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sample path of eta
1
1
0.8
0.9
0.6
0.8
0.7
0.4
0
2
4
6
histogram of beta
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0.2
10
15000
10000
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0.8
0.9
acf plot of beta
0
0.2
1
1
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0.5
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0
0
0
0.5
1
1.5
2
2
4
6
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2.5
0
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0.6
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0.5
1
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15000
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0.7
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2
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1.6
1.5
1.4
1.3
1.2
1.1
1
0
1000
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Estimators of log−volatilities
−2
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−10
−12
−14
0
50
100
150
200
250
300
350
400
450
500
350
400
450
500
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−2
−4
−6
−8
−10
−12
−14
0
50
100
150
200
250
300
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3000
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0
−0.1
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0.1
0.2
0.3
0.4
0.5
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0.6
0.7
0.8
0.9
3000
2000
1000
0
0.4
0.5
0.6
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0.8
0.9
1
0.75
0.8
0.85
0.9
0.95
1
4000
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0.7
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3500
3000
4000
2500
3000
2000
2000
1500
1000
1000
0
−0.5
500
0
0.5
1
0
0.4
1.5
0.6
0.8
T=300
3500
3000
3000
2500
2500
2000
2000
1500
1500
1000
1000
500
500
0.7
0.8
0.9
1.2
1.4
T=500
3500
0
0.6
1
1
0
0.7
1.1
0.8
Ñ25®@<?iB8k=ȧ’h25A]J_Ne®eiB>@‰ˆ?^5N@JBA“N@P ²
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Ózp
0.9
1
T=50, historical
T=100, historical
5000
3000
4000
2500
2000
3000
1500
2000
1000
1000
0
500
−1
−0.5
0
0.5
0
1
0
0.2
T=50, combined
0.4
0.6
0.8
1
0.8
1
T=100, combined
5000
3000
4000
2500
2000
3000
1500
2000
1000
1000
0
500
−1
−0.5
0
0.5
0
1
0
0.2
T=200, historical
0.4
0.6
T=500, historical
3000
3500
2500
3000
2500
2000
2000
1500
1500
1000
1000
500
0
500
0.6
0.8
0
0.75
1
0.8
T=200, combined
0.85
0.9
0.95
1
0.95
1
T=500, combined
3000
3500
2500
3000
2500
2000
2000
1500
1500
1000
1000
500
0
500
0.6
0.8
0
0.75
1
0.8
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k@Z
0.85
0.9
−4
−6
−8
−10
−12
−14
0
50
100
150
200
250
300
350
400
450
500
0
50
100
150
200
250
300
350
400
450
500
−4
−6
−8
−10
−12
Ñ25®@<?iB8ŽXOÈ:'N@‰ ˆ}>KiB25AjNe4&N@P ceNe^5>KJ_2V^52VJGŒ8AjJ_2V‰l>nJ_25N@4
0.0295
0.029
0.0285
Implied Vol
−14
0.028
0.0275
0.027
100
105
110
115
120
125
Strike Price
130
135
140
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kOW
145