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

Table 4. Regime-switching modelling for changes in implied volatility

_______________________(S&P 500 index)_______________________

	Model 1	Model 2 Model 3	Model 4	Model 5
^w1	-0.0793^a	Model Parameters -0.0788^a -0.0080	-0.1138^a	I -0.0146
^w 2	4.3311^a	4.3243^a -0.1302^a	-0.0133	-0.1106^a
δ		-0.0437^a	-0.0358^a	-0.0723^a
δ2		-0.1076^b	-0.0769^a	-0.0479^a
β	0.0965^a	0.0592^a -0.6216^a	-1.4887^a	-0.6243^a
β2	0.2078	0.1097 -1.5029^a	-0.6162^a	-1.5016^a
Y		5.5455^a	8.9329^a	5.8918^a
γ 2		9.21184^a	5.7441^a	9.5776^a
φ φ2 W₁ = w ₂	912.1114^a	Hypothesis Tests 898.6265^a 8.6952^a	6.1134^b	0.0184^c 0.0640^a 5.3364^b
δ = δ2		1.9562	6.9142^a	2.3351
β = β2	0.6735	0.1177 1306.9559^a	1364.9120^a	1298.9449^a
Y1 = γ 2		19.6618^a	15.0836^a	18.5454^a
φφ = φ2 P11 = P 22	16.6083^a	13.5024^a 87.9058^a	79.8012^a	5.2107^b 84.8625^a
LL	11893.48	11895.73 13453.93	13470.09	13473.32

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 + βr +ζ for Model 1, ∆v = w +δ∆v + βr +ζ for
t i i t-1 t t i i t-1 i t -1 t

Model 2, ∆v = w + βr +γ r² +ζ for Model 3,

t i i t-1 i t-1 t

∆v = w +δ∆v +βr +γ r² +ζ for Model 4, and
t i i t-1 i t -1 i t-1 t

∆ 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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