long memory and significant leverage effects while regime 2 is associated with expectations
of high volatility, and significant mean reversion in the absence of leverage effects.
The inferred probabilities of regime 1 from Model 4 are reported in Figures 2 and 3
for the US and Japanese markets, respectively. These figures suggest that in the absence of
long swings, the process of volatility expectations tends to switch randomly and abruptly
between regimes. It is clear from Figure 2 that there is a stronger likelihood for volatility
expectations to be governed by regime 1, which features positive serial correlation and
relatively less significant leverage effects. There are more frequent regime shifts in S&P 500
implied volatility index, particularly over the period associated with the onset of the Russian
debt default and LTCM crises in 1998 until the Latin American debt crisis in 2002. The
higher frequency of regime switches may be reflective of the increased uncertainty
generated by financial crises. Such events have the potential of increasing the likelihood of
the alternative regime, typically characterized by stronger leverage effects.
With respect to the Japanese market, it appears from Figure 3 that regime 1 tends to
prevail over the sample period, except for very short-lived switches to the alternative regime.
The predominant regime is characterized by expectations of low volatility levels, longer
memory, and significant leverage effects. Significant events such as the Asian financial
crisis seem to trigger shifts towards the volatility regime featuring expectations of higher
volatility, and significant mean reversion. Judging from the inferred probabilities reported
for both markets, it seems that financial crises are not associated with long swings in the
sense that they do not have the potential of shifting volatility expectations from one regime
to another for long protracted periods.
4.2. REGIME SHIFTS AND CHANGES IN VOLATILITY EXPECTATIONS
The dynamics of volatility expectations are also estimated with respect to first
differences in implied volatility. While retaining the features of previous regime-switching
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