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+KK>FYã1,-9>F²02;+ <DZ&s31%9).1FY8¦.¸0 6*>)m1sZ(9F²0(¦F²+ãn8*3[Z8®.1+)(*Jm137?Y.C)FY?YFE×M+)@£FY?Y 6/?Y?Üc;p1p 9 <H Z&;?Y?
ãn8*3[Z8M-9>FY0 FY89\+)K>.CK \1×MFY+]K3¡?Y;.;m1,3789314)(*31-9)FE378/+G376*.189:j)(9;8¦:* K >@«FY8*')(*'m137?Y.C)F²?YFEÁ×
+)@£F²?E\7FEm1;8¸%l×£)(*31)(* >]31-9)FE3789+ Hä 4
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0.19
0.19
0.185
0.185
Implied volatilities at t=60
Implied volatilities at t=50
0.18
0.175
0.17
0.165
2900
0.18
0.175
0.17
3000
3100
3200
0.165
2900
3300
Strike prices
3000
3100
3200
3300
Strike prices
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X (*31-9)FE378,mx.1?Y69c - :9.;×n+A?².CK >502378*Ø/>@B;:)(/FY+u(b×b-31)(*;+FY+ H â+K)FY@£.CK;+A31%9).1FY89;:ZFE)(J.-D.C>))FY0 ?E
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Implied volatility distributions at t=180
0.19
0.18
0.17
0.16
0.15
0.14
0.13
2900
2950
3000
3050
3100
3150
3200
3250
3300
3350
3400
3450
Strike prices
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m137?Y.C)FY?²FEÁ×à+@£FY?EoFY89:9F²0 .CK;+,)(9.CB)(9¸31-/)FE378 ZFE)( +KK>FEã1o-9>F²02¡;al69.1?&K3 , h1h FY+6989:* >)Ùf-9>FY02;:
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6989:9 >KÙf-9>FY02;: H ï537+KK >FY31>¡@B;.18Ú;+))FY@£.CK;+£31%/).1FY8*;:ÚZFY)(Ú=&?².10)ãbÙ n0(*37?Y;+«@B3n:*;?G.189:Ú-D.C>))FY0 ?E
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X (9MÁ×l-¦314'-9>);:/FY02)FE3789+B31%/).1FY8*;:µZFE)(Ú)(*¶Ý89+02;8`K;:Õï.C>))FY0 ?E¶ß5F²?EK >£Z& >)®m1 >×µ0 ?E37+K
,
0.17
Actual price
Prediction
Call price
0.16
0.15
0.14
0.13
0.12
0.11
0.1
20
22
24
26
28
30
32
34
36
38
0.06
Actual price
Prediction
Put price
0.05
0.04
0.03
0.02
0.01
0
10
15
20
25
30
35
40
45
Time (days)
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31-9)FE378 * +u-9>FY02;+ZFE)(02378*ØD:*;8902
FY8bK >)mC.1?Y+ h£+K).18/:9.C>:j:* mnFY.C)FE3789+ H
K3M)(*£@£;.1+)6*>);::9.C).¦.1+' mlF²:*;8902;:%l×®ßFE\76*>«p H ß5FY\76*>)jc - +)(*3Z+')(*B;+))FY@£.CK;:m137?Y.C)F²?YFEÁ×
.189:ªFY8`K >;+K>.CK¸4}31>s.¦02378bK>.102sZFE)(Û.®+KK>FEã1¡-9>FY02B314 , h1h H ï?E31)+314])(*¡ m137?Y6*)FE378à314G)(*
-9>)31%D.C%/FY?YFE×M:9FY+KK>_FE%/6*)FE378/+314&)(*£FY8bK >);+K'>.CK«.18/:ám137?Y.C)FY?YFE×®.C>)£:9 -/FY02K;:FY8ßFE\76*>;+Bc1c£.189:
c;h H
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@B )(*3n:s378.-D.1FE>A314D31-9)FE3789+5ZFY)(J+KK>_FEã1-/>FY02Gh1p1h HX (*]8*31>@£.1?YF ;:J+)al69.C>)& >)>)31>_+5.C>]:9 Ø/8*;:
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´ È Í
Ñ
´ È Í
Ñ
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FY8 ;.10_(µ-/.C>))F²0 ?EjØ/?EK > HÚX (/FY+s).C%/?EM+)(*3Z+B)(9.C <])(9F²+)FY@Bj%31)( )(*¦âÞß .189:µÝÞß ?E;: K3
,:9
−3
Interest rate
14
x 10
12
10
8
6
4
0
50
100
150
200
250
0
50
100
150
200
250
0.21
Volatility
0.2
0.19
0.18
0.17
0.16
0.15
0.14
Time (days)
p(rt|S0:t,tm,C0:t,P0:t)
ßFE\76*>)£c - ;&âÜ+K)FY@«.CK;:MFY8bK >);+KG>.CKs.189:om137?Y.C)FY?YFYÁ× H
0.4
0.2
0
200
150
0.02
100
0.015
0.01
50
0.005
Time (t)
0
rt
0
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,
p(σt|S0:t,tm,C0:t,P0:t)
1
0.5
0
200
150
0.25
100
0.2
50
0.15
Time (t)
0
σ
0.1
t
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