."8% 25.0% 23."0%

! 3.#8% 15.52% 2".80% 22.80%

".02% 15."8% 2"."0% 22.50%8 ".05% 15.38% 23.0% 22.00%

# ".0#% 15.2"% 23.30% 21.0%

10 ".13% 15.11% 23.00% 21.50%

12 ".1#% 1".!% 22.30% 20.#0%

15 ".2% 1".25% 21.50% 20.20%

20 ".3"% 13.!3% 20.!0% 1#.30%

25 ".3% 13.13% 1#.80% 18.!0%

30 ".3% 12.#% 1#.30% 18.10%

Interpolated par vols

1 2 3 " 50.25 10.""% 33."0% 32.10%

0.50 10.""% 33."0% 32.10%

0.5 10.""% 33."0% 32.10%

1.00 10.""% 33."0% 32.10%

1.25 11.58% 32.00% 30.20%

1.50 12.2% 30.!0% 28.30%

1.5 13.13% 30.50% 28.00%

2.00 13.53% 30."0% 2.0%

2.25 13.8"% 2#.8% 2.13%2.50 1".1!% 2#.15% 2!.55%

2.5 1"."% 28.53% 25.#8%

3.00 1".8% 2.#0% 25."0%

3.25 1".#0% 2.!0% 25.13%

3.50 15.03% 2.30% 2".85%

3.5 15.15% 2.00% 2".58%

".00 15.2% 2!.0% 2".30%

".25 15.32% 2!."5% 2".08%

".50 15.38% 2!.20% 23.85%

".5 15."3% 25.#5% 23.!3%


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5.00 15."8% 25.0% 23."0%

5.25 15."#% 25."8% 23.25%

5.50 15.50% 25.25% 23.10%

5.5 15.51% 25.03% 22.#5%

!.00 15.52% 2".80% 22.80%!.25 15.51% 2".0% 22.3%

!.50 15.50% 2".!0% 22.!5%

!.5 15."#% 2".50% 22.58%

.00 15."8% 2"."0% 22.50%

.25 15."!% 2".23% 22.38%

.50 15."3% 2".05% 22.25%

.5 15."1% 23.88% 22.13%

8.00 15.38% 23.0% 22.00%

8.25 15.35% 23.!0% 21.#3%

8.50 15.31% 23.50% 21.85%8.5 15.28% 23."0% 21.8%

#.00 15.2"% 23.30% 21.0%

#.25 15.21% 23.23% 21.!5%

#.50 15.18% 23.15% 21.!0%

#.5 15.1"% 23.08% 21.55%

10.00 15.11% 23.00% 21.50%

10.25 15.0% 22.#1% 21."3%

10.50 15.02% 22.83% 21.35%

10.5 1".#8% 22."% 21.28%11.00 1".#"% 22.!5% 21.20%

11.25 1".8#% 22.5!% 21.13%

11.50 1".85% 22."8% 21.05%

11.5 1".80% 22.3#% 20.#8%

12.00 1".!% 22.30% 20.#0%

12.25 1".2% 22.23% 20.8"%

12.50 1".!8% 22.1% 20.8%

12.5 1".!3% 22.10% 20.3%

13.00 1".5#% 22.03% 20.!%

13.25 1".55% 21.#% 20.!1%

13.50 1".51% 21.#0% 20.55%

13.5 1"."!% 21.83% 20."#%

1".00 1"."2% 21.% 20."3%

1".25 1".38% 21.0% 20.38%

1".50 1".3"% 21.!3% 20.32%

1".5 1".2#% 21.5% 20.2!%

15.00 1".25% 21.50% 20.20%

15.25 1".22% 21."!% 20.1!%

15.50 1".1#% 21."1% 20.11%15.5 1".1!% 21.3% 20.0%


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1!.00 1".13% 21.32% 20.02%

1!.25 1".10% 21.28% 1#.#8%

1!.50 1".0!% 21.23% 1#.#3%

1!.5 1".03% 21.1#% 1#.8#%

1.00 1".00% 21.1"% 1#.8"%1.25 13.#% 21.10% 1#.80%

1.50 13.#"% 21.05% 1#.5%

1.5 13.#1% 21.01% 1#.1%

18.00 13.88% 20.#!% 1#.!!%

18.25 13.85% 20.#2% 1#.!2%

18.50 13.82% 20.8% 1#.5%

18.5 13.#% 20.83% 1#.53%

1#.00 13.5% 20.8% 1#."8%

1#.25 13.2% 20."% 1#.""%

1#.50 13.!#% 20.!#% 1#.3#%1#.5 13.!!% 20.!5% 1#.35%

20.00 13.!3% 20.!0% 1#.30%

20.25 13.!1% 20.5!% 1#.2%

20.50 13.58% 20.52% 1#.23%

20.5 13.5!% 20."8% 1#.20%

21.00 13.53% 20.""% 1#.1!%

21.25 13.51% 20."0% 1#.13%

21.50 13."8% 20.3!% 1#.0#%

21.5 13."!% 20.32% 1#.0!%22.00 13."3% 20.28% 1#.02%

22.25 13."1% 20.2"% 18.##%

22.50 13.38% 20.20% 18.#5%

22.5 13.3!% 20.1!% 18.#2%

23.00 13.33% 20.12% 18.88%

23.25 13.31% 20.08% 18.85%

23.50 13.28% 20.0"% 18.81%

23.5 13.2!% 20.00% 18.8%

2".00 13.23% 1#.#!% 18."%

2".25 13.21% 1#.#2% 18.1%

2".50 13.18% 1#.88% 18.!%

2".5 13.1!% 1#.8"% 18.!"%

25.00 13.13% 1#.80% 18.!0%

25.25 13.11% 1#.8% 18.58%

25.50 13.10% 1#.5% 18.55%

25.5 13.08% 1#.3% 18.53%

2!.00 13.0!% 1#.0% 18.50%

2!.25 13.05% 1#.!8% 18."8%

2!.50 13.03% 1#.!5% 18."5%2!.5 13.01% 1#.!3% 18."3%


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2.00 12.##% 1#.!0% 18."0%

2.25 12.#8% 1#.58% 18.38%

2.50 12.#!% 1#.55% 18.35%

2.5 12.#"% 1#.53% 18.33%

28.00 12.#3% 1#.50% 18.30%28.25 12.#1% 1#."8% 18.28%

28.50 12.8#% 1#."5% 18.25%

28.5 12.88% 1#."3% 18.23%

2#.00 12.8!% 1#."0% 18.20%

2#.25 12.8"% 1#.38% 18.18%

2#.50 12.82% 1#.35% 18.15%

2#.5 12.81% 1#.33% 18.13%

30.00 12.#% 1#.30% 18.10%


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"ote# t$is s$eet onl% &ses linear interpolation - t$ere are' of co&rse' etter approac

t

2 2.25 2.5 .5 * 5 +30.20% 2.0% 2".80% 1!.20% 10.80% 10.0% 13."0% 1!."0%

2!.20% 2".10% 21.30% 15.#0% 12.80% 13.30% 15.80% 1.!0%

2".00% 21.#0% 20.80% 15.#0% 13.!0% 1".00% 1!.00% 1.!0%

22.30% 1#.30% 18.30% 1!.50% 15.00% 1".#0% 1!.20% 1.20%

21.30% 1#.50% 18.50% 1!.80% 15.50% 15.30% 1!.20% 1.10%

21.00% 1#.!0% 18.!0% 1.00% 15.80% 15.50% 1!.10% 1!.80%

20.80% 1#.50% 18.50% 1.00% 15.80% 15.50% 15.#0% 1!.50%

20.50% 1#.30% 18."0% 1!.#0% 15.80% 15.50% 15.0% 1!.20%20.30% 1#.20% 18.30% 1!.80% 15.80% 15."0% 15.50% 15.#0%

20.10% 1#.00% 18.10% 1!.0% 15.0% 15.30% 15.30% 15.!0%

20.00% 18.#0% 18.00% 1!.!0% 15.!0% 15.10% 15.00% 15.30%

1#.!0% 18.50% 1.0% 1!.30% 15.30% 1".80% 1".!0% 1".0%

1#.00% 18.00% 1.20% 15.#0% 15.00% 1"."0% 1".00% 1".00%

18.20% 1.30% 1!.!0% 15.30% 1"."0% 13.#0% 13.30% 13.20%

1.!0% 1!.0% 1!.00% 1".80% 1".00% 13."0% 12.80% 12.0%

1.10% 1!.30% 15.50% 1"."0% 13.!0% 13.10% 12.50% 12.50%

! 8 # 10 11 12 1330.20% 2.0% 2".80% 1!.20% 10.80% 10.0% 13."0% 1!."0%

30.20% 2.0% 2".80% 1!.20% 10.80% 10.0% 13."0% 1!."0%

30.20% 2.0% 2".80% 1!.20% 10.80% 10.0% 13."0% 1!."0%

30.20% 2.0% 2".80% 1!.20% 10.80% 10.0% 13."0% 1!."0%

28.20% 25.#0% 23.05% 1!.05% 11.80% 12.00% 1".!0% 1.00%

2!.20% 2".10% 21.30% 15.#0% 12.80% 13.30% 15.80% 1.!0%

25.10% 23.00% 21.05% 15.#0% 13.20% 13.!5% 15.#0% 1.!0%

2".00% 21.#0% 20.80% 15.#0% 13.!0% 1".00% 1!.00% 1.!0%

23.58% 21.25% 20.18% 1!.05% 13.#5% 1".23% 1!.05% 1.50%23.15% 20.!0% 1#.55% 1!.20% 1".30% 1"."5% 1!.10% 1."0%

22.3% 1#.#5% 18.#3% 1!.35% 1".!5% 1".!8% 1!.15% 1.30%

22.30% 1#.30% 18.30% 1!.50% 15.00% 1".#0% 1!.20% 1.20%

22.05% 1#.35% 18.35% 1!.58% 15.13% 15.00% 1!.20% 1.18%

21.80% 1#."0% 18."0% 1!.!5% 15.25% 15.10% 1!.20% 1.15%

21.55% 1#."5% 18."5% 1!.3% 15.38% 15.20% 1!.20% 1.13%

21.30% 1#.50% 18.50% 1!.80% 15.50% 15.30% 1!.20% 1.10%

21.23% 1#.53% 18.53% 1!.85% 15.58% 15.35% 1!.18% 1.03%

21.15% 1#.55% 18.55% 1!.#0% 15.!5% 15."0% 1!.15% 1!.#5%

21.08% 1#.58% 18.58% 1!.#5% 15.3% 15."5% 1!.13% 1!.88%


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21.00% 1#.!0% 18.!0% 1.00% 15.80% 15.50% 1!.10% 1!.80%

20.#5% 1#.58% 18.58% 1.00% 15.80% 15.50% 1!.05% 1!.3%

20.#0% 1#.55% 18.55% 1.00% 15.80% 15.50% 1!.00% 1!.!5%

20.85% 1#.53% 18.53% 1.00% 15.80% 15.50% 15.#5% 1!.58%

20.80% 1#.50% 18.50% 1.00% 15.80% 15.50% 15.#0% 1!.50%20.3% 1#."5% 18."8% 1!.#8% 15.80% 15.50% 15.85% 1!."3%

20.!5% 1#."0% 18."5% 1!.#5% 15.80% 15.50% 15.80% 1!.35%

20.58% 1#.35% 18."3% 1!.#3% 15.80% 15.50% 15.5% 1!.28%

20.50% 1#.30% 18."0% 1!.#0% 15.80% 15.50% 15.0% 1!.20%

20."5% 1#.28% 18.38% 1!.88% 15.80% 15."8% 15.!5% 1!.13%

20."0% 1#.25% 18.35% 1!.85% 15.80% 15."5% 15.!0% 1!.05%

20.35% 1#.23% 18.33% 1!.83% 15.80% 15."3% 15.55% 15.#8%

20.30% 1#.20% 18.30% 1!.80% 15.80% 15."0% 15.50% 15.#0%

20.25% 1#.15% 18.25% 1!.8% 15.8% 15.38% 15."5% 15.83%

20.20% 1#.10% 18.20% 1!.5% 15.5% 15.35% 15."0% 15.5%20.15% 1#.05% 18.15% 1!.3% 15.3% 15.33% 15.35% 15.!8%

20.10% 1#.00% 18.10% 1!.0% 15.0% 15.30% 15.30% 15.!0%

20.08% 18.#8% 18.08% 1!.!8% 15.!8% 15.25% 15.23% 15.53%

20.05% 18.#5% 18.05% 1!.!5% 15.!5% 15.20% 15.15% 15."5%

20.03% 18.#3% 18.03% 1!.!3% 15.!3% 15.15% 15.08% 15.38%

20.00% 18.#0% 18.00% 1!.!0% 15.!0% 15.10% 15.00% 15.30%

1#.#5% 18.85% 1.#!% 1!.5!% 15.5!% 15.0!% 1".#5% 15.23%

1#.#0% 18.80% 1.#3% 1!.53% 15.53% 15.03% 1".#0% 15.15%

1#.85% 18.5% 1.8#% 1!."#% 15."#% 1".##% 1".85% 15.08%1#.80% 18.0% 1.85% 1!."5% 15."5% 1".#5% 1".80% 15.00%

1#.5% 18.!5% 1.81% 1!."1% 15."1% 1".#1% 1".5% 1".#3%

1#.0% 18.!0% 1.8% 1!.38% 15.38% 1".88% 1".0% 1".85%

1#.!5% 18.55% 1."% 1!.3"% 15.3"% 1".8"% 1".!5% 1".8%

1#.!0% 18.50% 1.0% 1!.30% 15.30% 1".80% 1".!0% 1".0%

1#.55% 18."!% 1.!!% 1!.2% 15.28% 1".% 1".55% 1".!"%

1#.50% 18."2% 1.!2% 1!.23% 15.25% 1".3% 1".50% 1".58%

1#."5% 18.38% 1.58% 1!.20% 15.23% 1".0% 1"."5% 1".53%

1#."0% 18.33% 1.53% 1!.1% 15.20% 1".!% 1"."0% 1"."%

1#.35% 18.2#% 1."#% 1!.13% 15.18% 1".!3% 1".35% 1"."1%

1#.30% 18.25% 1."5% 1!.10% 15.15% 1".!0% 1".30% 1".35%

1#.25% 18.21% 1."1% 1!.0% 15.13% 1".5% 1".25% 1".2#%

1#.20% 18.1% 1.3% 1!.03% 15.10% 1".53% 1".20% 1".23%

1#.15% 18.13% 1.33% 1!.00% 15.08% 1".50% 1".15% 1".18%

1#.10% 18.08% 1.28% 15.#% 15.05% 1"."% 1".10% 1".12%

1#.05% 18.0"% 1.2"% 15.#3% 15.03% 1"."3% 1".05% 1".0!%

1#.00% 18.00% 1.20% 15.#0% 15.00% 1"."0% 1".00% 1".00%

18.#!% 1.#% 1.1% 15.8% 1".#% 1".38% 13.#% 13.#!%

18.#2% 1.#3% 1.1"% 15.8"% 1".#"% 1".35% 13.#3% 13.#2%18.88% 1.#0% 1.11% 15.81% 1".#1% 1".33% 13.#0% 13.88%


