本研究是應用極值理論，探討美國S&P500大盤指數以及S&P500指數之500家公司所編製之23個產業類股，其股價指數之極端風險是否因次級房貸風暴而有所改變。 我們分別觀察尾端風險 ( tail risk ) 及尾端指數 ( tail index ) 是否會因次級房貸風暴而有顯著性的改變，換言之， 我們關心次級房貸風暴前、後各產業指數上漲及下跌風險是否一致，此為「結構性改變」檢定；另一方面，我們也分別探討美國產業之左尾尾端指數 ( 下降風險值 ) ， 在次級房貸風暴前、後是否和右尾尾端指數 ( 潛在上升風險值 ) 有所不同，此即「非對稱性改變」檢定。

研究結果發現次級房貸風暴後，大多數產業股價之下降風險值大於潛在上升風險值，且產業股價之下降風險及潛在上升風險均有顯著增加，此結果顯示美國大多產業股價存在結構性改變，且次級房貸風暴過後，產業股價之非對稱性更為顯著。

　 This paper applies “extreme value theory” to examine if risk indices of 23 sectoral indices based on the firms which composes the S&P 500 index in U.S. stock market change due to subprime mortgage crisis. We respectively test if tail risk and tail quantile index significantly change due to subprime mortage crisis. That is, we concern if downside risk and upward potential risk before subprime mortgage crisis on each sectoral index are consistent with those after subprime mortgage crisis.

　　This is called “Structural Change test.” On the other side, we analyze if left risk index (downside risk) is the same before subprime mortgage crisis with the right risk index after subprime mortgage crisis, respectively. This is called “Asymmetric test.” Besides, this paper implements the tests on the asymmetric and structural change on co-movements for pairs of sectoral indices.

　　The empirical results find that down side risk is significantly larger than upward risk for most industries after subprime mortgage crisis. Both downside risk and upward potential risk also significantly increase after the subprime mortgage crisis. Our results provide the evidences that Subprime Mortgage Crisis cause the structural and asymmetric change on indices for most industries. After Subprime Mortgage Crisis, the asymmetry of risk indices is more significant.

