as the onset of the Asian financial crisis in 1997, Russian debt default and LTCM crisis in
1998. The increase in implied volatility associated with the burst of the IT bubble in 2000 is
less pronounced than that related to the Latin American debt crisis in 2002. These implied
volatility patterns may be indicative of a negative relationship between market volatility and
returns, which can be formally examined with Markov regime-switching modelling.
The distributional properties of stock returns and implied volatility are described
by Table 1. There is evidence that the Japanese market tends to be associated with lower
mean returns and higher volatility. The average implied volatility, as well as first differences,
is found to be higher than comparable statistics in the US market. Based on unit-root tests
following Augmented Dickey-Fuller and Phillipps-Perron tests, the time-series of stock
market returns and volatility are also found to be stationary in both markets.
4. Empirical Evidence
4.1. REGIME SWITCHING AND THE LEVEL OF IMPLIED VOLATILITY
The estimation results of the various first-order Markov regime-switching models
with respect to implied volatility levels are reported in Table 2 and 3 for the US and
Japanese markets, respectively. Model 1 allows for regime-dependency in the relationship
between expected volatility levels and stock market returns. There is evidence that the slope
coefficients in both regimes are negative for the US market, but insignificant for the
Japanese market. Evidence of negative slope suggests that market volatility is expected to
increase in bear periods and decrease in bull periods. Given the acceptance of the null of
equal slopes for both markets, it is the magnitude of drifts which defines regimes of high and
low expected levels of volatility.
Model 2 expresses the relationship between past returns and volatility upon the
inclusion of autoregressive terms. There is a significant increase in the log-likelihood
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