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18.8"% 1.8!% 1.08% 15.8% 1".88% 1".30% 13.8!% 13.8"%

18.80% 1.83% 1.05% 15.5% 1".85% 1".28% 13.83% 13.80%

18.!% 1.#% 1.02% 15.2% 1".82% 1".25% 13.#% 13.!%

18.2% 1.!% 1!.##% 15.!#% 1".#% 1".23% 13.!% 13.2%

18.!8% 1.2% 1!.#!% 15.!!% 1".!% 1".20% 13.2% 13.!8%18.!"% 1.!#% 1!.#3% 15.!3% 1".3% 1".18% 13.!#% 13.!"%

18.!0% 1.!5% 1!.#0% 15.!0% 1".0% 1".15% 13.!5% 13.!0%

18.5!% 1.!2% 1!.8% 15.5% 1".!% 1".13% 13.!2% 13.5!%

18.52% 1.58% 1!.8"% 15.5"% 1".!"% 1".10% 13.58% 13.52%

18."8% 1.55% 1!.81% 15.51% 1".!1% 1".08% 13.55% 13."8%

18.""% 1.51% 1!.8% 15."8% 1".58% 1".05% 13.51% 13.""%

18."0% 1."8% 1!.5% 15."5% 1".55% 1".03% 13."8% 13."0%

18.3!% 1.""% 1!.2% 15."2% 1".52% 1".00% 13.""% 13.3!%

18.32% 1."1% 1!.!#% 15.3#% 1"."#% 13.#8% 13."1% 13.32%

18.28% 1.3% 1!.!!% 15.3!% 1"."!% 13.#5% 13.3% 13.28%18.2"% 1.3"% 1!.!3% 15.33% 1"."3% 13.#3% 13.3"% 13.2"%

18.20% 1.30% 1!.!0% 15.30% 1"."0% 13.#0% 13.30% 13.20%

18.1% 1.2% 1!.5% 15.28% 1".38% 13.88% 13.28% 13.18%

18.1"% 1.2"% 1!.5"% 15.25% 1".3!% 13.85% 13.25% 13.15%

18.11% 1.21% 1!.51% 15.23% 1".3"% 13.83% 13.23% 13.13%

18.08% 1.18% 1!."8% 15.20% 1".32% 13.80% 13.20% 13.10%

18.05% 1.15% 1!."5% 15.18% 1".30% 13.8% 13.18% 13.08%

18.02% 1.12% 1!."2% 15.15% 1".28% 13.5% 13.15% 13.05%

1.##% 1.0#% 1!.3#% 15.13% 1".2!% 13.3% 13.13% 13.03%1.#!% 1.0!% 1!.3!% 15.10% 1".2"% 13.0% 13.10% 13.00%

1.#3% 1.03% 1!.33% 15.08% 1".22% 13.!8% 13.08% 12.#8%

1.#0% 1.00% 1!.30% 15.05% 1".20% 13.!5% 13.05% 12.#5%

1.8% 1!.#% 1!.2% 15.03% 1".18% 13.!3% 13.03% 12.#3%

1.8"% 1!.#"% 1!.2"% 15.00% 1".1!% 13.!0% 13.00% 12.#0%

1.81% 1!.#1% 1!.21% 1".#8% 1".1"% 13.58% 12.#8% 12.88%

1.8% 1!.88% 1!.18% 1".#5% 1".12% 13.55% 12.#5% 12.85%

1.5% 1!.85% 1!.15% 1".#3% 1".10% 13.53% 12.#3% 12.83%

1.2% 1!.82% 1!.12% 1".#0% 1".08% 13.50% 12.#0% 12.80%

1.!#% 1!.#% 1!.0#% 1".88% 1".0!% 13."8% 12.88% 12.8%

1.!!% 1!.!% 1!.0!% 1".85% 1".0"% 13."5% 12.85% 12.5%

1.!3% 1!.3% 1!.03% 1".83% 1".02% 13."3% 12.83% 12.3%

1.!0% 1!.0% 1!.00% 1".80% 1".00% 13."0% 12.80% 12.0%

1.58% 1!.!8% 15.#8% 1".8% 13.#8% 13.3#% 12.#% 12.!#%

1.55% 1!.!!% 15.#5% 1".!% 13.#!% 13.3% 12.% 12.!8%

1.53% 1!.!"% 15.#3% 1"."% 13.#"% 13.3!% 12.!% 12.!%

1.50% 1!.!2% 15.#0% 1".2% 13.#2% 13.3"% 12."% 12.!!%

1."8% 1!.!0% 15.88% 1".0% 13.#0% 13.33% 12.3% 12.!5%

1."5% 1!.58% 15.85% 1".!8% 13.88% 13.31% 12.1% 12.!"%1."3% 1!.5!% 15.83% 1".!!% 13.8!% 13.30% 12.0% 12.!3%


18/593

1."0% 1!.5"% 15.80% 1".!"% 13.8"% 13.28% 12.!8% 12.!2%

1.38% 1!.52% 15.8% 1".!2% 13.82% 13.2% 12.!% 12.!1%

1.35% 1!.50% 15.5% 1".!0% 13.80% 13.25% 12.!5% 12.!0%

1.33% 1!."8% 15.3% 1".58% 13.8% 13.2"% 12.!"% 12.5#%

1.30% 1!."!% 15.0% 1".5!% 13.!% 13.22% 12.!2% 12.58%1.28% 1!.""% 15.!8% 1".5"% 13."% 13.21% 12.!1% 12.5%

1.25% 1!."2% 15.!5% 1".52% 13.2% 13.1#% 12.5#% 12.5!%

1.23% 1!."0% 15.!3% 1".50% 13.0% 13.18% 12.58% 12.55%

1.20% 1!.38% 15.!0% 1"."8% 13.!8% 13.1!% 12.5!% 12.5"%

1.18% 1!.3!% 15.58% 1"."!% 13.!!% 13.15% 12.55% 12.53%

1.15% 1!.3"% 15.55% 1".""% 13.!"% 13.13% 12.53% 12.52%

1.13% 1!.32% 15.53% 1"."2% 13.!2% 13.12% 12.52% 12.51%

1.10% 1!.30% 15.50% 1"."0% 13.!0% 13.10% 12.50% 12.50%


19/593

$es

,radient for interpolation

! 0 ATM Vol 1.5 1.51#.20% 21.!0% 2".00% 1 0.0"5! -0.05! -0.0!

1#.00% 20.20% 22.10% 1.5 0.01!2 -0.00" -0.012

1#.00% 20.10% 22.10% 2 0.0125 -0.025 -0.023

18.20% 1#.10% 20.!0% 3 0.00"# -0.012 -0.011

1.#0% 18.0% 20.00% " 0.0021 -0.01 -0.00#

1.!0% 18.30% 1#.50% 5 0.000" -0.00# -0.00!

1.20% 1.80% 1#.00% ! -0.000" -0.00" -0.003

1!.80% 1."0% 18.50% -0.001 -0.00 -0.0051!."0% 1.00% 18.00% 8 -0.001" -0.00" -0.003

1!.10% 1!.!0% 1.!0% # -0.0013 -0.003 -0.002

15.80% 1!.30% 1.20% 10 -0.0015 -0.0035 -0.003

15.00% 15."0% 1!.30% 12 -0.001 -0.002!! -0.002333

1".30% 1".!0% 15.30% 15 -0.0012" -0.0018 -0.0018

13."0% 13.0% 1"."0% 20 -0.001 -0.001! -0.001"

12.#0% 13.20% 13.#0% 25 -0.000!8 -0.001 -0.001

12.0% 13.00% 13.0% 30

(Approimatel%) Implied for/ard v

1" 15 1! ATM Vol .50 .!51#.20% 21.!0% 2".00% 0.25 10.""% 33."0% 32.10%

1#.20% 21.!0% 2".00% 0.50 10.""% 33."0% 32.10%

1#.20% 21.!0% 2".00% 0.5 10.""% 33."0% 32.10%

1#.20% 21.!0% 2".00% 1.00 10.""% 33."0% 32.10%

1#.10% 20.#0% 23.05% 1.25 15.31% 25.!5% 20.#"%

1#.00% 20.20% 22.10% 1.50 1.33% 22.32% 15.!!%

1#.00% 20.15% 22.10% 1.5 15.33% 2#.8#% 2!.13%

1#.00% 20.10% 22.10% 2.00 1!.08% 2#.!#% 25.50%

18.80% 1#.85% 21.3% 2.25 1!.13% 2".20% 21.##%18.!0% 1#.!0% 21.35% 2.50 1!.1% 22.% 20.!%

18."0% 1#.35% 20.#8% 2.5 1.28% 21.2#% 1#.30%

18.20% 1#.10% 20.!0% 3.00 1.8!% 1#.!% 1.8#%

18.13% 1#.00% 20."5% 3.25 1!.30% 23.1% 21.55%

18.05% 18.#0% 20.30% 3.50 1!.5"% 23.05% 20.#5%

1.#8% 18.80% 20.15% 3.5 1!.% 22.38% 20.3"%

1.#0% 18.0% 20.00% ".00 1.00% 21.1% 1#.2%

1.83% 18.!0% 1#.88% ".25 1!.1"% 22.0% 20.1"%

1.5% 18.50% 1#.5% ".50 1!.2"% 21.51% 1#.!3%

1.!8% 18."0% 1#.!3% ".5 1!.3"% 20.#5% 1#.13%


20/593

1.!0% 18.30% 1#.50% 5.00 1!."5% 20.38% 18.!2%

1.50% 18.18% 1#.38% 5.25 15.!#% 20."!% 20.02%

1."0% 18.05% 1#.25% 5.50 15.1% 1#.#5% 1#.!#%

1.30% 1.#3% 1#.13% 5.5 15.3% 1#."3% 1#.3!%

1.20% 1.80% 1#.00% !.00 15.5% 18.#0% 1#.03%1.10% 1.0% 18.88% !.25 15.2% 22.1% 20.8"%

1.00% 1.!0% 18.5% !.50 15.25% 21.#5% 20.!#%

1!.#0% 1.50% 18.!3% !.5 15.23% 21."% 20.53%

1!.80% 1."0% 18.50% .00 15.21% 21.53% 20.3%

1!.0% 1.30% 18.38% .25 1"."% 18.!% 18.5"%

1!.!0% 1.20% 18.25% .50 1".!#% 18.2!% 18.2!%

1!.50% 1.10% 18.13% .5 1".!"% 1.8"% 1.#8%

1!."0% 1.00% 18.00% 8.00 1".58% 1."2% 1.!#%

1!.33% 1!.#0% 1.#0% 8.25 1".18% 20.1"% 1#.3%

1!.25% 1!.80% 1.80% 8.50 1".11% 1#.#2% 1#.21%1!.18% 1!.0% 1.0% 8.5 1".03% 1#.0% 1#.05%

1!.10% 1!.!0% 1.!0% #.00 13.#!% 1#."8% 18.8#%

1!.03% 1!.53% 1.50% #.25 13.##% 20.3"% 1#.%

15.#5% 1!."5% 1."0% #.50 13.#2% 20.18% 1#.!!%

15.88% 1!.38% 1.30% #.5 13.85% 20.02% 1#.5!%

15.80% 1!.30% 1.20% 10.00 13.8% 1#.8!% 1#."5%

15.0% 1!.1#% 1.0#% 10.25 13.20% 1#.0#% 18.1%

15.!0% 1!.08% 1!.#8% 10.50 13.10% 18.8#% 18.01%

15.50% 15.#!% 1!.8!% 10.5 13.01% 18.0% 1.8"%15."0% 15.85% 1!.5% 11.00 12.#1% 18.50% 1.!8%

15.30% 15."% 1!.!"% 11.25 12.82% 18.30% 1.51%

15.20% 15.!3% 1!.53% 11.50 12.2% 18.10% 1.3"%

15.10% 15.51% 1!."1% 11.5 12.!3% 1.#1% 1.1%

15.00% 15."0% 1!.30% 12.00 12.53% 1.1% 1.01%

1".#"% 15.33% 1!.22% 12.25 12.51% 18.!% 1.82%

1".88% 15.2% 1!.13% 12.50 12."2% 18.!1% 1.!#%

1".83% 15.20% 1!.05% 12.5 12.32% 18."!% 1.5!%

1".% 15.13% 15.#% 13.00 12.23% 18.31% 1."3%

1".1% 15.0% 15.88% 13.25 12.13% 18.1% 1.31%

1".!5% 15.00% 15.80% 13.50 12.0"% 18.02% 1.18%

1".5#% 1".#3% 15.2% 13.5 11.#5% 1.8% 1.05%

1".53% 1".8% 15.!3% 1".00 11.85% 1.2% 1!.#2%

1"."8% 1".80% 15.55% 1".25 11.5% 1.5% 1!.#%

1"."2% 1".3% 15."% 1".50 11.!!% 1."2% 1!.!!%

1".3!% 1".!% 15.38% 1".5 11.5!% 1.2% 1!.53%

1".30% 1".!0% 15.30% 15.00 11."% 1.11% 1!.3#%

1".2!% 1".5!% 15.2!% 15.25 12.22% 18.5!% 1.2"%

1".21% 1".51% 15.21% 15.50 12.15% 18."!% 1.1"%1".1% 1"."% 15.1% 15.5 12.08% 18.3!% 1.0"%


21/593

1".12% 1"."2% 15.12% 1!.00 12.01% 18.2!% 1!.#5%

1".08% 1".38% 15.08% 1!.25 11.#"% 18.1!% 1!.85%

1".03% 1".33% 15.03% 1!.50 11.88% 18.0% 1!.5%

13.##% 1".2#% 1".##% 1!.5 11.81% 1.#% 1!.!5%

13.#"% 1".2"% 1".#"% 1.00 11."% 1.8% 1!.55%13.#0% 1".20% 1".#0% 1.25 11.!% 1.% 1!."5%

