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 -0.3498^a -0.1257^a		1.2607^a	I 2.0495^a
^w 2	-3.4197^a	-0.0030	6.9409^a	-0.1317^a	-0.1290^a
δ δ₂β	-0.0112	-0.6558^a -0.1233^a -6.3270^a -0.3312^a		-1.4394^a -0.1352^a 4.5286^a	-1.7631^a -0.1145^a 5.6178^a
β2	-7.2362^a	-0.0434^a	6.8867^a	-0.3435^a	-0.3132^a
Y γ 2 φφ φ₂ W₁ = w ₂	1248.3519^a	3.9584^a -164.8804^a Hypothesis Tests 14.4029^a 5711.6400^a		61.5712^a 4.9217^a 295.9666^a	12.1322^a 4.4534^a -2.7179^a 0.0274^a 338.6405^a
δ = δ β = β2	9520.5489^a	318.7542^a 6397.2327^a 13819.9404^a		2294.9900^a 6756.7345^a	2630.6941^a 7119.3876^a
Y1 = γ 2 φφ = φ₂ P11 = P 22	2.0749	4639.8593^a 43.6718^a 33.1734^a		523.5600^a 162.7422^a	3.1972^c 1574.2915^a 102.2636^a
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 = w_i + β_ir ₁ +ζ for Model 1, ∆v = w_i +δ_i∆v ₁ +β_ir ₁ +ζ for

t i i t -1 t t i i t -1 i t -1 t

Model 2, ∆v_t = w_i + β_ir_t_-₁ + γ_i r_t²_-₁ +ζ_t for Model 3,

∆v_t = w_i +δ_i∆v_t_-₁ + β_ir_t_-₁ + γ_i r_t²_-₁ +ζ_t for Model 4, and

∆v_t = w_i + δ_i∆v_t_-₁ + β_ir_t_-₁ + γ_ir_t-₁ + φ_i∆σ_rt_-₁ + ζ_t for Model 5. The model
parameters w and σ_e are scaled by 10². The null hypothesis tests are
distributed asχ²(1) . LL refers to the log maximum likelihood function.

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