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

Table 3. Regime-switching modelling of implied volatility _______________________(Nikkei 225 index)______________________
	Model 1	Model 2	Model 3	Model 4
		Model parameters		I
w1	0.3106^a	0.1522^a	0.3030^a	0.0048^a
w 2	0.2080^a	0.0088^a	0.2057^a	0.3494^a
δι		0.7995^a		0.9747^a
δ2		0.9611^a		-0.0693^a
βι	-0.0339	0.5529^a	-0.1489^a	-0.3231^a
β2	0.0044	0.0072	-0.0991	0.8789^a
Y1			20.5833^a	5.7630^a
γ 2			11.6824^a	-24.6102^a
Ψ1
Ψ2
		Hypothesis tests		I
w₁ = w ₂	4590.3206^a	1764.6474^a	3844.3931^a	10957.0160^a
δι = δ2		225.7556^a		9901.6532^a
βι = β2	0.1639	85.26211^a	0.3771	430.3168^a
Yi = γ 2			28.2025^a	432.8464^a
Φ1 = Ψ2	4.5052^b		5.4429^b
P11 = P 22	4.5052^b	20.8045^a	5.4429^b	175.5199^a
LL	6822.32	11007.45	6883.55	11386.28
Notes: Significance at the 1, 5 and 10 % level is denoted by ^a, ^b and

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

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

likelihood function.