13.85% 1".15% 1".85% 1.50 11.!0% 1.!% 1!.35%

13.81% 1".11% 1".81% 1.5 11.53% 1.5% 1!.25%

13.!% 1".0!% 1".!% 18.00 11."!% 1."% 1!.15%

13.2% 1".02% 1".2% 18.25 11."0% 1.3% 1!.05%

13.!% 13.#% 1".!% 18.50 11.33% 1.2% 15.#5%

13.!3% 13.#3% 1".!3% 18.5 11.2!% 1.1% 15.8"%

13.58% 13.88% 1".58% 1#.00 11.1#% 1.0% 15."%

13.5"% 13.8"% 1".5"% 1#.25 11.12% 1!.#% 15.!"%

13."#% 13.#% 1"."#% 1#.50 11.05% 1!.8% 15.5"%13."5% 13.5% 1"."5% 1#.5 10.#8% 1!.% 15.""%

13."0% 13.0% 1"."0% 20.00 10.#1% 1!.!% 15.33%

13.38% 13.!8% 1".38% 20.25 11."3% 1.0!% 1!.22%

13.35% 13.!5% 1".35% 20.50 11.3% 1!.#% 1!.1"%

13.33% 13.!3% 1".33% 20.5 11.32% 1!.88% 1!.0%

13.30% 13.!0% 1".30% 21.00 11.2!% 1!.#% 15.##%

13.28% 13.58% 1".28% 21.25 11.21% 1!.0% 15.#1%

13.25% 13.55% 1".25% 21.50 11.15% 1!.!1% 15.83%

13.23% 13.53% 1".23% 21.5 11.10% 1!.52% 15.!%13.20% 13.50% 1".20% 22.00 11.0"% 1!."3% 15.!8%

13.18% 13."8% 1".18% 22.25 10.#8% 1!.3"% 15.!0%

13.15% 13."5% 1".15% 22.50 10.#3% 1!.25% 15.52%

13.13% 13."3% 1".13% 22.5 10.8% 1!.1!% 15.""%

13.10% 13."0% 1".10% 23.00 10.82% 1!.0% 15.3!%

13.08% 13.38% 1".08% 23.25 10.!% 15.#8% 15.2#%

13.05% 13.35% 1".05% 23.50 10.0% 15.8#% 15.21%

13.03% 13.33% 1".03% 23.5 10.!5% 15.#% 15.13%

13.00% 13.30% 1".00% 2".00 10.5#% 15.0% 15.05%

12.#8% 13.28% 13.#8% 2".25 10.53% 15.!1% 1".#%

12.#5% 13.25% 13.#5% 2".50 10."8% 15.52% 1".8#%

12.#3% 13.23% 13.#3% 2".5 10."2% 15."2% 1".81%

12.#0% 13.20% 13.#0% 25.00 10.3!% 15.33% 1".3%

12.8#% 13.1#% 13.8#% 25.25 11.28% 1.0#% 15.88%

12.88% 13.18% 13.88% 25.50 11.25% 1.0"% 15.82%

12.8% 13.1% 13.8% 25.5 11.21% 1!.#8% 15.%

12.8!% 13.1!% 13.8!% 2!.00 11.1% 1!.#3% 15.1%

12.85% 13.15% 13.85% 2!.25 11.1"% 1!.8% 15.!!%

12.8"% 13.1"% 13.8"% 2!.50 11.10% 1!.82% 15.!0%12.83% 13.13% 13.83% 2!.5 11.0!% 1!.!% 15.55%


22/593

12.82% 13.12% 13.82% 2.00 11.02% 1!.1% 15."#%

12.81% 13.11% 13.81% 2.25 10.##% 1!.!!% 15.""%

12.80% 13.10% 13.80% 2.50 10.#5% 1!.!0% 15.38%

12.#% 13.0#% 13.#% 2.5 10.#1% 1!.55% 15.33%

12.8% 13.08% 13.8% 28.00 10.88% 1!."#% 15.2%12.% 13.0% 13.% 28.25 10.8"% 1!.""% 15.22%

12.!% 13.0!% 13.!% 28.50 10.80% 1!.38% 15.1!%

12.5% 13.05% 13.5% 28.5 10.!% 1!.33% 15.11%

12."% 13.0"% 13."% 2#.00 10.2% 1!.2% 15.05%

12.3% 13.03% 13.3% 2#.25 10.!#% 1!.22% 1".##%

12.2% 13.02% 13.2% 2#.50 10.!5% 1!.1!% 1".#"%

12.1% 13.01% 13.1% 2#.5 10.!1% 1!.10% 1".88%

12.0% 13.00% 13.0% 30.00 10.5% 1!.05% 1".83%


23/593

2 2.25 2.5 3 3.5 " 5 !

-0.08 -0.02 -0.0 -0.00! 0.0" 0.052 0.0"8 0.02"

-0.0"" -0.0"" -0.01 0 0.01! 0.01" 0.00" 0

-0.01 -0.02! -0.025 0.00! 0.01" 0.00# 0.002 -0.00"

-0.01 0.002 0.002 0.003 0.005 0.00" 0 -0.001

-0.003 0.001 0.001 0.002 0.003 0.002 -0.001 -0.003

-0.002 -0.001 -0.001 0 0 0 -0.002 -0.003

-0.003 -0.002 -0.001 -0.001 0 0 -0.002 -0.003

-0.002 -0.001 -0.001 -0.001 0 -0.001 -0.002 -0.003-0.002 -0.002 -0.002 -0.001 -0.001 -0.001 -0.002 -0.003

-0.001 -0.001 -0.001 -0.001 -0.001 -0.002 -0.003 -0.003

-0.002 -0.002 -0.0015 -0.0015 -0.0015 -0.0015 -0.002 -0.003

-0.002 -0.001!! -0.001!! -0.001333 -0.001 -0.001333 -0.002 -0.002333

-0.001! -0.001" -0.0012 -0.0012 -0.0012 -0.001 -0.001" -0.001!

-0.0012 -0.0012 -0.0012 -0.001 -0.0008 -0.001 -0.001 -0.001

-0.001 -0.0008 -0.001 -0.0008 -0.0008 -0.000! -0.000! -0.000"

ols

2.00 2.25 2.50 .00 .50 *.00 5.00 +.0030.20% 2.0% 2".80% 1!.20% 10.80% 10.0% 13."0% 1!."0%

30.20% 2.0% 2".80% 1!.20% 10.80% 10.0% 13."0% 1!."0%

30.20% 2.0% 2".80% 1!.20% 10.80% 10.0% 13."0% 1!."0%

30.20% 2.0% 2".80% 1!.20% 10.80% 10.0% 13."0% 1!."0%

18.11% 1!.88% 1".01% 15.""% 15.15% 1!.1#% 18.!"% 1#.21%

11.#3% 11.""% 8.10% 15.13% 1!.#"% 18."8% 20.#% 20.3"%

1.0% 1".% 1#."8% 15.#0% 15.38% 15.5#% 1!."#% 1.!0%

1".0% 11.5% 18.#!% 15.#0% 1!.12% 1!.2"% 1!.!8% 1.!0%

1#.85% 15.0% 1".22% 1.20% 1!."8% 15.#1% 1!.""% 1!.!8%18.#0% 13."0% 12.!0% 1."#% 1.13% 1!.3"% 1!.5"% 1!."%

1.#3% 11.5#% 10.85% 1.8% 1.% 1!.!% 1!.!"% 1!.2%

1!.#"% #.58% 8.8#% 18.0% 18."2% 1.18% 1!."% 1!.0!%

18.#% 1#.#"% 18.#"% 1."5% 1!.55% 1!.15% 1!.20% 1!.8%

18.2"% 20.0"% 1#.0"% 1.!0% 1!.#% 1!.3"% 1!.20% 1!.82%

1.!8% 20.1"% 1#.1"% 1."% 1.03% 1!.5"% 1!.20% 1!.%

1.12% 20.2"% 1#.23% 1.8#% 1.2% 1!.3% 1!.20% 1!.2%

1#.##% 1#.#2% 18.#2% 1.!3% 1!.3% 1!.13% 15.% 15.8%

1#.83% 1#.#% 18.#% 1.3% 1!.8% 1!.23% 15.2% 15.!2%

1#.!8% 20.02% 1#.02% 1.83% 1.02% 1!.32% 15.!% 15."!%


24/593

1#.52% 20.0% 1#.0% 1.#2% 1.1!% 1!."2% 15.!2% 15.31%

1#.#2% 1#.0% 18.0% 1.00% 15.80% 15.50% 15.02% 15.15%

1#.82% 1#.02% 18.02% 1.00% 15.80% 15.50% 1".#1% 1".##%

1#.2% 18.#% 1.#% 1.00% 15.80% 15.50% 1".81% 1".83%

1#.!1% 18.#2% 1.#2% 1.00% 15.80% 15.50% 1".0% 1".!%18.8"% 18.21% 1.8!% 1!.3!% 15.80% 15.50% 1".!0% 1".51%

18.!8% 18.11% 1.81% 1!.31% 15.80% 15.50% 1"."#% 1".35%

18.52% 18.00% 1.!% 1!.2!% 15.80% 15.50% 1".3#% 1".1#%

18.3!% 1.#0% 1.1% 1!.21% 15.80% 15.50% 1".28% 1".02%

1#.00% 18.5!% 1.!!% 1!.1!% 15.80% 1".!% 1".18% 13.8!%

18.8#% 18.51% 1.!1% 1!.11% 15.80% 1".1% 1".0% 13.0%

18.#% 18."!% 1.5!% 1!.0!% 15.80% 1".!!% 13.#% 13.53%

18.!8% 18."1% 1.51% 1!.01% 15.80% 1".!0% 13.8!% 13.3%

18.58% 1."% 1!.5% 15.#5% 1".#5% 1".55% 13.5% 13.20%

18."% 1.3% 1!."% 15.#0% 1".#0% 1".50% 13.!5% 13.0"%18.3% 1.2!% 1!.3!% 15.85% 1".85% 1"."5% 13.5"% 12.8%

18.2!% 1.1!% 1!.25% 15.80% 1".80% 1"."0% 13."3% 12.0%

1#.15% 18.05% 1.15% 15.5% 1".5% 13.33% 12.22% 12.53%

1#.10% 18.00% 1.10% 15.0% 1".0% 13.22% 12.05% 12.3!%

1#.05% 1.#5% 1.05% 15.!5% 1".!"% 13.11% 11.88% 12.1#%

1#.00% 1.#0% 1.00% 15.5#% 1".5#% 13.00% 11.1% 12.02%

1.8"% 1!.3% 1!.3#% 1".##% 13.#8% 13."8% 12.#% 11.8"%

1.3% 1!.!2% 1!.31% 1".#1% 13.#0% 13."0% 12.!8% 11.!%

1.!2% 1!.51% 1!.23% 1".83% 13.82% 13.32% 12.5% 11."#%1.52% 1!."1% 1!.1!% 1".5% 13."% 13.2"% 12."!% 11.31%

1."1% 1!.30% 1!.08% 1".!% 13.!!% 13.1!% 12.35% 11.1"%

1.30% 1!.1#% 1!.00% 1".5#% 13.58% 13.08% 12.2"% 10.#!%

1.1#% 1!.08% 15.#2% 1".51% 13.50% 13.00% 12.13% 10.%

1.0#% 15.#% 15.8"% 1"."3% 13."2% 12.#2% 12.02% 10.5#%

1!.#8% 1!.33% 15.53% 1".58% 1".02% 13.0% 11.#1% 11.50%

1!.8% 1!.2"% 15.""% 1".51% 13.#% 13.00% 11.#% 11.3!%

1!.!% 1!.1!% 15.35% 1".""% 13.#2% 12.#2% 11.!8% 11.23%

1!.!5% 1!.0% 15.2!% 1".3!% 13.8% 12.85% 11.5% 11.0#%

1!.5"% 15.#8% 15.1% 1".2#% 13.81% 12.8% 11."5% 10.#!%

1!."3% 15.8#% 15.08% 1".22% 13.!% 12.1% 11.3"% 10.82%

1!.32% 15.80% 1".##% 1".15% 13.1% 12.!"% 11.22% 10.!8%

1!.21% 15.1% 1".#0% 1".08% 13.!5% 12.5!% 11.11% 10.5"%

1!.10% 15.!2% 1".81% 1".01% 13.!0% 12."#% 10.##% 10."0%

15.##% 15.52% 1".1% 13.#"% 13.55% 12."2% 10.88% 10.2!%

15.88% 15."3% 1".!2% 13.8!% 13.50% 12.35% 10.!% 10.11%

15.% 15.3"% 1".53% 13.#% 13.""% 12.2% 10.!"% #.#%

1!.38% 15.2% 15.2!% 13.#5% 13.0"% 12.#% 11.!% 11.30%

1!.30% 15.!5% 15.20% 13.8#% 12.#8% 12.3% 11.!0% 11.21%1!.21% 15.5% 15.13% 13.82% 12.#1% 12.!8% 11.52% 11.12%


25/593

1!.12% 15.50% 15.0% 13.!% 12.85% 12.!3% 11.""% 11.03%

1!.03% 15."2% 15.01% 13.!#% 12.8% 12.5% 11.3!% 10.#"%

15.#5% 15.3"% 1".#"% 13.!3% 12.2% 12.52% 11.28% 10.85%

15.8!% 15.2% 1".88% 13.5!% 12.!5% 12."!% 11.21% 10.!%

15.% 15.1#% 1".81% 13.50% 12.5#% 12."1% 11.13% 10.!!%15.!8% 15.12% 1".5% 13."3% 12.52% 12.3!% 11.05% 10.5%

15.5#% 15.0"% 1".!8% 13.3% 12."!% 12.30% 10.#% 10."8%

15.51% 1".#!% 1".!2% 13.30% 12.3#% 12.25% 10.8#% 10.38%

15."2% 1".8#% 1".55% 13.2"% 12.32% 12.1#% 10.81% 10.2#%

15.33% 1".81% 1"."#% 13.1% 12.2!% 12.1"% 10.3% 10.20%

15.2"% 1".3% 1"."2% 13.11% 12.1#% 12.0#% 10.!5% 10.10%

15.15% 1".!5% 1".3!% 13.0"% 12.13% 12.03% 10.5% 10.01%

15.0!% 1".58% 1".2#% 12.#% 12.0!% 11.#8% 10."#% #.#1%

1".#% 1".50% 1".23% 12.#1% 11.##% 11.#2% 10."1% #.81%

1".88% 1"."2% 1".1!% 12.8"% 11.#3% 11.8% 10.32% #.2%1".#% 1".3"% 1".0#% 12.% 11.8!% 11.81% 10.2"% #.!2%

