Long-run and short-run modeling of asset return volatility

Asset return volatility (variance and covariance of returns) plays an important role in many area of finance theory, such as asset pricing, option pricing, optimal portfolio selection, and hedging strategy, etc.. Besides the time-varying pattern of volatility in financial markets, one common finding in the literature is that asset return volatility is a non-stationary or persistent process. This motivates the studies in this thesis on the long-run and the short-run modeling of asset return volatility through decomposition.; The first chapter of my thesis develops a statistical component model built upon the Auto-Regressive Conditional Heterskedasticity (ARCH) methodology, which decomposes the conditional variance of asset returns into a permanent (trend) and a transitory component. The transitory component is mean reverting towards the slowly-evolving martingale trend. Thus the components represent the long-run and the short-run movement of volatility. The component model is successful in describing volatility in US and Japanese stock markets. In particular, it is found that risk premium seems to respond more significantly to the long-run volatility than to the short-run volatility in the stock market. The quick recovery of stock market after the 87's Crash can be well captured by the component model that the transitory component changes more dramatically within and after the crash. Stock return volatility has an asymmetric structure in response to 'good' and 'bad' market news. This so-called 'leverage effect', due to firms' difficulty to adjust debt-equity ratio, is found to be only a temporary behavior in the stock market just as finance theories may indicate.; The second chapter extends the component model into a multivariate framework in which components of the conditional covariance matrix of assets can be modeled. Different asset returns may show a common persistence in volatility. In the component model, this co-persistence issue can be studied by examining only the trend of the covariance, regardless of its short-run structure. Also, the permanent trend of the covariance reveals the long-run correlation between assets, which has direct implications in long-term financial management. The empirical study examines daily returns on the S&P500 stock index and the index futures. The co-persistence relationship found implies that the difference of returns on the two market is non-systematic or idiosyncratic,since shocks to the return difference has no persistent effect on volatility of the two market. On the other hand, the two markeys could deviate from each other considerably, especially when the markets are experiencing serious shocks e.g. the correlation was merely 0.10 right after the October 87' Crash. However, the long-run correlation between the two markets remains very high, 0.93 by average over a ten-year period, indicating that the two markets are of no fundamental difference.; The third chapter is an application of the component model, which studies the long-run forecast of volatility for individual stocks using market information. In the APT structure, time-varying volatility of asset returns is due either to the factors or the idiosyncratic shocks. Individual assets and the market portfolio would be co-persistent if the idiosyncrasy has non-persistent volatility. The data, however, rejects this hypothesis finding that the idiosyncratic volatility itself is persistent. In effect, the long-run forecast of individual stock volatility depends on the market shocks as well as the idiosyncratic shocks.