A Comparative Study of VaR Estimation for Structured Products
Table 4
Daily VaRs of selected time series models for alternative notes during various periods.
Time series model
The whole period
The low oil period
The high oil period
VaR
VaR
VaR
Panel A: RUD notes
AR()-ARCH(5)
0.000084
0.000052
0.000088
0.000121
0.000283
0.000033
AR()-GARCH(1,1)
0.000101
0.000038
0.000265
0.000124
0.000247
0.000017
AR()-GARCH(1,4)
0.000041
0.000041
0.000212
0.000106
0.000252
0.000018
AR()-EGARCH(1,1)
0.000512
0.000036
0.000312
0.000115
0.000502
0.000016
Panel B: SPO notes
AR()-ARCH(5)
0.000512
0.000541
0.000112
0.000112
0.000412
0.000211
AR()-GARCH(1,1)
0.000426
0.000521
0.000312
0.000512
0.000408
0.000312
AR()-GARCH(2,5)
0.000451
0.000212
0.000122
0.000552
0.000410
0.000224
AR()-EGARCH(1,1)
0.000554
0.000312
0.000613
0.000126
0.000511
0.000266
Panel C: DJQ notes
AR()-ARCH(5)
0.000405
0.000062
0.000056
0.000460
0.000671
0.000056
AR()-GARCH(2,1)
0.000311
0.000094
0.000013
0.000049
0.000524
0.000085
AR()-GARCH(2,5)
0.000377
0.000093
0.000086
0.000033
0.000495
0.000074
AR()-EGARCH(2,1)
0.000293
0.000110
0.000366
0.000038
0.000505
0.000092
AR()-EGARCH(2,2)
0.000364
0.000095
0.000258
0.000040
0.000536
0.000096
Note that the VaRs are for a one-day-ahead horizon and a 99% confidence level for losses. and denote the expected value and the forecast variance of asset returns over a one-period horizon, respectively.
