A new analytical approach for identifying market contagion

Financial Innovation

Table 1 Contagion dynamics table

Classifi-cation	Causal volatility			Structure break			Contagion check
Classifi-cation	\(\frac{{\theta_{y} }}{{\theta_{x} }}\)	\(\eta_{x}\)	\(\eta_{y}\)	Short-term effect \(\left( {\beta_{L0} } \right)\)	Long-term effect \(\left( {{\upgamma }_{{\text{L}}} } \right)\)	Correlated-ness \((\beta_{L2}\))	Contagion check
S-1	NC	NC	NC	NSB	NLB	NCRB	No
S-2	NC	C	C	NSB	NLB	CRB	No
S-3	NC	NC	C	NSB	LB	NCRB	Contained
S-4	C	C	NC	SB	NLB	NCRB	Contained
S-5	NC	C	UND	NSB	LB	CRB	Contained
S-6	C	UND	UND	SB	NLB	CRB	Additional check required
S-7	C	C	UND	SB	LB	NCRB	Additional check required
S-8	C	UND	UND	SB	LB	CRB	Additional check required

This table shows eight possible situations that can occur when a shock hits market X based on Eq. 6. In addition, it shows the causality relationship between volatility change and structural breaks due to a shock to market X. “C” and “NC” in the causal volatility columns denote “change” and “no change,” respectively. “UND” denotes that “change” or “no change” are possible but undecided. “SB,” “LB,” “CRB,” “NSB,” “NLB,” and “NCRB” in the structure break columns denote short-term break, long-term break, correlatedness break, no short-term break, no long-term break, and no correlatedness break, respectively. The last column shows a contagion check, where “No” and “Contained” indicate avoidance of contagion while “Additional check required” indicates that a further check is needed to determine contagion