1".0% 1".2% 1".03% 12.1% 11.#% 11.!% 10.1!% #.52%

15.58% 1".!% 13.#!% 13.12% 12.!8% 11.0% 11.0#% 10.##%

15.52% 1".!1% 13.#0% 13.0% 12.!"% 11.!5% 11.0"% 10.#"%

15."5% 1".5"% 13.83% 13.01% 12.5#% 11.5#% 10.#8% 10.88%

15.3#% 1"."% 13.!% 12.#!% 12.55% 11.5"% 10.#3% 10.83%

15.32% 1"."1% 13.0% 12.#0% 12.51% 11."8% 10.8% 10.%

15.2!% 1".3"% 13.!3% 12.85% 12."!% 11."3% 10.82% 10.1%

15.1#% 1".28% 13.5!% 12.#% 12."2% 11.3% 10.!% 10.!!%15.12% 1".21% 13.50% 12."% 12.38% 11.32% 10.0% 10.!0%

15.0!% 1".1"% 13."3% 12.!8% 12.33% 11.2!% 10.!5% 10.55%

1".##% 1".08% 13.3!% 12.!3% 12.2#% 11.20% 10.5#% 10."#%

1".#3% 1".01% 13.30% 12.5% 12.25% 11.15% 10.53% 10."3%

1".8!% 13.#"% 13.23% 12.52% 12.20% 11.0#% 10."8% 10.38%

1".#% 13.88% 13.1!% 12."!% 12.1!% 11.0"% 10."2% 10.32%

1".3% 13.81% 13.0#% 12."1% 12.12% 10.#8% 10.3!% 10.2!%

1".!!% 13."% 13.03% 12.35% 12.0% 10.#2% 10.31% 10.21%

1".5#% 13.!% 12.#!% 12.30% 12.03% 10.8% 10.25% 10.15%

1".52% 13.!1% 12.8#% 12.2"% 11.##% 10.81% 10.1#% 10.0#%

1"."!% 13.5"% 12.82% 12.18% 11.#"% 10.5% 10.1"% 10.03%

1".3#% 13."% 12.5% 12.13% 11.#0% 10.0% 10.08% #.#8%

1".32% 13."0% 12.!8% 12.0% 11.85% 10.!"% 10.02% #.#2%

1".8!% 1".5"% 13.2"% 12.!2% 11.81% 11.#% 11.18% 11.!5%

1".81% 1".50% 13.18% 12.58% 11.% 11.!% 11.15% 11.!3%

1".5% 1"."!% 13.13% 12.53% 11.2% 11.2% 11.12% 11.!0%

1".0% 1"."1% 13.0% 12."#% 11.!8% 11.!#% 11.0#% 11.58%

1".!"% 1".3% 13.02% 12."5% 11.!3% 11.!!% 11.05% 11.5!%

1".5#% 1".33% 12.#!% 12."0% 11.5#% 11.!3% 11.02% 11.5"%1".53% 1".28% 12.#0% 12.3!% 11.55% 11.!0% 10.##% 11.52%


26/593

1"."8% 1".2"% 12.85% 12.31% 11.50% 11.5!% 10.#!% 11.50%

1"."2% 1".20% 12.#% 12.2% 11."!% 11.53% 10.#2% 11."8%

1".3% 1".15% 12.3% 12.23% 11."1% 11.50% 10.8#% 11."!%

1".31% 1".11% 12.!8% 12.18% 11.3% 11."% 10.8!% 11.""%

1".2!% 1".0!% 12.!2% 12.1"% 11.32% 11."3% 10.83% 11."2%1".20% 1".02% 12.5!% 12.0#% 11.28% 11."0% 10.#% 11.3#%

1".1"% 13.#8% 12.51% 12.05% 11.23% 11.3% 10.!% 11.3%

1".0#% 13.#3% 12."5% 12.00% 11.1#% 11.3"% 10.3% 11.35%

1".03% 13.8#% 12.3#% 11.#!% 11.1"% 11.30% 10.0% 11.33%

13.#% 13.85% 12.3"% 11.#1% 11.10% 11.2% 10.!!% 11.31%

13.#2% 13.80% 12.28% 11.8% 11.05% 11.2"% 10.!3% 11.2#%

13.8!% 13.!% 12.22% 11.82% 11.01% 11.20% 10.!0% 11.2%

13.81% 13.1% 12.1!% 11.8% 10.#!% 11.1% 10.5!% 11.25%


27/593

8 10

-0.00" -0.028 -0.038

0 -0.002 0

-0.008 -0.01 -0.015

-0.003 -0.00" -0.00!

-0.003 -0.00" -0.005

-0.00" -0.005 -0.005

-0.00" -0.00" -0.005

-0.00" -0.00" -0.005-0.003 -0.00" -0.00"

-0.003 -0.003 -0.00"

-0.00" -0.00"5 -0.00"5

-0.002333 -0.002!! -0.003333

-0.0018 -0.0018 -0.0018

-0.001 -0.001 -0.001

-0.000" -0.000" -0.000"

,radient of 1or/ard vols

!.00 .00 0.00 .50 .!5 2.001#.20% 21.!0% 2".00% 0.25 -520% -!0% -1000%

1#.20% 21.!0% 2".00% 0.50 -520% -!0% -1000%

1#.20% 21.!0% 2".00% 0.5 -520% -!0% -1000%

1#.20% 21.!0% 2".00% 1.00 -520% -!0% -1000%

18.!#% 1.83% 18.8% 1.25 -1882% -1132% -"#3%

18."#% 1!.25% 1!.55% 1.50 -2!!5% -1"8#% -1##%

1#.00% 1#.85% 22.10% 1.5 -150!% -3!23% -#21%

1#.00% 1#.5% 22.10% 2.00 -1!!% -"53% -###%

1.12% 1.2% 18."5% 2.25 -88"% -85!% -1#11%1!.!#% 1.1#% 1.!2% 2.50 -83#% -0% -2200%

1!.2% 1!.!"% 1!.% 2.5 -#3% -550% -253"%

15.83% 1!.10% 15.#0% 3.00 -"% -38"% -2#"0%

1.20% 1.!% 18.5!% 3.25 -8!1% -110"% "5#%

1.0"% 1.55% 18.2"% 3.50 -83#% -1083% 1#%

1!.8#% 1.3"% 1.#2% 3.5 -81% -10!2% #82%

1!.3% 1.13% 1.!0% ".00 -#5% -10"1% 12"%

1!.58% 1!.#2% 1.!% ".25 -3% -!0% -2!%

1!."2% 1!.1% 1."#% ".50 -50% #% 55%

1!.2% 1!.50% 1.22% ".5 -2% 21#% 13%


28/593

1!.11% 1!.28% 1!.#5% 5.00 -0"% 3!2% 220%

15.3!% 15."!% 1!.!8% 5.25 -1#% -3% -3"2%

15.15% 15.1#% 1!."1% 5.50 -10"% 53% -321%

1".#3% 1".#1% 1!.13% 5.5 -2% 1""% -301%

1".1% 1".!3% 15.8!% !.00 51% 235% -280%1"."#% 15.10% 15.58% !.25 -528% -803% -251%

1".2% 1".88% 15.30% !.50 -50!% -80"% -22#%

1".05% 1".!!% 15.01% !.5 -"8"% -80"% -20%

13.83% 1".""% 1".3% .00 -"!2% -805% -185%

13.!0% 1".22% 1".""% .25 -5"% 18"% -1"%

13.38% 13.##% 1".15% .50 -1% 25"% -153%

13.15% 13.% 13.8!% .5 52% 325% -132%

12.#2% 13.5"% 13.5% 8.00 10% 3#% -110%

13.1% 13.31% 1".3"% 8.25 -30% -31% -""2%

13.5"% 13.08% 1".11% 8.50 -28"% -2#5% -""2%13.38% 12.8"% 13.88% 8.5 -2!0% -22% -""2%

13.21% 12.!1% 13.!5% #.00 -23!% -250% -""2%

13.0"% 13.55% 13."1% #.25 -230% -2"5% -""1%

12.8% 13.38% 13.18% #.50 -208% -22"% -""1%

12.0% 13.21% 12.#"% #.5 -185% -202% -""1%

12.53% 13.0"% 12.0% 10.00 -1!2% -180% -""1%

10.#8% 10.!% 11.3% 10.25 -3!5% -135% -""3%

10.3% 10."% 11."5% 10.50 -353% -112% -""3%

10."% 10.1% 11.1!% 10.5 -3"1% -88% -""3%10.21% #.8% 10.8!% 11.00 -32#% -!"% -"""%

#.#5% #.5!% 10.5!% 11.25 -31% -"1% -"""%

#.!8% #.2"% 10.2!% 11.50 -305% -1% -"""%

#."1% 8.#2% #.#5% 11.5 -2#3% 8% -"""%

#.1"% 8.5#% #.!3% 12.00 -280% 32% -""5%

11.81% 11.!#% 11.53% 12.25 -35% -33!% -258%

11.!% 11.5"% 11.32% 12.50 -3!8% -32#% -250%

11.5"% 11.38% 11.11% 12.5 -3!0% -321% -2"2%

11."0% 11.22% 10.#0% 13.00 -352% -313% -235%

11.2% 11.0!% 10.!#% 13.25 -3""% -305% -22%

11.13% 10.#0% 10."% 13.50 -33!% -2#% -21#%

10.##% 10."% 10.2!% 13.5 -328% -28#% -211%

10.85% 10.5% 10.0"% 1".00 -320% -282% -203%

10.1% 10."1% #.81% 1".25 -312% -2"% -1#!%

10.5% 10.2"% #.5#% 1".50 -30"% -2!5% -188%

10."3% 10.0% #.3!% 1".5 -2#5% -25% -180%

10.2#% #.#0% #.12% 15.00 -28% -2"#% -12%

11.23% 11.5"% 12.2!% 15.25 -52!% -3""% -2!"%

11.13% 11."3% 12.15% 15.50 -52!% -33#% -25#%11.02% 11.33% 12.05% 15.5 -52% -33"% -25"%


29/593

10.#2% 11.23% 11.#5% 1!.00 -52% -330% -250%

10.81% 11.12% 11.8"% 1!.25 -52% -325% -2"5%

10.1% 11.02% 11."% 1!.50 -52% -321% -2"1%

10.!0% 10.#1% 11.!"% 1!.5 -528% -31!% -23!%

10."#% 10.81% 11.53% 1.00 -528% -311% -231%10.3#% 10.0% 11."3% 1.25 -528% -30!% -22%

10.28% 10.5#% 11.32% 1.50 -52#% -302% -222%

10.1% 10."#% 11.21% 1.5 -52#% -2#% -21%

10.0!% 10.38% 11.11% 18.00 -52#% -2#2% -212%

#.#5% 10.2% 11.00% 18.25 -530% -28% -208%

#.8"% 10.1!% 10.8#% 18.50 -530% -283% -203%

#.3% 10.05% 10.#% 18.5 -531% -28% -1#8%

#.!2% #.#"% 10.!8% 1#.00 -531% -23% -1#3%

#.51% #.83% 10.5% 1#.25 -531% -2!8% -188%

#."0% #.2% 10."!% 1#.50 -532% -2!3% -183%#.2#% #.!1% 10.35% 1#.5 -532% -258% -18%

#.1% #."#% 10.2"% 20.00 -533% -253% -1"%

11.20% 11.50% 12.21% 20.25 -335% -255% -3!5%

11.1"% 11."5% 12.1!% 20.50 -330% -251% -3!5%

11.08% 11.3#% 12.10% 20.5 -325% -2"!% -3!5%

11.03% 11.33% 12.05% 21.00 -320% -2"1% -3!5%

10.#% 11.28% 11.##% 21.25 -31!% -23!% -3!5%

10.#2% 11.22% 11.#"% 21.50 -311% -232% -3!5%

10.8!% 11.1% 11.88% 21.5 -30!% -22% -3!!%10.81% 11.11% 11.82% 22.00 -301% -222% -3!!%

10.5% 11.0!% 11.% 22.25 -2#!% -21% -3!!%

10.!#% 11.00% 11.1% 22.50 -2#1% -212% -3!!%

10.!"% 10.#"% 11.!!% 22.5 -28!% -20% -3!!%

10.58% 10.8#% 11.!0% 23.00 -281% -202% -3!!%

10.52% 10.83% 11.55% 23.25 -2% -1#8% -3!%

10."% 10.% 11."#% 23.50 -22% -1#3% -3!%

10."1% 10.2% 11."3% 23.5 -2!% -188% -3!%

10.35% 10.!!% 11.38% 2".00 -2!2% -183% -3!%

10.30% 10.!0% 11.32% 2".25 -25!% -18% -3!8%

10.2"% 10.55% 11.2!% 2".50 -251% -13% -3!8%

10.18% 10."#% 11.21% 2".5 -2"!% -1!8% -3!8%

10.12% 10."3% 11.15% 25.00 -2"1% -1!3% -3!8%

11.85% 12.15% 12.85% 25.25 -"8!% -"05% -12#%

11.83% 12.13% 12.83% 25.50 -"8!% -"05% -12"%

11.81% 12.11% 12.81% 25.5 -"8!% -"0!% -120%

11.8% 12.0#% 12.#% 2!.00 -"8!% -"0!% -115%

11.!% 12.0!% 12.% 2!.25 -"8!% -"0!% -110%

11."% 12.0"% 12.5% 2!.50 -"8!% -"0!% -105%11.2% 12.02% 12.3% 2!.5 -"8!% -"0!% -100%


30/593

11.0% 12.00% 12.0% 2.00 -"8% -"0!% -#!%

11.!8% 11.#8% 12.!8% 2.25 -"8% -"0% -#1%

11.!!% 11.#!% 12.!!% 2.50 -"8% -"0% -8!%

11.!"% 11.#"% 12.!"% 2.5 -"8% -"0% -81%

11.!2% 11.#2% 12.!2% 28.00 -"8% -"0% -!%11.!0% 11.#0% 12.!0% 28.25 -"88% -"0% -1%

