亞洲主要股價指數價格非連續跳躍與自我相關條件異質變異之實證研究

An Empirical Study of GARCH-Jump Process in Major Asian Stock Indices

戴世文(Shih-Wen Tai) ； 郭美美(Mei-Mei Kuo)

《國立虎尾科技大學學報》 30卷4期 (2012/06) Pp. 39-48

https://doi.org/10.6425/JNHUST.201206.0039

摘要

標的資產的價格對於其相關衍生性金融商品的評價影響甚劇，因此其標的資產價格行為對衍生性商品評價是一關鍵因素。傳統上對股價行為是假設其服從一隨機擴散程序，在此假設之下，股票報酬率呈常態分配。但實證研究文獻上常指出股價報酬率分配存在非零的偏態與高峰態，與常態分配假設並不相符，因此後續研究多採放寬相關假設以求股價模型能更接近市場實際資料。本文使用Lin et al.（2008）所發展結合跳躍－擴散與自我相關條件異質變異之修正模型（GARCH-Jump模型）與傳統純擴散模型、跳躍－擴散模型及GARCH模型等進行最大概似估計相關係數及配適度檢定之比較。實證樣本是亞洲主要五種股價指數（包含日經225指數、韓國KOSPI綜合指數，香港恆生指數、上海綜合指數與台灣發行量加權股價指數等），採樣期間由1997年元月至2008年10月，橫跨1997亞洲金融風暴與近來美國次級房貸風暴所造成全球的金融危機。實證結果發現對亞洲五種主要股價指數價格行為的描述，GARCH-Jump模型較其他三種模型皆能有更好的配適。

關鍵字

股價指數 ； 擴散模型 ； 跳躍－擴散模型 ； 一般化自我相關條件異質變異（GARCH）模型 ； GARCH-Jump模型

並列摘要

The influence of the prices of the underlying assets on derivatives pricing are important, so the behavior of the underlying assets' prices is a key issue. According to the widely-used assumption, the behavior of the stock price dynamics follow a diffusion process, in which the continuous compound stock return, is normally distributed. A large amount of empirical evidences show that the statistical characteristics of stock return distributions, such as a non-zero value of skewness and a high level of kurtosis are incompatible with the Gaussian distribution. Thus, to deregulate the relative assumption to fit the real market data is necessary for following studies. This paper explores the GARCH-Jump model proposed by Lin et al. (2008) and compares it with the diffusion model, jump-diffusion model and GARCH model. We use maximum likelihood estimation to estimate parameters in these models, and take the likelihood ratio test to examine nested hypotheses. Five major Asian stock indices, including NIKKEI 225, Korea Composite Stock Price Index (KOSPI), Hong Kong Hang Seng Index, Shanghai composite index, and Taiwan TSE weight Stock Index, are analyzed. The period of the sample is from January 1997 to October 2008, which across the Asia financial crisis and the U.S. subprime mortgage crisis. The empirical evidences show that the GARCH-Jump model fits better than the other models in five major Asian stock indices.

並列關鍵字

stock market index ； diffusion model ； jump-diffusion model ； Generalized Autoregressive Conditional Heteroskedasticity model (GARCH model) ； GARCH-Jump model

參考文獻

Bachelier, L. Theory of Speculation, Paris: Gauthier-Villars.(1900), Translated by A. James Boness and reprinted in Cootner, loc. Cit

Duan, J.C., Ritchken, P.H. and Sun, Z. (2005), “Jump starting GARCH pricing and hedging option with jumps in returns and volatilities”, Working Paper, University of Toronto and Case Western Reserve University

Lin, B.H., Hong, M.W., Wang, J.Y. and Wu, T.H. (2008), A lattice model for option pricing under GARCH-Jump Process, National Taiwan University of Science and Technology Working Paper

Bakshi, G.,Cao, C.,Chen, Z.(1997).Empirical performance of alternative option pricing models.The Journal of Finance.52(5),2003-2049.

Bates, D.(1996).Jumps and stochastic volatility: Exchange rate processes implicit in Deutsche Mark options.The Review of Financial Studies.9(1),69-107.