In this paper, we develop a statistical unobserved component model for stock market volatility. The volatility, which is measured by the conditional variance of stock returns, is decomposed into a permanent or long-run and a transitory or short-run component. The transitory component is mean- reverting towards the trend component. Analysis of US and Japanese stock data supports the decomposition and reinforce the common finding in the literature of persistent stock return volatility. The component model is successful in describing the effect of the October 87 Crash on stock volatility changes. We hypothesize that the leverage effect as discussed in Black (1976) and Christie (1982) is a short- run phenomenon in the stock market and there is no asymmetric structure of volatility in the long run. The data strongly supports this hypothesis for US and Japanese stock indices.
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