11.5% 11.88% 12.58% 28.50 -"88% -"0% -!%

11.55% 11.85% 12.5!% 28.5 -"88% -"08% -!2%

11.53% 11.83% 12.5"% 2#.00 -"88% -"08% -5%

11.51% 11.81% 12.52% 2#.25 -"88% -"08% -52%

11."#% 11.#% 12."#% 2#.50 -"8#% -"08% -"%

11."% 11.% 12."% 2#.5 -"8#% -"08% -"2%

11."5% 11.5% 12."5% 30.00 -"8#% -"0#% -3%


31/593

2.25 2.50 .00 .50 *.00 5.00-11!0% -120% -1080% -20% 20% 300%

-11!0% -120% -1080% -20% 20% 300%

-11!0% -120% -1080% -20% 20% 300%

-11!0% -120% -1080% -20% 20% 300%

-11"!% 285% -5!% 20% 2"!% 5%

-133"% 1"05% 3!2% 308% 231% -"5%

1885% -1% -103% "1% #0% 111%

2#55% -!12% "5% 23% ""% #2%

-3"2% 5#% -1""% -115% 53% 23%-320% ##% -2% -15#% 21% -%

-2#8% 138!% -1% -203% -12% -38%

-2#% 183!% 0% -2"% -""% -!8%

-"00% -2#8% -180% -80% 5% !%

-"00% -288% -1!1% -8#% -1"% !2%

-"00% -2#% -1"3% -#8% -3"% 5%

-"00% -2!#% -12"% -108% -53% 52%

-"00% -258% -180% -120% -3!% 1%

-"00% -2"8% -11% -130% -51% -10%

-"00% -23#% -1!1% -13#% -!!% -21%


32/593

-"00% -22#% -152% -1"8% -80% -31%

-"00% -21"% -2"0% -!0% -"8% 13%

-"00% -203% -2"0% -!0% -5#% 8%

-"00% -1#3% -2"0% -!0% -!#% 2%

-"00% -183% -2"0% -!0% -80% -3%-138% -300% -113% -!0% -#0% -#%

-11% -300% -103% -!0% -101% -15%

-#5% -300% -#2% -!0% -111% -20%

-"% -300% -82% -!0% -122% -2!%

-3!0% -300% -2% -208% -58% -32%

-3!0% -300% -!2% -21#% -!3% -38%

-3!0% -300% -51% -22#% -!#% -"3%

-3!0% -300% -"1% -23#% -"% -"#%

-3!2% -123% -200% -80% -80% -55%

-3!2% -112% -200% -80% -85% -!1%-3!2% -102% -200% -80% -#1% -!%

-3!2% -#1% -200% -80% -#!% -3%

-3!0% -280% -200% -28"% -110% 31%

-3!1% -280% -200% -2#5% -11% 31%

-3!1% -280% -200% -30% -123% 31%

-3!1% -281% -200% -318% -12#% 31%

-13"% -281% -201% -101% -!#% -#5%

-123% -281% -201% -101% -2% -101%

-112% -281% -201% -101% -5% -108%-100% -282% -201% -101% -8% -115%

-8#% -282% -201% -101% -81% -122%

-8% -282% -201% -101% -8"% -128%

-!!% -282% -202% -101% -8% -135%

-55% -282% -202% -101% -#0% -1"3%

-323% -1#0% -111% -1#1% -11!% -"1%

-323% -18!% -10% -1#5% -120% -"3%

-323% -183% -10"% -1##% -12"% -"5%

-323% -1#% -100% -203% -12#% -"%

-323% -15% -#!% -20!% -133% -50%

-323% -11% -#2% -210% -13% -52%

-323% -1!% -8#% -21"% -1"1% -55%

-32"% -1!"% -85% -218% -1"!% -5%

-32"% -1!0% -81% -222% -150% -5#%

-32"% -15!% -% -22!% -15"% -!2%

-32"% -152% -"% -230% -15#% -!"%

-32"% -1"8% -0% -23"% -1!3% -!%

-18"% -2!2% -182% -52% -111% -3%

-180% -2!2% -182% -"#% -11"% -38%-15% -2!2% -182% -"% -11!% -"0%


33/593

-11% -2!2% -182% -"5% -118% -"1%

-1!!% -2!2% -182% -"2% -121% -"2%

-1!1% -2!2% -182% -"0% -123% -""%

-15% -2!3% -182% -38% -12!% -"5%

-152% -2!3% -182% -35% -128% -"!%-1"% -2!3% -182% -33% -131% -"8%

-1"3% -2!3% -182% -31% -133% -"#%

-138% -2!3% -182% -28% -13!% -51%

-133% -2!3% -183% -2!% -13#% -52%

-12#% -2!3% -183% -2"% -1"1% -53%

-12"% -2!3% -183% -21% -1""% -55%

-11#% -2!3% -183% -1#% -1"!% -5!%

-11"% -2!"% -183% -1!% -1"#% -58%

-110% -2!"% -183% -1"% -152% -5#%

-105% -2!"% -183% -12% -15"% -!1%-100% -2!"% -183% -#% -15% -!2%

-#5% -2!"% -183% -% -1!0% -!"%

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-28"% -1!!% -8!% -1#% -!1% -10%

-28"% -1!"% -8"% -200% -!1% -10%

-28"% -1!1% -82% -202% -!1% -10%

-285% -15#% -#% -205% -!1% -10%

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-285% -15"% -5% -210% -!1% -10%-285% -152% -2% -212% -!1% -10%

-285% -1"#% -0% -215% -!1% -10%

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-285% -1"5% -!5% -220% -!1% -10%

-28!% -1"2% -!3% -222% -!1% -10%

-28!% -1"0% -!0% -225% -!1% -10%

-28!% -13% -58% -228% -!1% -10%

-28!% -135% -5!% -230% -!1% -10%

-28!% -132% -53% -233% -!2% -10%

-28% -130% -51% -235% -!2% -10%

-28% -12% -"8% -238% -!2% -10%

-28% -125% -"!% -2"1% -!2% -10%

-28% -122% -"3% -2"3% -!2% -10%

-521% -12"% -1!2% -"% -!1% "!%

-52!% -121% -1!2% -2% -!1% "%

-531% -11#% -1!2% 1% -!1% "#%

-53!% -11!% -1!2% 3% -!1% 50%

-5"1% -11"% -1!2% 5% -!1% 51%

-5"!% -112% -1!2% 8% -!1% 52%-552% -10#% -1!3% 10% -!1% 53%


34/593

-55% -10% -1!3% 12% -!1% 5"%

-5!2% -10"% -1!3% 15% -!1% 55%

-5!% -102% -1!3% 1% -!1% 5%

-52% -##% -1!3% 20% -!1% 58%

-5% -#% -1!3% 22% -!1% 5#%-583% -#"% -1!3% 25% -!1% !0%

-588% -#2% -1!3% 2% -!1% !1%

-5#3% -8#% -1!3% 30% -!1% !2%

-5#8% -8% -1!3% 32% -!1% !"%

-!0"% -8"% -1!3% 3"% -!1% !5%

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-!15% -#% -1!3% 3#% -!1% !%

-!20% -% -1!"% "2% -!1% !8%


35/593

3mo

$orards

+.00 !.00 .00 0.00 0280% 2"0% 120% 0.25 .5!5

280% 2"0% 120% 0.50 .+0

280% 2"0% 120% 0.5 .+5*

280% 2"0% 120% 1.00 .!2

-52% -8% "% 1.25 .5

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36/593

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37/593

-11% 31% 3!% 1!.00 *.!0*

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20% 31% 3!% 21.00 *.++

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20% 31% 3!% 23.00 *.5+

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38/593

20% 30% 35% 2.00 *.!+

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20% 30% 35% 28.00 *.*220% 30% 35% 28.25 *.5

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39/593

$s Smoothing Val'e of

#2".35!% ATM saps

1 00.##11"0 0.2"8 0.0000% 1 0.0000

0.#822#! 0."#3" 0.0000% 1.5 0.0000

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0.#552"# 1.21!! 0.0000% " 0.0000

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0.8###55 2.!01" 0.0000% 10 0.0000

0.8#00 2.82"1 0.0000% 12 0.0000

0.88100 3.0""5 0.0000% 15 0.0000

0.82882 3.2!2 0.0000% 20 0.0000

0.8!"203 3."88 0.0000% 25 0.0000

0.855!15 3.!#2 0.0000% 30 0.0000

0.8"0" 3.#0"5 0.0000%

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40/593

0.821!3" ".520 0.0000%

0.81318 ".303 0.0000%

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0.#!3"5 5.130! 0.0000%

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0.1313 5.153 0.0000%

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0.!150# #.15#" 0.0000%

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0.518103 11.21 0.0000%

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41/593

0.50021! 11.!513 0.0000%

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0."88!# 11.8#1 0.0000%

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0.""35 12.132 0.0000%0."1#1# 12.2552 0.0000%

0."!!"3 12.318 0.0000%

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0."5053 12.13 0.0000%

0.""5355 12.8250 0.0000%

0.""023! 12.#351 0.0000%

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0."30183 13.151" 0.0000%

0."252"! 13.25 0.0000%0."203!8 13.3!28 0.0000%

0."155"5 13."!! 0.0000%

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0."0!0! 13.!0# 0.0000%

0."01"12 13.13 0.0000%

0.3#!812 13.805 0.0000%

0.3#22!# 13.#!85 0.0000%

0.3882 1".0!55 0.0000%

0.383351 1".1!13 0.0000%0.38#! 1".25!1 0.0000%

0.3"!5 1".3"# 0.0000%

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0.35#"3 1".13# 0.0000%

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0.3"5##3 1".#!3 0.0000%

0.3"2121 15.0!1# 0.0000%

0.338303 15.1"!" 0.0000%

0.33"5"0 15.2301 0.0000%

0.330832 15.3128 0.0000%

0.3218 15.3#"! 0.0000%

0.3235 15."55 0.0000%

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0.31!52! 15.!3"! 0.0000%

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0.30#!!# 15.#03 0.0000%0.30!310 15.8!!# 0.0000%


42/593

0.302##5 15.#"2! 0.0000%

0.2##23 1!.015 0.0000%

0.2#!"#" 1!.0#1 0.0000%

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0.2#015! 1!.235 0.0000%0.280"5 1!.30#3 0.0000%

0.283#1 1!.3803 0.0000%

0.280#33 1!."505 0.0000%

0.2#30 1!.5200 0.0000%

0.2"#!2 1!.588 0.0000%

0.2202! 1!.!5! 0.0000%

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43/593

T$is is a for/ard volatilit% tale' centralised aro&nd

ottom edge of ta(le 1.50%

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3ears -.5 -.0 -2.5 -2.0 -.50.25 33."% 33."% 33."% 33.0% 2#."%

0.50 33."% 33."% 33."% 32.#% 2#.2%

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1.00 33."% 33."% 33."% 32.2% 2.#%

1.25 25.!% 25.!% 25.!% 20.0% 15.#%

1.50 22.3% 22.3% 22.3% 13.8% #.8%

1.5 2#.#% 2#.#% 2#.#% 22.!% 1!.!%

2.00 2#.% 2#.% 2#.% 18.5% 1!.1%

2.25 2".2% 2".2% 23.8% 1#.0% 1".5%2.50 22.8% 22.8% 21.!% 1!.0% 13.#%

2.5 21.3% 21.3% 1#.#% 13.!% 13.2%

3.00 1#.8% 1#.8% 18.!% 12."% 11.%

3.25 23.% 23.% 23.0% 1#.2% 18.%

3.50 23.0% 23.0% 22.% 18.5% 18.#%

3.5 22."% 22."% 22.2% 1.#% 1#.1%

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".5 20.#% 20.#% 20.3% 1#.8% 18.8%


44/593

5.00 20."% 20."% 1#.5% 1#.8% 18.8%

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5.50 1#.#% 1#.#% 1#.% 1#.2% 1.!%

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!.00 18.#% 18.#% 1#.0% 18.#% 1."%!.25 22.2% 22.2% 20.!% 18.2% 1.0%

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8.50 1#.#% 1#.#% 18.!% 1!.!% 15.#%8.5 1#.% 1#.% 18.3% 1!."% 15.8%

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10.5 18.% 18.5% 1.3% 1!.1% 1".%11.00 18.5% 18.3% 1.2% 1!.0% 1".!%

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11.5 1.#% 1.!% 1!.% 15.!% 1".3%

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12.5 18.5% 1.8% 1!.3% 15.0% 1".2%

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45/593

1!.00 18.3% 1.2% 15.!% 1".5% 13."%

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1!.5 18.0% 1.0% 15."% 1"."% 13.2%

1.00 1.#% 1!.#% 15."% 1".3% 13.2%1.25 1.8% 1!.8% 15.3% 1".3% 13.1%

1.50 1.% 1!.8% 15.2% 1".2% 13.1%

1.5 1.!% 1!.% 15.1% 1".2% 13.0%

18.00 1.5% 1!.!% 15.1% 1".1% 12.#%

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18.50 1.3% 1!.5% 1".#% 1".0% 12.8%

18.5 1.2% 1!."% 1".#% 1".0% 12.8%

1#.00 1.1% 1!.3% 1".8% 13.#% 12.%

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20.00 1!.% 15.#% 1".5% 13.% 12."%

20.25 1.1% 1!.!% 15.1% 13.% 13.0%

20.50 1.0% 1!.5% 15.0% 13.% 12.#%

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21.00 1!.8% 1!."% 1".#% 13.5% 12.8%

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21.50 1!.!% 1!.2% 1".8% 13."% 12.%

21.5 1!.5% 1!.1% 1".% 13."% 12.%22.00 1!."% 1!.1% 1".% 13.3% 12.%

22.25 1!.3% 1!.0% 1".% 13.3% 12.!%

22.50 1!.3% 15.#% 1".!% 13.2% 12.!%

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23.50 15.#% 15.% 1".5% 13.0% 12."%

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2!.50 1!.8% 1!.8% 15.0% 13.5% 12.5%2!.5 1!.8% 1!.8% 15.0% 13.5% 12.5%


46/593

2.00 1!.% 1!.% 15.0% 13.5% 12."%

2.25 1!.% 1!.% 15.0% 13.5% 12."%

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2.5 1!.5% 1!.5% 1".#% 13.5% 12.3%

28.00 1!.5% 1!.5% 1".#% 13.5% 12.3%28.25 1!."% 1!."% 1".#% 13.5% 12.2%

28.50 1!."% 1!."% 1".8% 13.5% 12.2%

28.5 1!.3% 1!.3% 1".8% 13.5% 12.2%

2#.00 1!.3% 1!.3% 1".8% 13.5% 12.1%

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2#.50 1!.2% 1!.2% 1".% 13."% 12.0%

