金融商品波動度最佳預測模型的認定

Abstract

波動度在金融市場中具有舉足輕重的地位,它不僅是風險控管的重要衡量工具,也是資產評價不可或缺的因素。過去從事資產價格行為的相關研究都假設資產的價格過程是隨機的,且呈對數常態分配、變異數固定。然而實證結果一再顯示:變異數是隨時間而變動的(如Mandelbrot(1963)、Fama(1965))。為預測波動度(或變異數),Eagle(1982)首先提出了ARCH模型,允許預期條件變異數作為過去殘差的函數,因此變異數能隨時間而改變。此後Bollerslev(1986)提出GARCH模型,修正ARCH模型線性遞減遞延結構,將過去的殘差及變異數同時納入條件變異數方程式中。Nelson(1991)則提出EGARCH模型以改進GARCH模型的三大缺點,此模型對具有高度波動性的金融資產提供更成功的另一估計模式。除上列之ARCH-type模型外,Hull and White(1987)提出連續型隨機波動模型(Continuous time stochastic volatility model),用以評價股票選擇權。他們的模型不僅將過去的變異數納入條件變異數的方程式中,同時該條件變異數也會因隨機噪音(random noise)而變動。近年來,上述模型均被廣泛運用在模擬金融資產的波動性,均是相當實用的模型。 本計畫擬以隨機漫步(random walk)、GARCH(1,1)、EGACH(1,1)及隨機波動模型(stochastic volatility),並以1980年至1996年為樣本期間,將五國外匯及股價指數收盤價轉換為報酬率型態,進行不同期間下波動度之預測。以實證結果判斷上述四種模型在預測外匯及股價指數波動度的能力表現,同時,比較上述模型的預測能力。波動度的預測在投資組合的選擇、避險策略、資產管理,以及金融資產的評價上是關鍵性因素。因此,在波動度變化甚巨的台灣股市中,找出具有良好預測波動度能力的模型,是絕對必要的。

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 stock price behavior usually assumed that stock price behavior follows random walk, and its probability distribution is a normal distribution with a constant variance (or constant volatility). This assumption is in fact in violation of empirical evidence showing that volatility tend 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 model to develop on 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 research proposal attempts to forecast exchange rate volatility (five countries) and Taiwan stocks return volatility over the period from 1980 to 1996 by means of four forecast models such as Random Walk, GARCH(1,1), EGARCH and Random Volatility forecast models in and out of sample periods. Volatility forecast is extremely important factor in portfolio choice, hedging strategies, asset management, asset pricing and option pricing. Taiwan stock market has been evidenced to be highly volatile. Consequently, Identifying a good forecast model of volatility is absolutely necessary, especially for the highly volatile Taiwan market.