ARE VOLATILITY EXPECTATIONS CHARACTERIZED BY REGIME SHIFTS? EVIDENCE FROM IMPLIED VOLATILITY INDICES



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
δ
2
β

-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
γ
2
φφ
φ
2

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
β
= β2

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 +δiv 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 +δivt-1 + βirt-1 + γi rt2-1 +ζt      for Model 4, and

vt = wi + δivt-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 as
χ2(1) . LL refers to the log maximum likelihood function.

25



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