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                      ∣

0.2664^a     -0.0129^a    0.2581^a     0.0033^a

01612^a      0.0093^a    0.1561^a     0.0035^a

1.1093^a                 0.9810^a

0.9393^a                 0.9796^a

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

-0.3991^a     0.0632^a    -0.5627^a    -1.4508^a

40.4928^a     7.0033^a

90.7546^a     9.9678^a

Hypothesis tests                         ∣

6074.104^a   122.558^a   5423.406^a    0.0377

585.366^a                0.0798

1.588      45.094^a     0.118     1184.4911^a

50.754^a     12.8244^a

2.022      50.034^a     2.626     71.5032^a

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 v_t = w_i +β_ir_t-1 +ζ_t for Model 1,
v_t = w_i + δ_iv_t-1 + β_ir_t-1 +ζ_t        for        Model        2,

v_t = w_i + β_ir_t-1 + γ_i r_t²_-1 +ζ_t     for Model      3,      and

v_t = w_i +δ_iv_t-1 + β_ir_t-1 + γ_i r_t²_-1 +ζ_t for Model 4. The null