| Summary: | 碩士 === 國立政治大學 === 金融研究所 === 86 === Volatility forecast is extremely important factor in portfolio choice, hedging strategies, asset management, asset pricing and option pricing. Identifying a good forecast model of volatility is absolutely necessary, especially for the highly volatile Taiwan stock market. Due to increasing attention to the impact of market risk on asset returns, academic researchers and practicians have developed ways to control risk and methodologies to forecast return volatility. Past researches on asset price behavior usually assumed that asset price behavior follows random walk, and its probability distribution is a log-normal distribution with a constant variance (or constant volatility). This assumption is in fact in violation of empirical evidence showing that volatility tends to vary over time (e.g., Mandelbrot[1963] and Fama[1965]). To forecast volatility (or variance), Engle(1982) is the first scholar to propose a forecast model, now well-known as ARCH, whose conditional variance is a function of past squared returns residuals. Accordingly, the forecast variance (or volatility) varies over time. Bollerslev(1986) proposed a generalized model, called GARCH, which allows the current conditional variance depends not only on past squared residuals, but also on past conditional variances. However, Nelson(1991) has recently proposed a new model, called EGARCH, which attempts to remove the weakness of the GARCH model. The EGARCH model has been shown to be successful to forecast volatility and to describe successful stock price behavior. In addition, Hull and white(1987) employed a continuous-time stochastic volatility model to develop in option pricing model. Their stochastic volatility model not only admits the past variance, but also depends on random noise of volatility. The above-mentioned models have been widely implemented in practice to simulate and to forecast asset return volatility.
This thesis investigates whether random walk, GARCH(1,1), EGARCH(1,1) and stochastic volatility model differ in their ability to predict the volatility of stock index and currency returns over short-term and long-term horizons. The results strongly support that the best volatility predictions are generated by the stochastic volatility model. Therefore, it is recommended that financial institutions may adopt stochastic volatility model to predict asset return volatility.
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