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



Table 2. Regime-switching modelling of implied volatility
_____________________
(S&P 500 index)____________________

Model 1    Model 2 Model 3 Model 4

w1
w 2
δι
δ2
βι
β2

Y1

γ 2
Ψ1

Ψ2

W1 = w 2
δι = δ2
βι = β2
Yi = γ 2
Φ1 = V2
P11 = P 22

LL

Model parameters                      

0.2664a     -0.0129a    0.2581a     0.0033a

01612a      0.0093a    0.1561a     0.0035a

1.1093a                 0.9810a

0.9393a                 0.9796a

-0.5693a     -0.2328a    -0.6094a     -0.6226a

-0.3991a     0.0632a    -0.5627a    -1.4508a

40.4928a     7.0033a

90.7546a     9.9678a

Hypothesis tests                         

6074.104a   122.558a   5423.406a    0.0377

585.366a                0.0798

1.588      45.094a     0.118     1184.4911a

50.754a     12.8244a

2.022      50.034a     2.626     71.5032a

7166.36    11997.22   7369.75    13491.68

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
vt = wi +βirt-1 +ζt for Model 1,
vt = wi + δivt-1 + βirt-1 +ζt        for        Model        2,

vt = wi + βirt-1 + γi rt2-1 +ζt     for Model      3,      and

vt = wi +δivt-1 + βirt-1 + γi rt2-1 +ζt for Model 4. The null

hypothesis tests are distributed asχ2(1) . LL is the log maximum

likelihood function.

22



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