models in terms of mean reversion and asymmetric impact of returns (leverage effects with
respect to changes in expected volatility), it is also possible to test for nonlinearities in the
relationship between changes in implied volatility and the dynamics of realized volatility.
δ vt = wi + δA vt-1 + βirt-1 + Yirt-1 + φ^σr,t-1 + ζt (9)
Given the definition of the new implied volatility index as the approximation of
volatility implicit in a hypothetical option with thirty days remaining to maturity, realized
volatility is defined at time t as the ex post annualized measure of standard deviation of
returns until option expiration, from t + 1 to t + 30 . The sign and significance of
parameters φ in Model (9) across regimes can provide evidence on the adjustment process
that governs the formation of expectations about market volatility. It allows for the
examination of the important issue of whether implied volatility rises following a marginal
increase in realized volatility.
Tables 4 and 5 report the estimation results for Models (1) to (5) with respect to
changes in implied volatility for the US and Japanese markets, respectively. Judging from
the LR test, the dynamics of expected volatility are better described according to Model 5
based on all conditioning variables, including past changes in realized volatility. The degree
of mean reversion does not differ across regimes in the US market. In the Japanese market
instead, it is the sensitivity to the magnitude, as opposed to the sign, of shocks in the
return-generating process that is hardly different across regimes.
There is at least, one regime of expectations for decreasing volatility in both markets
(regime 2). Anticipations of decreasing volatility are characterized by the asymmetric
impact of news and positive relationship with changes in realized volatility. This evidence
suggests that marginal decreases in realized volatility are conducive to expectations of
lower volatility. With respect to the Japanese market, this regime is also associated with
slower mean reversion. The alternative regime featuring anticipations of increasing
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