1. By: Andrey Fradkin Date: 1/22/08
The Informational Content of Implied Volatility in Individual Stocks and the Market
By: Andrey Fradkin
Date: 1/22/08

2. Andrey Fradkin: Informational Content of Volatility
Introduction
Examine relative informational content of implied volatility forecasts against historical volatility forecasts using high frequency data for 10 large cap stocks trading on NYSE and for the SPY.
Important prior studies on this subject are Andersen et al(2007) and Jiang and Tian(2006). Find contradictory evidence as to which measure is better.
This study is first to use individual stocks, HAR-RV CJ model, RAV, and robust regression in examining this question.
HAR-RV-CJ model allows for the separation of the jump component of variance from continuous component of volatility.
Andrey Fradkin: Informational Content of Volatility

3. Andrey Fradkin: Informational Content of Volatility
Outline
Jump Detection
HAR-RV-CJ Models
Data Preparation
Summary Statistics
Summary Plots
Significance of Jump Statistics in HAR-RV-CJ Models
Andrey Fradkin: Informational Content of Volatility

4. Background Mathematics
Andrey Fradkin
1/31/2007
Background Mathematics
Realized Variation:
Realized Bi-Power Variation:
Andrey Fradkin: Informational Content of Volatility

5. Background Mathematics Part 2
Andrey Fradkin
1/31/2007
Background Mathematics Part 2
Tri-Power Quarticity
Quad-Power Quarticity
Andrey Fradkin: Informational Content of Volatility

6. Background Mathematics Part 3
Andrey Fradkin
1/31/2007
Background Mathematics Part 3
Z-statistics (max version) – Paper uses .999 significance level
Andrey Fradkin: Informational Content of Volatility

7. Andrey Fradkin: Informational Content of Volatility
1/31/2007
Original HAR-RV-J Model (Developed in Andersen, Bollerslev, Diebold 2006, Extended for use with RAV measure in Forsberg and Ghysels(2007))
Andrey Fradkin: Informational Content of Volatility

8. Andrey Fradkin: Informational Content of Volatility
1/31/2007
The HAR-RV-CJ Model
Andrey Fradkin: Informational Content of Volatility

9. Mincer-Zarnowitz Regressions
Standard framework for evaluating implied volatility forecasts.
Implied volatilities are obtained from the OptionMetrics database. One implied volatility is used per day. This implied volatility is taken from an at-the-money call option expiring about a month ahead.
Andrey Fradkin: Informational Content of Volatility

10. Andrey Fradkin: Informational Content of Volatility
Combined Regressions
Combine implied forecasts with historical forecasts.
Compare marginal improvements from historical to combined and from implied to combined.
Two types of combined forecasts, one using RAV and the other using RV-CJ
Andrey Fradkin: Informational Content of Volatility

11. Andrey Fradkin: Informational Content of Volatility
Combined Regressions
Andrey Fradkin: Informational Content of Volatility

12. Andrey Fradkin: Informational Content of Volatility
Data Management
Uses TAQ high-frequency data that was cleaned by Tzuo Law. Prices are sampled at five minute intervals.
10 equities and the SPY are used in the study. Equities chosen are based on the high open interest in their options.
In-Sample data ranges from 2001 through 2004
The Out-of-Sample data encompasses all of 2005
Andrey Fradkin: Informational Content of Volatility

13. 10 Stocks Referred to from now on by Ticker
BMY - Bristol-Meyers
C - Citigroup
GE - General Electric
GS -Goldman Sachs
HD - Home Depot
KO – Coca Cola
MDT - Medtronic
MOT – Motorola
NOK – Nokia
TXN – Texas Instruments
SPY – SPY RV’s with Vix Implied Volatility
SPX – SPY RV’s with SPX Option Implied Volatility
Andrey Fradkin: Informational Content of Volatility

14. Andrey Fradkin: Informational Content of Volatility
Summary Statistics
Variable
Mean
Std. Dev.
Min
Max rv
3.17
4.11
0.27
45.28
imp vol
4.04
3.25
0.45
21.27
BMY
rav
1.42
0.73
0.44
6.32
jump
0.04
0.00
6.70
2.98
5.26
0.17
97.38
3.60
3.40
0.10
34.81
Citigroup
1.39
0.84
0.30
9.29
0.02
0.21
5.90
2.65
3.69
0.11
53.55
3.54
2.92
0.40
17.24 GE
1.34
0.75
0.23
6.21
0.01
4.29
2.54
2.88
39.50
4.30
3.35
0.80
20.99 GS
1.36
0.61
4.58
0.03
0.70
24.09
3.26
4.01
50.42
4.43
3.42
1.00
20.56 HD
1.49
0.74
0.26
6.06
0.24
4.83
Andrey Fradkin: Informational Content of Volatility

