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Working Papers Series
Testing the Stability of Implied
Probability Density Functions
By: Robert R. Bliss and Nicolaos
Panigirtzoglou
Working Papers Series
Research Department
WP 99-21
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Figure 1: The effect of Price Perturbations on Implied Volatility
(Tick size = 0.01)
1.6
1.4
1.0
At-the-money
(+ or - 1/2 tick)
Call Price
1.2
0.8
0.6
0.4
0.2
0.0
6
7
8
9
8
9
Strike Price
0.16
At-the-money
Implied Volatility
(at original and perturbed prices)
0.18
0.14
0.12
0.10
6
7
Strike Price
Figure 2a: Short Sterling Option Cross-Sections
1.0
Time to Expiry (Year)
0.8
0.6
0.4
0.2
0.0
J
F
M
A
M
J
J
A
S
O
N
D
N
D
Quote Date (1997)
Figure 2b: FTSE 100 Option Cross-Sections
1.0
Time to Expiry (Year)
0.8
0.6
0.4
0.2
0.0
J
F
M
A
M
J
J
Quote Date (1997)
A
S
O
Figure 3: Comparison of SML and DLN Summary Statistics
FTSE 100 VOFs
Short Sterling VOFs
Corr = 0.726
Corr = 0.094
e0
Smoothed IV Smile
Smoothed IV Smile
e3
e-1
e-2
e2
e1
e-3
e0
e-4
e-1
e-4
e-3
e-2
e-1
e0
e-1
FTSE 100 Skew1
e1
e2
e3
Short Sterling Skew1
2.0
Corr = 0.378
Corr = 0.710
1
e0
1.5
Smoothed IV Smile
Smoothed IV Smile
0
-1
-2
-3
1.0
0.5
0.0
-0.5
-4
-1.0
-5
-5
-4
-3
-2
-1
0
-1.5
-1.5
1
FTSE 100 Kurtosis
0.0
0.5
1.0
1.5
2.0
Corr = 0.377
50
25
10
-0.5
Short Sterling Kurtosis
55
Corr = 0.501
Smoothed IV Smile
Smoothed IV Smile
100
-1.0
20
15
10
5
0
1
1
10
Double-Lognormal
100
0
5
10
15
20
Double-Lognormal
2550 55
Figure 4: Comparison of Day-to-Day Changes in SML and DLN Summary Statistics
FTSE 100 Skew1
1.0
Short Sterling Skew1
1.0
Corr = 0.278
Corr = 0.136
0.5
Smoothed IV Smile
Smoothed IV Smile
0.5
0.0
-0.5
0.0
-0.5
-1.0
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
-1.0
-2.0
2.0
FTSE 100 Kurtosis
3
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
Short Sterling Kurtosis
4
Corr = 0.181
Corr = 0.329
3
2
Smoothed IV Smile
Smoothed IV Smile
2
1
0
-1
1
0
-1
-2
-2
-3
-3
-4
-6
-4
-2
0
2
4
6
-10
FTSE 100 X01
-8
-6
-4
-2
0
2
4
6
8
10
Short Sterling X01
1.0
Corr = 0.013
Corr = 0.393
400
Smoothed IV Smile
Smoothed IV Smile
0.5
200
0
-200
0.0
-0.5
-400
-1000 -800 -600 -400 -200
0
200 400 600 800 1000
Double-Lognormal
-1.0
-1.5
-1.0
-0.5
0.0
0.5
Double-Lognormal
1.0
1.5
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