Table 5. Table 4. Regime-switching modelling for changes in implied volatility
____________________________(Nikkei 225 index)____________________________
Model 1 |
Model 2 |
Model 3 |
Model 4 |
Model 5 | |
w1 |
0.0047 |
Model Parameters -0.3498a -0.1257a |
1.2607a |
I 2.0495a | |
w 2 |
-3.4197a |
-0.0030 |
6.9409a |
-0.1317a |
-0.1290a |
δ |
-0.0112 |
-0.6558a -0.1233a -6.3270a -0.3312a |
-1.4394a -0.1352a 4.5286a |
-1.7631a -0.1145a 5.6178a | |
β2 |
-7.2362a |
-0.0434a |
6.8867a |
-0.3435a |
-0.3132a |
Y W1 = w 2 |
1248.3519a |
3.9584a -164.8804a Hypothesis Tests 14.4029a 5711.6400a |
61.5712a 4.9217a 295.9666a |
12.1322a 4.4534a -2.7179a 0.0274a 338.6405a | |
δ = δ |
9520.5489a |
318.7542a 6397.2327a 13819.9404a |
2294.9900a 6756.7345a |
2630.6941a 7119.3876a | |
Y1 = γ 2 φφ = φ2 P11 = P 22 |
2.0749 |
4639.8593a 43.6718a 33.1734a |
523.5600a 162.7422a |
3.1972c 1574.2915a 102.2636a | |
LL |
10855.93 |
10930.50 |
11133.54 |
11183.11 |
11209.71 |
Notes: Significance at the 1, 5 and 10 % level is denoted by a, b and c respectively.
The estimated Markov regime-switching models are represented
by ∆v = wi + βir 1 +ζ for Model 1, ∆v = wi +δi∆v 1 +βir 1 +ζ for
t i i t -1 t t i i t -1 i t -1 t
Model 2, ∆vt = wi + βirt-1 + γi rt2-1 +ζt for Model 3,
∆vt = wi +δi∆vt-1 + βirt-1 + γi rt2-1 +ζt for Model 4, and
∆vt = wi + δi∆vt-1 + βirt-1 + γirt-1 + φi∆σrt-1 + ζt for Model 5. The model
parameters w and σe are scaled by 102. The null hypothesis tests are
distributed asχ2(1) . LL refers to the log maximum likelihood function.
25
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