2#.5 1!.1% 1!.1% 1".!% 13."% 12.0%

30.00 1!.0% 1!.0% 1".!% 13.3% 11.#%


47/593

ATM

ATM

-.0 -0.5 0 0.5 .0 .5 2.0 2.523.5% 15."% 10.""% 10.#% 12.3% 13.!% 15.1% 1!.!%

23.1% 15.1% 10.""% 11.0% 12.3% 13.% 15.2% 1!.%

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20.8% 13.% 10.""% 11.3% 12.% 1".1% 15.!% 1.0%

15.0% 15.2% 15.31% 1.0% 18.2% 18.8% 1#.1% 1#.0%

13.3% 1!.5% 1.33% 1#.3% 20.5% 20.!% 20."% 1#.!%

1.0% 15.5% 15.33% 15.#% 1!.3% 1!.#% 1."% 18.1%

1!.5% 1!.1% 1!.08% 1!."% 1!.!% 1.1% 1.5% 18.2%

1.1% 1!."% 1!.13% 1!.2% 1!.5% 1!.!% 1!.% 1!.#%1."% 1!.#% 1!.1% 1!.5% 1!.5% 1!.5% 1!.5% 1!.!%

1.8% 1."% 1.28% 1!.% 1!.!% 1!."% 1!.3% 1!.3%

18.2% 18.0% 1.8!% 1!.#% 1!.!% 1!.3% 1!.0% 15.#%

1.3% 1!.5% 1!.30% 1!.2% 1!.3% 1!.!% 1!.#% 1.1%

1.5% 1!.8% 1!.5"% 1!.3% 1!.2% 1!.5% 1!.8% 1!.#%

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1.!% 1!.8% 1!.2"% 15.#% 15.% 15.% 15.% 1!.1%

1.% 1!.#% 1!.3"% 15.#% 15.% 15.5% 15.5% 15.#%


48/593

1.% 1.0% 1!."5% 15.#% 15.!% 15."% 15."% 15.8%

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13.8% 13.3% 13.01% 12.5% 12.0% 11."% 10.#% 10.5%13.% 13.2% 12.#1% 12."% 11.8% 11.2% 10.% 10.2%

13.!% 13.1% 12.82% 12.3% 11.% 11.0% 10.5% #.#%

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13."% 12.#% 12.!3% 12.0% 11.3% 10.!% 10.0% #."%

13.3% 12.8% 12.53% 11.8% 11.1% 10."% #.% #.1%

13.% 12.#% 12.51% 11.8% 11.!% 11.5% 11.% 11.8%

13.!% 12.8% 12."2% 11.% 11.5% 11."% 11.!% 11.!%

13.5% 12.% 12.32% 11.!% 11."% 11.3% 11."% 11.5%

13."% 12.!% 12.23% 11.5% 11.2% 11.2% 11.3% 11."%

13.3% 12.5% 12.13% 11.3% 11.1% 11.0% 11.2% 11.2%

13.3% 12."% 12.0"% 11.2% 11.0% 10.#% 11.0% 11.1%

13.2% 12.3% 11.#5% 11.1% 10.8% 10.8% 10.#% 10.#%

13.1% 12.2% 11.85% 11.0% 10.% 10.!% 10.8% 10.8%

13.0% 12.1% 11.5% 10.8% 10.5% 10.5% 10.!% 10.!%

13.0% 12.0% 11.!!% 10.% 10."% 10.3% 10.5% 10.5%

12.#% 12.0% 11.5!% 10.!% 10.3% 10.2% 10."% 10.3%

12.#% 11.#% 11."% 10.5% 10.1% 10.0% 10.2% 10.2%

12.#% 12.5% 12.22% 11.!% 11."% 11.3% 11.2% 11.3%

12.#% 12.5% 12.15% 11.5% 11.3% 11.2% 11.2% 11.2%12.8% 12."% 12.08% 11."% 11.2% 11.1% 11.1% 11.1%


49/593

12.8% 12."% 12.01% 11."% 11.2% 11.0% 11.0% 11.0%

12.% 12.3% 11.#"% 11.3% 11.1% 10.#% 10.#% 10.#%

12.!% 12.3% 11.88% 11.2% 11.0% 10.8% 10.8% 10.8%

12.!% 12.2% 11.81% 11.1% 10.#% 10.% 10.!% 10.%

12.5% 12.2% 11."% 11.0% 10.8% 10.!% 10.5% 10.!%12.5% 12.1% 11.!% 11.0% 10.% 10.5% 10."% 10."%

12."% 12.1% 11.!0% 10.#% 10.!% 10."% 10.3% 10.3%

12.3% 12.0% 11.53% 10.8% 10.!% 10.3% 10.2% 10.2%

12.3% 12.0% 11."!% 10.% 10.5% 10.3% 10.1% 10.1%

12.2% 11.#% 11."0% 10.!% 10."% 10.2% 10.0% 10.0%

12.2% 11.#% 11.33% 10.!% 10.3% 10.1% #.#% #.#%

12.1% 11.8% 11.2!% 10.5% 10.2% 10.0% #.8% #.8%

12.0% 11.8% 11.1#% 10."% 10.1% #.#% #.% #.%

12.0% 11.% 11.12% 10.3% 10.0% #.8% #.!% #.!%

11.#% 11.!% 11.05% 10.2% #.#% #.% #.5% #."%11.8% 11.!% 10.#8% 10.2% #.8% #.!% #."% #.3%

11.8% 11.5% 10.#1% 10.1% #.8% #.5% #.3% #.2%

12."% 11.!% 11."3% 11.1% 11.0% 11.0% 11.1% 11.2%

12."% 11.!% 11.3% 11.0% 11.0% 11.0% 11.1% 11.2%

12.3% 11.5% 11.32% 11.0% 10.#% 10.#% 11.0% 11.1%

12.3% 11.5% 11.2!% 10.#% 10.#% 10.#% 11.0% 11.1%

12.2% 11."% 11.21% 10.#% 10.8% 10.8% 10.#% 11.0%

12.2% 11.3% 11.15% 10.8% 10.8% 10.% 10.8% 11.0%

12.2% 11.3% 11.10% 10.% 10.% 10.% 10.8% 10.#%12.1% 11.2% 11.0"% 10.% 10.!% 10.!% 10.% 10.8%

12.1% 11.2% 10.#8% 10.!% 10.!% 10.!% 10.% 10.8%

12.1% 11.1% 10.#3% 10.!% 10.5% 10.5% 10.!% 10.%

12.0% 11.1% 10.8% 10.5% 10.5% 10.5% 10.!% 10.%

12.0% 11.0% 10.82% 10.5% 10."% 10."% 10.5% 10.!%

12.0% 11.0% 10.!% 10."% 10."% 10.3% 10."% 10.5%

12.0% 10.#% 10.0% 10."% 10.3% 10.3% 10."% 10.5%

12.0% 10.#% 10.!5% 10.3% 10.3% 10.2% 10.3% 10."%

11.#% 10.8% 10.5#% 10.2% 10.2% 10.2% 10.3% 10."%

11.#% 10.8% 10.53% 10.2% 10.1% 10.1% 10.2% 10.3%

11.#% 10.% 10."8% 10.1% 10.1% 10.0% 10.1% 10.2%

11.#% 10.% 10."2% 10.1% 10.0% 10.0% 10.1% 10.2%

11.#% 10.% 10.3!% 10.0% 10.0% #.#% 10.0% 10.1%

11.#% 11.8% 11.28% 11.2% 11."% 11.!% 11.% 11.8%

11.8% 11.8% 11.25% 11.2% 11."% 11.!% 11.% 11.8%

11.8% 11.% 11.21% 11.2% 11.3% 11.!% 11.% 11.8%

11.8% 11.% 11.1% 11.1% 11.3% 11.5% 11.% 11.8%

11.8% 11.% 11.1"% 11.1% 11.3% 11.5% 11.!% 11.%

11.8% 11.!% 11.10% 11.1% 11.2% 11.5% 11.!% 11.%11.% 11.!% 11.0!% 11.1% 11.2% 11.5% 11.!% 11.%


50/593

11.% 11.5% 11.02% 11.0% 11.2% 11."% 11.!% 11.%

11.% 11.5% 10.##% 11.0% 11.1% 11."% 11.!% 11.%

11.!% 11.5% 10.#5% 11.0% 11.1% 11."% 11.5% 11.!%

11.!% 11."% 10.#1% 11.0% 11.1% 11.3% 11.5% 11.!%

11.!% 11."% 10.88% 10.#% 11.0% 11.3% 11.5% 11.!%11.5% 11."% 10.8"% 10.#% 11.0% 11.3% 11.5% 11.!%