15. Andrey Fradkin: Informational Content of Volatility
Variable
Mean
Std. Dev.
Min
Max rv
1.69
1.90
0.15
25.48
imp vol
2.13
1.56
0.29
11.41 KO
rav
1.11
0.49
0.25
4.98
jump
0.02
0.18
0.00
4.18
2.24
2.70
0.22
34.90
2.89
1.86
0.59
12.29
MDT
1.23
0.57
0.30
5.40
0.05
0.56
17.33
6.99
8.89
0.34
175.37
9.90
7.18
1.17
46.31
MOT
2.17
1.04
0.41
10.05
0.09
0.80
19.92
4.17
0.20
43.54
9.21
6.86
1.38
38.54
NOK
0.91
0.32
6.41
0.04
0.65
21.50
7.80
8.35
0.51
62.92
10.14
7.10
1.39
41.08
TXN
2.33
1.14
8.07
0.12
0.90
17.12
1.03
1.30
16.25
1.89
0.42
8.06
SPY
0.85
0.43
0.16
3.54
0.01
0.23
7.94
Andrey Fradkin: Informational Content of Volatility

16. HAR-RV-CJ – Level Month Ahead – Newey-West Standard Errors Lag(60)
BMY C GE GS HD KO
MDT
MOT
NOK
TXN
SPY
SPX cv
0.075**
0.148***
0.121***
0.153***
0.172***
0.184**
0.108**
0.081*
0.156***
0.152***
(0.03)
(0.02)
(0.04)
(0.06) c5
0.449***
0.125
0.256*
0.257**
0.266**
0.171*
0.338**
0.313***
0.398***
0.439***
0.328***
(0.13)
(0.08)
(0.11)
(0.09)
(0.12)
(0.05)
(0.10)
(0.07)
c22
0.236
0.348***
0.277**
0.407***
0.191**
0.333***
0.214
0.260**
0.242**
0.112
0.212*** j
0.117
0.378**
0.237
-0.064***
0.013
0.185**
-0.094**
0.034
0.052
0.15
-0.135***
(0.29)
(0.01)
(0.17) j5
-1.284
-0.052
1.472
-0.148
3.444*
0.876
0.509*
-0.507
-0.590*
-0.631
-0.424**
(1.11)
(1.08)
(2.23)
(1.63)
(0.56)
(0.20)
(0.42)
(0.30)
(0.85)
(0.15)
j22
8.317
1.388
5.596
-1.300***
3.114
-1.945**
2.380***
2.72
-0.684
4.908
0.046
(6.47)
(2.64)
(10.78)
(0.18)
(4.72)
(0.59)
(0.35)
(1.76)
(0.60)
(3.88)
(1.00)
Constant
0.500*
1.065**
0.797**
0.454**
0.996**
0.532**
0.633***
2.187**
0.821**
1.732**
0.326**
(0.21)
(0.41)
(0.28)
(0.16)
(0.71)
(0.31)
(0.61)
* p<0.05, ** p<0.01, *** p<0.001
Andrey Fradkin: Informational Content of Volatility

17. HAR-RV-CJ – 1 week Newey-West Standard Errors Lag(60)
BMY C GE GS HD KO
MDT
MOT
NOK
TXN
SPY
SPX c
0.097***
0.296***
0.190***
0.257***
0.245***
0.318**
0.132**
0.104*
0.192**
0.186***
0.208** c5
0.499***
0.161*
0.317***
0.259***
0.455***
0.325**
0.553***
0.501***
0.468***
0.544***
0.447***
c22
0.286**
0.326***
0.299***
0.423***
0.107
0.192*
0.154
0.217*
0.263**
0.15
0.211** j
0.315**
0.884*
-0.09
-0.143***
-0.039
0.329**
-0.204***
0.015
0.166***
0.336
-0.177** j5
-0.271
-0.008
2.994*
-0.244**
0.671
0.719
0.423
0.493
-0.684*
-0.606
-0.617***
j22
2.491
-0.299
3.539
-0.678*
6.846
-0.669
1.413***
0.034
-0.78
1.83
-0.167
Constant
0.289*
0.634*
0.416*
0.189
0.422**
0.279**
0.314***
1.235**
0.365*
0.802**
0.159**
Andrey Fradkin: Informational Content of Volatility

18. HAR-RV-CJ – Level Day Ahead – Newey-West Standard Errors Lag(60)
BMY C GE GS HD KO
MDT
MOT
NOK
TXN
SPY
SPX c
0.155***
0.576***
0.326***
0.550***
0.352***
0.349*
0.116
0.082
0.394***
0.329 c5
0.485***
0.084
0.307***
0.096
0.447***
0.448***
0.627***
0.579***
0.359*
0.355***
0.400*
c22
0.278**
0.221***
0.244***
0.339**
0.086
0.105
0.15
0.217*
0.250*
0.181*
0.202* j
0.575*
0.600**
1.583
-0.024
-0.821***
-0.062
-0.372***
0.443**
0.387***
0.616
-0.249 j5
0.305
1.351*
-0.965
-0.482***
1.308
1.289***
0.278
-0.051
-0.415
-0.091
-0.541**
j22
0.84
-0.392
4.057
-0.374
4.76
-0.584*
1.210***
0.119
-0.793
0.852
-0.287
Constant
0.213*
0.330*
0.259*
0.078
0.238*
0.167**
0.224***
0.857**
0.209*
0.463**
0.097**
Andrey Fradkin: Informational Content of Volatility

19. Realized Variance and IV
Andrey Fradkin: Informational Content of Volatility

20. Realized Variance and RAV
Andrey Fradkin: Informational Content of Volatility

21. Andrey Fradkin: Informational Content of Volatility
SPY RV and RAV
Andrey Fradkin: Informational Content of Volatility