Transcript VOLATILITY FORECASTING

VOLATILITY FORECASTING
Global Investment Management
Steven Poher
Ramzi Rached
Ricardo Uribe
Dongting Zheng
AGENDA
• Objective
• Background Information
• Forecasting Models
• Data set
• Methodology
• Results
• Conclusion
OBJECTIVE
• Objective
• To establish a variance forecasting model
• Why?
• Important for risk managers (VaR)
• Used to price options
• Volatility + Return = investment
decision
BACKGROUND INFORMATION
• Realized / observed volatility is measured by
squared returns
• Volatility displays a positive correlation
with its own past
• Simple Model
1 m 2
 t 1   R t 1
m  1
2
• PB : Equal weights on the past m
observations
FORECASTING MODELS
• More flexible model  Simple GARCH or
GARCH (1,1)
 2t 1    Rt 2    t 2
• Extended to Local and Global
Instruments

•
2
t 1
    Rt    t  i 1 ( iL ZiL   iG ZiG )
2
2
n
Models to be tested for this project
1.
2.
3.
4.
GARCH
GARCH
GARCH
GARCH
(1,1)
(1,1) + Local
(1,1) + Global
(1,1) + Local + Global
DATA SET
• Source
• Period
• Granularity
DataStream
3/27/1998 - 3/28/2008 (10 years)
1 day
Country
Index
NIKKEI 225
CAC 40
DAX 30
FTSE 100
S&P 500
DATA SET
• Local Instruments
• Change in Exchange Rates
• EUR / USD / JPY / GBP
• Change in short-term interest rates
• T-Bill (US) / BTAN (FR)
• Global Instruments
• Change in Short-term Eurodollar rate
• Change in the Term Structure spread
METHODOLOGY
• Using EXCEL, test our 4 models for each of our 5 markets
• Use Maximum Likelihood Estimation (MLE) to estimate  /
 /  /  EXCEL Solver
• Test the models using a regression of Squared Returns vs.
Forecasted Variance
• Discuss the statistical significance of the regression /
Select the best model for a given country
METHODOLOGY - EXAMPLE
GR
Estimating GARCH(1,1) w ith Local and Global Instrum ents - German Market
DATE
GERMANY
DAX 30
% Change in Ū/£ Term Structure
Exchange Rate
Spread
Return
Squared
Returns
Conditional
Variance
Likelihood
Wi thout Vari ance Targeti ng
Mar 27, 98
5,438.86
Mar 30, 98
Mar 31, 98
5,311.90
5,396.16
0.44%
0.04%
0.24%
0.24%
-2.36%
1.57%
0.000558
0.000248
0.000238
0.000265
2.080044
2.731626
Apr 01, 98
Apr 02, 98
5,450.07
5,475.79
-0.03%
-0.37%
0.24%
0.24%
0.99%
0.47%
0.000099
0.000022
0.000261
0.000246
3.016659
3.191489
Apr 03, 98
Apr 06, 98
Apr 07, 98
Apr 08, 98
Apr 09, 98
Apr 10, 98
Apr 13, 98
Apr 14, 98
Apr 15, 98
Apr 16, 98
Apr 17, 98
Apr 20, 98
Apr 21, 98
Apr 22, 98
Apr 23, 98
Apr 24, 98
Apr 27, 98
Apr 28, 98
Apr 29, 98
Apr 30, 98
May 01, 98
May 04, 98
May 05, 98
May 06, 98
5,530.61
5,595.27
5,697.96
5,649.06
5,721.73
5,721.73
5,704.71
5,828.16
5,864.82
5,760.89
5,701.19
5,905.46
5,886.94
5,851.94
5,710.36
5,604.24
5,560.93
5,467.96
5,570.09
5,566.62
5,614.38
5,834.77
5,772.30
5,796.04
-0.45%
-0.18%
0.14%
-0.56%
0.02%
0.00%
0.00%
-0.11%
-0.18%
0.75%
-0.47%
-0.55%
-0.72%
0.07%
-0.17%
-0.05%
-0.08%
0.12%
0.16%
0.08%
-1.09%
0.00%
-0.64%
-0.23%
0.24%
0.25%
0.25%
0.25%
0.25%
0.25%
0.25%
0.25%
0.25%
0.25%
0.25%
0.22%
0.22%
0.22%
0.22%
0.22%
0.27%
0.27%
0.27%
0.27%
0.27%
0.30%
0.30%
0.30%
1.00%
1.16%
1.82%
-0.86%
1.28%
0.00%
-0.30%
2.14%
0.63%
-1.79%
-1.04%
3.52%
-0.31%
-0.60%
-2.45%
-1.88%
-0.78%
-1.69%
1.85%
-0.06%
0.85%
3.85%
-1.08%
0.41%
0.000099
0.000135
0.000331
0.000074
0.000163
0.000000
0.000009
0.000458
0.000039
0.000320
0.000109
0.001239
0.000010
0.000036
0.000600
0.000352
0.000060
0.000284
0.000342
0.000000
0.000073
0.001483
0.000116
0.000017
0.000226
0.000216
0.000208
0.000218
0.000207
0.000202
0.000184
0.000168
0.000192
0.000179
0.000195
0.000189
0.000279
0.000259
0.000238
0.000268
0.000273
0.000253
0.000254
0.000259
0.000236
0.000232
0.000336
0.000318
3.058406
2.988255
2.525438
3.126785
2.927757
3.334149
3.357209
2.064456
3.257141
2.501362
3.074001
0.087533
3.154881
3.141278
1.994152
2.536585
3.074337
2.660274
2.545737
3.208788
3.102717
0.067145
2.908149
3.081275





MLE
R2
F Stati stic
0.084361
0.901481
0.000002
0.095203
0.000242
7,532.98
0.1556
480.62
RESULTS
Best models for each country
Country
Model
GARCH + % Change in Term Structure
Spread (G)
R2
1.21 %
GARCH + % Change in €/£ (L)
14.12 %
GARCH + % Change in €/£ (L) + %
Change in Term Structure Spread (G)
15.56 %
GARCH (1,1) + % Change in $/£ (L) +
% Change in ST Eurodollar (G)
14.23 %
GARCH
10.58 %
RESULTS
• Best model for German Market
• R2 of 15.56%
• Final equation
• Simple GARCH +
• % Change in €/£ Exchange (L) +
• % Change in Term Structure Spread (G)
 2 t 1  0.000002  0.084361Rt 2  0.901481 t 2  0.095203L 3  0.000242 Z G 1
RESULTS
DE MARKET - SIMPLE GARCH + Ū/£ + Term Structure Spread
0.0024
Realized
Forecasts
0.0020
0.0016
0.0012
0.0008
0.0004
0.0000
Mar
98
Sep
98
Mar
99
Sep
99
Mar
00
Sep
00
Mar
01
Sep
01
Mar
02
Sep
02
Mar
03
Sep
03
Mar
04
Sep
04
Mar
05
Sep
05
Mar
06
Sep
06
Mar
07
Sep
07
CONCLUSION
• No universal model
• Different countries = different models
• Good proxy for DE / Bad for JP
• GARCH could also be extended
• Leverage effects
• Day-of-week effects
• Jumps
• Economic intuition & reality check
QUESTIONS?
THANK YOU