11.5% 11.3% 10.80% 10.#% 11.0% 11.3% 11."% 11.5%

11.5% 11.3% 10.!% 10.8% 10.#% 11.2% 11."% 11.5%

11."% 11.2% 10.2% 10.8% 10.#% 11.2% 11."% 11.5%

11."% 11.2% 10.!#% 10.8% 10.#% 11.2% 11."% 11.5%

11."% 11.2% 10.!5% 10.% 10.8% 11.2% 11."% 11.5%

11.3% 11.1% 10.!1% 10.% 10.8% 11.1% 11.3% 11."%

11.3% 11.1% 10.5% 10.% 10.8% 11.1% 11.3% 11."%


51/593

.0 .518.0% 1#."%

18.1% 1#."%

18.2% 1#.!%

18."% 1#.8%

18.8% 18."%

18.% 1.%

18.8% 1#.3%

18.#% 1#.3%

1.1% 1."%1!.8% 1.0%

1!.3% 1!.5%

15.#% 1!.0%

1.2% 1.5%

1.1% 1.3%

1!.#% 1.1%

1!.% 1!.#%

1!.!% 1!.8%

1!."% 1!.!%

1!.3% 1!."%


52/593

1!.1% 1!.2%

15."% 15."%

15.2% 15.2%

1".#% 1".#%

1".% 1".%1".% 15.0%

1".5% 1".8%

1".2% 1".5%

1".0% 1".3%

13.8% 1".1%

13.5% 13.#%

13.3% 13.!%

13.1% 13."%

13.5% 13.3%

13.3% 13.1%13.1% 12.8%

12.#% 12.!%

13.3% 13.5%

13.2% 13."%

13.0% 13.2%

12.8% 13.0%

10.#% 10.8%

10.!% 10.5%

10.3% 10.2%10.0% #.#%

#.% #.!%

#."% #.3%

#.1% #.0%

8.8% 8.%

11.% 11.%

11.!% 11.5%

11."% 11."%

11.3% 11.2%

11.1% 11.0%

11.0% 10.8%

10.8% 10.%

10.!% 10.5%

10.5% 10.3%

10.3% 10.2%

10.2% 10.0%

10.0% #.8%

11.5% 11.!%

11.3% 11.5%11.2% 11."%


53/593

11.1% 11.3%

11.0% 11.2%

10.#% 11.1%

10.8% 11.0%

10.% 10.#%10.!% 10.8%

10.5% 10.%

10."% 10.5%

10.3% 10."%

10.2% 10.3%

10.1% 10.2%

#.#% 10.1%

#.8% 10.0%

#.% #.#%

#.!% #.8%#.5% #.%

#."% #.5%

11."% 11.!%

11.3% 11.5%

11.3% 11."%

11.2% 11."%

11.2% 11.3%

11.1% 11.3%

11.1% 11.2%11.0% 11.2%

10.#% 11.1%

10.#% 11.0%

10.8% 11.0%

10.8% 10.#%

10.% 10.#%

10.!% 10.8%

10.!% 10.%

10.5% 10.%

10.5% 10.!%

10."% 10.!%

10.3% 10.5%

10.3% 10."%

12.0% 12.1%

12.0% 12.1%

11.#% 12.1%

11.#% 12.1%

11.#% 12.0%

11.#% 12.0%11.8% 12.0%


54/593

11.8% 12.0%

11.8% 11.#%

11.8% 11.#%

11.% 11.#%

11.% 11.#%11.% 11.8%

11.% 11.8%

11.% 11.8%

11.!% 11.8%

11.!% 11.8%

11.!% 11.%

11.!% 11.%

11.5% 11.%


55/593

Step length 0.25

Volatilities ottom edge of ta(le4 -3.5%

Top edge of ta(le4 3.5%

-3.5% -3.0% -2.5% -2.0% -1.5% -1.0%

1 10."% 10."% 10."% 10."% 10."% 10."%

2 10."% 10."% 10."% 10."% 10."% 10."%

3 10."% 10."% 10."% 10."% 10."% 10."%

" 10."% 10."% 10."% 10."% 10."% 10."%

5 15.3% 15.3% 15.3% 15.3% 15.3% 15.3%

! 1.3% 1.3% 1.3% 1.3% 1.3% 1.3%

15.3% 15.3% 15.3% 15.3% 15.3% 15.3%

8 1!.1% 1!.1% 1!.1% 1!.1% 1!.1% 1!.1%

# 1!.1% 1!.1% 1!.1% 1!.1% 1!.1% 1!.1%

10 1!.% 1!.% 1!.% 1!.% 1!.% 1!.%

11 1.3% 1.3% 1.3% 1.3% 1.3% 1.3%

12 1.#% 1.#% 1.#% 1.#% 1.#% 1.#%

13 1!.3% 1!.3% 1!.3% 1!.3% 1!.3% 1!.3%

1" 1!.5% 1!.5% 1!.5% 1!.5% 1!.5% 1!.5%

15 1!.8% 1!.8% 1!.8% 1!.8% 1!.8% 1!.8%

1! 1.0% 1.0% 1.0% 1.0% 1.0% 1.0%

1 1!.1% 1!.1% 1!.1% 1!.1% 1!.1% 1!.1%

18 1!.2% 1!.2% 1!.2% 1!.2% 1!.2% 1!.2%

1# 1!.3% 1!.3% 1!.3% 1!.3% 1!.3% 1!.3%

20 1!."% 1!."% 1!."% 1!."% 1!."% 1!."%

21 15.% 15.% 15.% 15.% 15.% 15.%

22 15.% 15.% 15.% 15.% 15.% 15.%

23 15.% 15.% 15.% 15.% 15.% 15.%

2" 15.% 15.% 15.% 15.% 15.% 15.%

25 15.3% 15.3% 15.3% 15.3% 15.3% 15.3%

2! 15.2% 15.2% 15.2% 15.2% 15.2% 15.2%

2 15.2% 15.2% 15.2% 15.2% 15.2% 15.2%28 15.2% 15.2% 15.2% 15.2% 15.2% 15.2%

2# 1".% 1".% 1".% 1".% 1".% 1".%

30 1".% 1".% 1".% 1".% 1".% 1".%

31 1".!% 1".!% 1".!% 1".!% 1".!% 1".!%

32 1".!% 1".!% 1".!% 1".!% 1".!% 1".!%

33 1".2% 1".2% 1".2% 1".2% 1".2% 1".2%

3" 1".1% 1".1% 1".1% 1".1% 1".1% 1".1%

35 1".0% 1".0% 1".0% 1".0% 1".0% 1".0%

3! 1".0% 1".0% 1".0% 1".0% 1".0% 1".0%

3 1".0% 1".0% 1".0% 1".0% 1".0% 1".0%38 13.#% 13.#% 13.#% 13.#% 13.#% 13.#%


56/593

3# 13.#% 13.#% 13.#% 13.#% 13.#% 13.#%

"0 13.8% 13.8% 13.8% 13.8% 13.8% 13.8%

"1 13.2% 13.2% 13.2% 13.2% 13.2% 13.2%

"2 13.1% 13.1% 13.1% 13.1% 13.1% 13.1%

"3 13.0% 13.0% 13.0% 13.0% 13.0% 13.0%

"" 12.#% 12.#% 12.#% 12.#% 12.#% 12.#%

"5 12.8% 12.8% 12.8% 12.8% 12.8% 12.8%

"! 12.% 12.% 12.% 12.% 12.% 12.%

" 12.!% 12.!% 12.!% 12.!% 12.!% 12.!%

"8 12.5% 12.5% 12.5% 12.5% 12.5% 12.5%

"# 12.5% 12.5% 12.5% 12.5% 12.5% 12.5%

50 12."% 12."% 12."% 12."% 12."% 12."%

51 12.3% 12.3% 12.3% 12.3% 12.3% 12.3%

52 12.2% 12.2% 12.2% 12.2% 12.2% 12.2%

53 12.1% 12.1% 12.1% 12.1% 12.1% 12.1%

5" 12.0% 12.0% 12.0% 12.0% 12.0% 12.0%

55 11.#% 11.#% 11.#% 11.#% 11.#% 11.#%

5! 11.#% 11.#% 11.#% 11.#% 11.#% 11.#%

5 11.8% 11.8% 11.8% 11.8% 11.8% 11.8%

58 11.% 11.% 11.% 11.% 11.% 11.%

5# 11.!% 11.!% 11.!% 11.!% 11.!% 11.!%

!0 11.5% 11.5% 11.5% 11.5% 11.5% 11.5%

!1 12.2% 12.2% 12.2% 12.2% 12.2% 12.2%

!2 12.1% 12.1% 12.1% 12.1% 12.1% 12.1%

!3 12.1% 12.1% 12.1% 12.1% 12.1% 12.1%

!" 12.0% 12.0% 12.0% 12.0% 12.0% 12.0%

!5 11.#% 11.#% 11.#% 11.#% 11.#% 11.#%

!! 11.#% 11.#% 11.#% 11.#% 11.#% 11.#%

! 11.8% 11.8% 11.8% 11.8% 11.8% 11.8%

!8 11.% 11.% 11.% 11.% 11.% 11.%

!# 11.% 11.% 11.% 11.% 11.% 11.%

0 11.!% 11.!% 11.!% 11.!% 11.!% 11.!%

1 11.5% 11.5% 11.5% 11.5% 11.5% 11.5%

2 11.5% 11.5% 11.5% 11.5% 11.5% 11.5%

3 11."% 11."% 11."% 11."% 11."% 11."%" 11.3% 11.3% 11.3% 11.3% 11.3% 11.3%

5 11.3% 11.3% 11.3% 11.3% 11.3% 11.3%

! 11.2% 11.2% 11.2% 11.2% 11.2% 11.2%

11.1% 11.1% 11.1% 11.1% 11.1% 11.1%

8 11.0% 11.0% 11.0% 11.0% 11.0% 11.0%

# 11.0% 11.0% 11.0% 11.0% 11.0% 11.0%

80 10.#% 10.#% 10.#% 10.#% 10.#% 10.#%

81 11."% 11."% 11."% 11."% 11."% 11."%

82 11."% 11."% 11."% 11."% 11."% 11."%

83 11.3% 11.3% 11.3% 11.3% 11.3% 11.3%8" 11.3% 11.3% 11.3% 11.3% 11.3% 11.3%


57/593

85 11.2% 11.2% 11.2% 11.2% 11.2% 11.2%

8! 11.2% 11.2% 11.2% 11.2% 11.2% 11.2%

8 11.1% 11.1% 11.1% 11.1% 11.1% 11.1%

88 11.0% 11.0% 11.0% 11.0% 11.0% 11.0%

8# 11.0% 11.0% 11.0% 11.0% 11.0% 11.0%

#0 10.#% 10.#% 10.#% 10.#% 10.#% 10.#%

#1 10.#% 10.#% 10.#% 10.#% 10.#% 10.#%

#2 10.8% 10.8% 10.8% 10.8% 10.8% 10.8%

#3 10.8% 10.8% 10.8% 10.8% 10.8% 10.8%

#" 10.% 10.% 10.% 10.% 10.% 10.%

#5 10.!% 10.!% 10.!% 10.!% 10.!% 10.!%

#! 10.!% 10.!% 10.!% 10.!% 10.!% 10.!%

# 10.5% 10.5% 10.5% 10.5% 10.5% 10.5%

#8 10.5% 10.5% 10.5% 10.5% 10.5% 10.5%

## 10."% 10."% 10."% 10."% 10."% 10."%

100 10."% 10."% 10."% 10."% 10."% 10."%

101 11.3% 11.3% 11.3% 11.3% 11.3% 11.3%

102 11.2% 11.2% 11.2% 11.2% 11.2% 11.2%

103 11.2% 11.2% 11.2% 11.2% 11.2% 11.2%

10" 11.2% 11.2% 11.2% 11.2% 11.2% 11.2%

105 11.1% 11.1% 11.1% 11.1% 11.1% 11.1%

10! 11.1% 11.1% 11.1% 11.1% 11.1% 11.1%

10 11.1% 11.1% 11.1% 11.1% 11.1% 11.1%

108 11.0% 11.0% 11.0% 11.0% 11.0% 11.0%

10# 11.0% 11.0% 11.0% 11.0% 11.0% 11.0%

110 10.#% 10.#% 10.#% 10.#% 10.#% 10.#%

111 10.#% 10.#% 10.#% 10.#% 10.#% 10.#%

112 10.#% 10.#% 10.#% 10.#% 10.#% 10.#%

113 10.8% 10.8% 10.8% 10.8% 10.8% 10.8%

11" 10.8% 10.8% 10.8% 10.8% 10.8% 10.8%

115 10.8% 10.8% 10.8% 10.8% 10.8% 10.8%

11! 10.% 10.% 10.% 10.% 10.% 10.%

11 10.% 10.% 10.% 10.% 10.% 10.%

118 10.!% 10.!% 10.!% 10.!% 10.!% 10.!%

11# 10.!% 10.!% 10.!% 10.!% 10.!% 10.!%120 10.!% 10.!% 10.!% 10.!% 10.!% 10.!%

0 1 2 3 " 5

$orards 3.55% 3.!01% 3.!5"% 3.32% 3.835% 3.83%

ATM Vol 10.""% 10.""% 10.""% 10.""% 15.31%

0.##11"0 0.#822#! 0.#3"05 0.#!""08 0.#552"# 0.#"!088

&rice of disco'nt (ond 0.#822#! 0.#3"05 0.#!""08 0.#552"# 0.#"!088

)rror 0.000000 0.000000 0.000000 0.000000 0.000000

"ote - onl% t$e first 20 periods $ave een calirated to 4eroAppro* Step length 0.20% 0.20% 0.21% 0.31%


58/593

Act'al rate 3.5#% 3.!""% 3.1% 3.815% 3.81#%

0 1 2 3 " 5

120 3.50% 3.50% 3.50% 3.50%

11# 3.50% 3.50% 3.50% 3.50%

118 3.50% 3.50% 3.50% 3.50%

11 3.50% 3.50% 3.50% 3.50%

11! 3.50% 3.50% 3.50% 3.50%

115 3.50% 3.50% 3.50% 3.50%

11" 3.50% 3.50% 3.50% 3.50%

113 3.50% 3.50% 3.50% 3.50%

112 3.50% 3.50% 3.50% 3.50%

111 3.50% 3.50% 3.50% 3.50%

110 3.50% 3.50% 3.50% 3.50%

10# 3.50% 3.50% 3.50% 3.50%

108 3.50% 3.50% 3.50% 3.50%

10 3.50% 3.50% 3.50% 3.50%

10! 3.50% 3.50% 3.50% 3.50%

105 3.50% 3.50% 3.50% 3.50%

10" 3.50% 3.50% 3.50% 3.50%

103 3.50% 3.50% 3.50% 3.50%

102 3.50% 3.50% 3.50% 3.50%

101 3.50% 3.50% 3.50% 3.50%

100 3.50% 3.50% 3.50% 3.50%

## 3.50% 3.50% 3.50% 3.50%

#8 3.50% 3.50% 3.50% 3.50%

# 3.50% 3.50% 3.50% 3.50%

#! 3.50% 3.50% 3.50% 3.50%

#5 3.50% 3.50% 3.50% 3.50%

#" 3.50% 3.50% 3.50% 3.50%

#3 3.50% 3.50% 3.50% 3.50%

#2 3.50% 3.50% 3.50% 3.50%

#1 3.50% 3.50% 3.50% 3.50%#0 3.50% 3.50% 3.50% 3.50%

8# 3.50% 3.50% 3.50% 3.50%

88 3.50% 3.50% 3.50% 3.50%

8 3.50% 3.50% 3.50% 3.50%

8! 3.50% 3.50% 3.50% 3.50%

85 3.50% 3.50% 3.50% 3.50%

8" 3.50% 3.50% 3.50% 3.50%

83 3.50% 3.50% 3.50% 3.50%

82 3.50% 3.50% 3.50% 3.50%

81 3.50% 3.50% 3.50% 3.50%80 3.50% 3.50% 3.50% 3.50%


59/593

# 3.50% 3.50% 3.50% 3.50%

8 3.50% 3.50% 3.50% 3.50%

3.50% 3.50% 3.50% 3.50%

! 3.50% 3.50% 3.50% 3.50%

5 3.50% 3.50% 3.50% 3.50%

" 3.50% 3.50% 3.50% 3.50%

3 3.50% 3.50% 3.50% 3.50%

2 3.50% 3.50% 3.50% 3.50%

1 3.50% 3.50% 3.50% 3.50%

0 3.50% 3.50% 3.50% 3.50%

!# 3.50% 3.50% 3.50% 3.50%

!8 3.50% 3.50% 3.50% 3.50%

! 3.50% 3.50% 3.50% 3.50%

!! 3.50% 3.50% 3.50% 3.50%

!5 3.50% 3.50% 3.50% 3.50%

!" 3.50% 3.50% 3.50% 3.50%

!3 3.50% 3.50% 3.50% 3.50%

!2 3.50% 3.50% 3.50% 3.50%

!1 3.50% 3.50% 3.50% 3.50%

!0 3.50% 3.50% 3.50% 3.50%

5# 3.50% 3.50% 3.50% 3.50%

58 3.50% 3.50% 3.50% 3.50%

5 3.50% 3.50% 3.50% 3.50%

5! 3.50% 3.50% 3.50% 3.50%

55 3.50% 3.50% 3.50% 3.50%

5" 3.50% 3.50% 3.50% 3.50%

53 3.50% 3.50% 3.50% 3.50%

52 3.50% 3.50% 3.50% 3.50%

51 3.50% 3.50% 3.50% 3.50%

50 3.50% 3.50% 3.50% 3.50%

"# 3.50% 3.50% 3.50% 3.50%

"8 3.50% 3.50% 3.50% 3.50%

" 3.50% 3.50% 3.50% 3.50%

"! 3.50% 3.50% 3.50% 3.50%

"5 3.50% 3.50% 3.50% 3.50%"" 3.50% 3.50% 3.50% 3.50%

"3 3.50% 3.50% 3.50% 3.50%

"2 3.50% 3.50% 3.50% 3.50%

"1 3.50% 3.50% 3.50% 3.50%

"0 3.50% 3.50% 3.50% 3.50%

3# 3.50% 3.50% 3.50% 3.50%

38 3.50% 3.50% 3.50% 3.50%

3 3.50% 3.50% 3.50% 3.50%

3! 3.50% 3.50% 3.50% 3.50%

35 3.50% 3.50% 3.50% 3.50%3" 3.50% 3.50% 3.50% 3.50%


60/593

33 3.50% 3.50% 3.50% 3.50%

32 3.50% 3.50% 3.50% 3.50%

31 3.50% 3.50% 3.50% 3.50%

30 3.50% 3.50% 3.50% 3.50%

2# 3.50% 3.50% 3.50% 3.50%

28 3.50% 3.50% 3.50% 3.50%

2 3.50% 3.50% 3.50% 3.50%

2! 3.50% 3.50% 3.50% 3.50%

25 3.50% 3.50% 3.50% 3.50%

2" 3.50% 3.50% 3.50% 3.50%

23 3.50% 3.50% 3.50% 3.50%

22 3.50% 3.50% 3.50% 3.50%

21 3.50% 3.50% 3.50% 3.50%

20 3.50% 3.50% 3.50% 3.50%

1# 3.50% 3.50% 3.50% 3.50%

18 3.50% 3.50% 3.50% 3.50%

1 3.33% 3."0% 3."#% 3.50%

1! 3.13% 3.20% 3.2#% 3.50%

15 2.#"% 3.00% 3.08% 3.50%

1" 2."% 2.80% 2.88% 3.50%

13 2.55% 2.!0% 2.!% 3.50%

12 2.35% 2."0% 2."% 3.50%

11 2.15% 2.20% 2.2!% 3.3#%

10 1.#!% 2.00% 2.0!% 3.08%

# 1.!% 1.80% 1.85% 2.%

8 1.5% 1.!0% 1.!"% 2."%

1.3% 1."0% 1.""% 2.1!%

! 1.1% 1.20% 1.23% 1.85%

5 0.#8% 1.00% 1.03% 1.5"%

" 0.8% 0.80% 0.82% 1.23%

3 0.5#% 0.!0% 0.!2% 0.#2%

2 0.3#% 0."0% 0."1% 0.!2%

1 0.20% 0.20% 0.21% 0.31%

ATM 0 0.0% 0.00% 0.00% 0.00% 0.00%

-1 -0.20% -0.20% -0.21% -0.31%-2 -0.3#% -0."0% -0."1% -0.!2%

-3 -0.5#% -0.!0% -0.!2% -0.#2%

-" -0.8% -0.80% -0.82% -1.23%

-5 -0.#8% -1.00% -1.03% -1.5"%

-! -1.1% -1.20% -1.23% -1.85%

- -1.3% -1."0% -1.""% -2.1!%

-8 -1.5% -1.!0% -1.!"% -2."%

-# -1.!% -1.80% -1.85% -2.%

-10 -1.#!% -2.00% -2.0!% -3.08%

-11 -2.15% -2.20% -2.2!% -3.3#%-12 -2.35% -2."0% -2."% -3.50%


61/593

-13 -2.55% -2.!0% -2.!% -3.50%

-1" -2."% -2.80% -2.88% -3.50%

-15 -2.#"% -3.00% -3.08% -3.50%

-1! -3.13% -3.20% -3.2#% -3.50%

-1 -3.33% -3."0% -3."#% -3.50%

-18 -3.50% -3.50% -3.50% -3.50%

-1# -3.50% -3.50% -3.50% -3.50%

-20 -3.50% -3.50% -3.50% -3.50%

-21 -3.50% -3.50% -3.50% -3.50%

-22 -3.50% -3.50% -3.50% -3.50%

-23 -3.50% -3.50% -3.50% -3.50%

-2" -3.50% -3.50% -3.50% -3.50%

-25 -3.50% -3.50% -3.50% -3.50%

-2! -3.50% -3.50% -3.50% -3.50%

-2 -3.50% -3.50% -3.50% -3.50%

-28 -3.50% -3.50% -3.50% -3.50%

-2# -3.50% -3.50% -3.50% -3.50%

-30 -3.50% -3.50% -3.50% -3.50%

-31 -3.50% -3.50% -3.50% -3.50%

-32 -3.50% -3.50% -3.50% -3.50%

-33 -3.50% -3.50% -3.50% -3.50%

-3" -3.50% -3.50% -3.50% -3.50%

-35 -3.50% -3.50% -3.50% -3.50%

-3! -3.50% -3.50% -3.50% -3.50%

-3 -3.50% -3.50% -3.50% -3.50%

-38 -3.50% -3.50% -3.50% -3.50%

-3# -3.50% -3.50% -3.50% -3.50%

-"0 -3.50% -3.50% -3.50% -3.50%

-"1 -3.50% -3.50% -3.50% -3.50%

-"2 -3.50% -3.50% -3.50% -3.50%

-"3 -3.50% -3.50% -3.50% -3.50%

-"" -3.50% -3.50% -3.50% -3.50%

-"5 -3.50% -3.50% -3.50% -3.50%

-"! -3.50% -3.50% -3.50% -3.50%

-" -3.50% -3.50% -3.50% -3.50%-"8 -3.50% -3.50% -3.50% -3.50%

-"# -3.50% -3.50% -3.50% -3.50%

-50 -3.50% -3.50% -3.50% -3.50%

-51 -3.50% -3.50% -3.50% -3.50%

-52 -3.50% -3.50% -3.50% -3.50%

-53 -3.50% -3.50% -3.50% -3.50%

-5" -3.50% -3.50% -3.50% -3.50%

-55 -3.50% -3.50% -3.50% -3.50%

-5! -3.50% -3.50% -3.50% -3.50%

-5 -3.50% -3.50% -3.50% -3.50%-58 -3.50% -3.50% -3.50% -3.50%


62/593

-5# -3.50% -3.50% -3.50% -3.50%

-!0 -3.50% -3.50% -3.50% -3.50%

-!1 -3.50% -3.50% -3.50% -3.50%

-!2 -3.50% -3.50% -3.50% -3.50%

-!3 -3.50% -3.50% -3.50% -3.50%

-!" -3.50% -3.50% -3.50% -3.50%

-!5 -3.50% -3.50% -3.50% -3.50%

-!! -3.50% -3.50% -3.50% -3.50%

-! -3.50% -3.50% -3.50% -3.50%

-!8 -3.50% -3.50% -3.50% -3.50%

-!# -3.50% -3.50% -3.50% -3.50%

-0 -3.50% -3.50% -3.50% -3.50%

-1 -3.50% -3.50% -3.50% -3.50%

-2 -3.50% -3.50% -3.50% -3.50%

-3 -3.50% -3.50% -3.50% -3.50%

-" -3.50% -3.50% -3.50% -3.50%

-5 -3.50% -3.50% -3.50% -3.50%

-! -3.50% -3.50% -3.50% -3.50%

- -3.50% -3.50% -3.50% -3.50%

-8 -3.50% -3.50% -3.50% -3.50%

-# -3.50% -3.50% -3.50% -3.50%

-80 -3.50% -3.50% -3.50% -3.50%

-81 -3.50% -3.50% -3.50% -3.50%

-82 -3.50% -3.50% -3.50% -3.50%

-83 -3.50% -3.50% -3.50% -3.50%

-8" -3.50% -3.50% -3.50% -3.50%

-85 -3.50% -3.50% -3.50% -3.50%

-8! -3.50% -3.50% -3.50% -3.50%

-8 -3.50% -3.50% -3.50% -3.50%

-88 -3.50% -3.50% -3.50% -3.50%

-8# -3.50% -3.50% -3.50% -3.50%

-#0 -3.50% -3.50% -3.50% -3.50%

-#1 -3.50% -3.50% -3.50% -3.50%

-#2 -3.50% -3.50% -3.50% -3.50%

-#3 -3.50% -3.50% -3.50% -3.50%-#" -3.50% -3.50% -3.50% -3.50%

-#5 -3.50% -3.50% -3.50% -3.50%

-#! -3.50% -3.50% -3.50% -3.50%

-# -3.50% -3.50% -3.50% -3.50%

-#8 -3.50% -3.50% -3.50% -3.50%

-## -3.50% -3.50% -3.50% -3.50%

-100 -3.50% -3.50% -3.50% -3.50%

-101 -3.50% -3.50% -3.50% -3.50%

-102 -3.50% -3.50% -3.50% -3.50%

-103 -3.50% -3.50% -3.50% -3.50%-10" -3.50% -3.50% -3.50% -3.50%


63/593

-105 -3.50% -3.50% -3.50% -3.50%

-10! -3.50% -3.50% -3.50% -3.50%

-10 -3.50% -3.50% -3.50% -3.50%

-108 -3.50% -3.50% -3.50% -3.50%

-10# -3.50% -3.50% -3.50% -3.50%

-110 -3.50% -3.50% -3.50% -3.50%

-111 -3.50% -3.50% -3.50% -3.50%

-112 -3.50% -3.50% -3.50% -3.50%

-113 -3.50% -3.50% -3.50% -3.50%

-11" -3.50% -3.50% -3.50% -3.50%

-115 -3.50% -3.50% -3.50% -3.50%

-11! -3.50% -3.50% -3.50% -3.50%

-11 -3.50% -3.50% -3.50% -3.50%

-118 -3.50% -3.50% -3.50% -3.50%

-11# -3.50% -3.50% -3.50% -3.50%

-120 -3.50% -3.50% -3.50% -3.50%

1 2 3 " 5

1 0 -1 -2 -3 -"

2 0 0 0 -1 -2

3 1 0 0 0

" 2 1 0

5 3 2

! "

8

#

10

11

12

13

1"

15

1!

118

1#

20

21

22

23

2"

25

2!

228


64/593

2#

30

31

32

33

3"

35

3!

3

38

3#

"0

"1

"2

"3

""

"5

"!

"

"8

"#

50

1 10.""% 10.""% 10.""% 10.""% 15.31%

2 10.""% 10.""% 10.""% 10.""% 15.31%

3 0.00% 10.""% 10.""% 10.""% 15.31%

" 0.00% 0.00% 10.""% 10.""% 15.31%

5 0.00% 0.00% 0.00% 10.""% 15.31%

! 0.00% 0.00% 0.00% 0.00% 15.31%

0.00% 0.00% 0.00% 0.00% 0.00%

8 0.00% 0.00% 0.00% 0.00% 0.00%

# 0.00% 0.00% 0.00% 0.00% 0.00%

10 0.00% 0.00% 0.00% 0.00% 0.00%

11 0.00% 0.00% 0.00% 0.00% 0.00%

12 0.00% 0.00% 0.00% 0.00% 0.00%13 0.00% 0.00% 0.00% 0.00% 0.00%

1" 0.00% 0.00% 0.00% 0.00% 0.00%

15 0.00% 0.00% 0.00% 0.00% 0.00%

1! 0.00% 0.00% 0.00% 0.00% 0.00%

1 0.00% 0.00% 0.00% 0.00% 0.00%

18 0.00% 0.00% 0.00% 0.00% 0.00%

1# 0.00% 0.00% 0.00% 0.00% 0.00%

20 0.00% 0.00% 0.00% 0.00% 0.00%

21 0.00% 0.00% 0.00% 0.00% 0.00%

22 0.00% 0.00% 0.00% 0.00% 0.00%23 0.00% 0.00% 0.00% 0.00% 0.00%


65/593

2" 0.00% 0.00% 0.00% 0.00% 0.00%

25 0.00% 0.00% 0.00% 0.00% 0.00%

2! 0.00% 0.00% 0.00% 0.00% 0.00%

2 0.00% 0.00% 0.00% 0.00% 0.00%

28 0.00% 0.00% 0.00% 0.00% 0.00%

2# 0.00% 0.00% 0.00% 0.00% 0.00%

30 0.00% 0.00% 0.00% 0.00% 0.00%

31 0.00% 0.00% 0.00% 0.00% 0.00%

32 0.00% 0.00% 0.00% 0.00% 0.00%

33 0.00% 0.00% 0.00% 0.00% 0.00%

3" 0.00% 0.00% 0.00% 0.00% 0.00%

35 0.00% 0.00% 0.00% 0.00% 0.00%

3! 0.00% 0.00% 0.00% 0.00% 0.00%

3 0.00% 0.00% 0.00% 0.00% 0.00%

38 0.00% 0.00% 0.00% 0.00% 0.00%

3# 0.00% 0.00% 0.00% 0.00% 0.00%

"0 0.00% 0.00% 0.00% 0.00% 0.00%

"1 0.00% 0.00% 0.00% 0.00% 0.00%

"2 0.00% 0.00% 0.00% 0.00% 0.00%

"3 0.00% 0.00% 0.00% 0.00% 0.00%

"" 0.00% 0.00% 0.00% 0.00% 0.00%

"5 0.00% 0.00% 0.00% 0.00% 0.00%

"! 0.00% 0.00% 0.00% 0.00% 0.00%

" 0.00% 0.00% 0.00% 0.00% 0.00%

"8 0.00% 0.00% 0.00% 0.00% 0.00%

"# 0.00% 0.00% 0.00% 0.00% 0.00%

50 0.00% 0.00% 0.00% 0.00% 0.00%

0

0.00

&arterl% rate tree /it$ no smile

0 1 2 3 " 5

1 3.55% 3.8#3% ".0"51% ".3"2% ".012% 5.!00!%

2 0.000% 3."13!% 3.!""1% 3.#1!2% ".2352% ".805"%3 0.000% 0.0000% 3.282#% 3.5280% 3.8153% ".1231%

" 0.000% 0.0000% 0.0000% 3.182% 3."31% 3.53%

5 0.000% 0.0000% 0.0000% 0.0000% 3.0#!3% 3.035"%

! 0.000% 0.0000% 0.0000% 0.0000% 0.0000% 2.!0""%

0.000% 0.0000% 0.0000% 0.0000% 0.0000% 0.0000%

8 0.000% 0.0000% 0.0000% 0.0000% 0.0000% 0.0000%

# 0.000% 0.0000% 0.0000% 0.0000% 0.0000% 0.0000%

10 0.000% 0.0000% 0.0000% 0.0000% 0.0000% 0.0000%

11 0.000% 0.0000% 0.0000% 0.0000% 0.0000% 0.0000%

12 0.000% 0.0000% 0.0000% 0.0000% 0.0000% 0.0000%13 0.000% 0.0000% 0.0000% 0.0000% 0.0000% 0.0000%


66/593

1" 0.000% 0.0000% 0.0000% 0.0000% 0.0000% 0.0000%

15 0.000% 0.0000% 0.0000% 0.0000% 0.0000% 0.0000%

1! 0.000% 0.0000% 0.0000% 0.0000% 0.0000% 0.0000%

1 0.000% 0.0000% 0.0000% 0.0000% 0.0000% 0.0000%

18 0.000% 0.0000% 0.0000% 0.0000% 0.0000% 0.0000%

1# 0.000% 0.0000% 0.0000% 0.0000% 0.0000% 0.0000%

20 0.000% 0.0000% 0.0000% 0.0000% 0.0000% 0.0000%

21 0.000% 0.0000% 0.0000% 0.0000% 0.0000% 0.0000%

22 0.000% 0.0000% 0.0000% 0.0000% 0.0000% 0.0000%

23 0.000% 0.0000% 0.0000% 0.0000% 0.0000% 0.0000%

2" 0.000% 0.0000% 0.0000% 0.0000% 0.0000% 0.0000%

25 0.000% 0.0000% 0.0000% 0.0000% 0.0000% 0.0000%

2! 0.000% 0.0000% 0.0000% 0.0000% 0.0000% 0.0000%

2 0.000% 0.0000% 0.0000% 0.0000% 0.0000% 0.0000%

28 0.000% 0.0000% 0.0000% 0.0000% 0.0000% 0.0000%

2# 0.000% 0.0000% 0.0000% 0.0000% 0.0000% 0.0000%

30 0.000% 0.0000% 0.0000% 0.0000% 0.0000% 0.0000%

31 0.000% 0.0000% 0.0000% 0.0000% 0.0000% 0.0000%

32 0.000% 0.0000% 0.0000% 0.0000% 0.0000% 0.0000%

33 0.000% 0.0000% 0.0000% 0.0000% 0.0000% 0.0000%

3" 0.000% 0.0000% 0.0000% 0.0000% 0.0000% 0.0000%

35 0.000% 0.0000% 0.0000% 0.0000% 0.0000% 0.0000%

3! 0.000% 0.0000% 0.0000% 0.0000% 0.0000% 0.0000%

3 0.000% 0.0000% 0.0000% 0.0000% 0.0000% 0.0000%

38 0.000% 0.0000% 0.0000% 0.0000% 0.0000% 0.00

ch 11.67 bdt with a smile

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