一、中文部分
陳淑儀(2010)，「921地震對台灣股價是否有非對稱性及結構性改變之探討」，國立成功大學經濟學系碩士論文

二、英文部分
Beirlant, J., Dierckx, G., Goegebeur, Y., & Matthys, G. (1999). Tail index estimation and an exponential regression model. Extremes, 2(2), pp.177-200.
Boothe, P., & Glassman, D. (1987). The statistical distribution of exchange rates: empirical evidence and economic implications. Journal of International Economics, 22(3-4), pp.297-319.
Brown, J.R., Cummins, J.D., Lewis, C.M., & Wei, R. (2004). An empirical analysis of the economic impact of federal terrorism reinsurance. Journal of Monetary Economics, 51(5),pp.861-898.
Buiter, W. (2008). Lessons from the 2007 financial crisis.
Carter, D.A., & Simkins, B.J. (2004). The market’s reaction to unexpected, catastrophic events: the case of airline stock returns and the September 11th attacks. The Quarterly Review of Economics and Finance, 44(4), pp.539-558.
Chen, A.H., & Siems, T.F. (2004). The effects of terrorism on global capital markets. European Journal of Political Economy, 20(2), pp.349-366.
Coles, S. (2001). An introduction to statistical modeling of extreme values: Springer Verlag.
Danielsson, J., & De Vries, C.G. (2000). Value-at-risk and extreme returns. Annales d'Economie et de Statistique, pp.239-270.
Dekkers, A.L.M., & De Haan, L. (1989). On the estimation of the extreme-value index and large quantile estimation. The Annals of Statistics, pp.1795-1832.
Duffie, D., & Pan, J. (1997). An overview of value at risk. The Journal of Derivatives, 4(3), pp.7-49.
Eichengreen, B., Mody, A., Nedeljkovic, M., & Sarno, L. (2009). How the subprime crisis went global: evidence from bank credit default swap spreads: National Bureau of Economic Research.
Emrechts, P. (2000). Extreme Value Theory: Potential and Limitations as an Integrated Risk Management Tool Derivatives Use. Trading & Regulation, 6, pp.449-456.
Forbes, K.J., & Rigobon, R. (2002). No contagion, only interdependence: measuring stock market comovements. The Journal of Finance, 57(5), pp.2223-2261.
Ghose, D., & Kroner, K.F. (1995). The relationship between GARCH and symmetric stable processes: Finding the source of fat tails in financial data. Journal of empirical finance, 2(3), pp.225-251.
Ghosh, A., Saidi, R., & Johnson, K.H. (1999). Who Moves the Asia‐Pacific Stock Markets—US or Japan? Empirical Evidence Based on the Theory of Cointegration. Financial review, 34(1), pp.159-169.
Gorton, G. B. (2008). The Subprime Panic. NBER Working Paper(w14398), National Bureau of Economic Research.
Ha, I.B., Khil, J., & Lee, B.S. (2001). On the rationality of Korea's stock market: was the recent Korean financial crisis due to fundamental factors? Journal of International Financial Markets, Institutions and Money, 11(3-4), pp.423-441.
Hall, P. (1982). On some simple estimates of an exponent of regular variation. Journal of the Royal Statistical Society. Series B (Methodological), pp.37-42.
Hall, P., Horowitz, J.L., & Jing, B.Y. (1995). On blocking rules for the bootstrap with dependent data. Biometrika, 82(3), pp.561-574.
Hall, P., & Welsh, AH. (1985). Adaptive estimates of parameters of regular variation. The Annals of Statistics, 13(1), pp.331-341.
Hamao, Y., Masulis, R.W., & Ng, V. (1990). Correlations in price changes and volatility across international stock markets. Review of Financial studies, 3(2), pp.281-307.
Hartmann, P., Straetmans, S., & Vries, C.G. (2004). Asset market linkages in crisis periods. Review of Economics and Statistics, 86(1), pp.313-326.
Evaluation of Value-at-Risk Models
Using Historical Data (1996).
Hill, B.M. (1975). A simple general approach to inference about the tail of a distribution. The Annals of Statistics, pp.1163-1174.
Hill, J., & Schneeweis, T. (1983). The effect of Three Mile Island on electric utility stock prices: A note. Journal of Finance, 38(4), pp.1285-1292.
Huisman, R., Koedijk, GK, & Pownall, AJR. (1999). Asset Allocation in a Value at Risk Framework. Erasmus University, Rotterdam, Faculty of Business Administration.
Huisman, R., Koedijk, K.G., & Pownall, R.A.J. (1998). VaR-x: fat tails in financial risk management. Journal of Risk, 1(1), pp.47-61.
Hwang, I., In, F., & Kim, T.S. (2010). Contagion effects of the US subprime crisis on international stock markets.
Jang, H., & Sul, W. (2002). The Asian financial crisis and the co-movement of Asian stock markets. Journal of Asian Economics, 13(1), pp.94-104.
Jansen, D.W., & De Vries, C.G. (1991). On the frequency of large stock returns: Putting booms and busts into perspective. The Review of Economics and Statistics, pp.18-24.
Jondeau, E., & Rockinger, M. (2003). Testing for differences in the tails of stock-market returns. Journal of empirical finance, 10(5), pp.559-581.
Jorion, P. (2000). Value at risk: the new benchmark for managing financial risk. New York.
King, M.A., & Wadhwani, S. (1990). Transmission of volatility between stock markets. Review of Financial studies, 3(1), pp.5-33.
Koedijk, K.G., Stork, P.A., & De Vries, C.G. (1992). Differences between foreign exchange rate regimes: the view from the tails. Journal of International Money and Finance, 11(5), pp.462-473.
Lee, S.B., & Kim, K.J. (1993). Does the October 1987 crash strengthen the co-movements among national stock markets. Review of Financial Economics, 3(1), pp.89-102.
Longin, F., & Solnik, B. (2001). Extreme correlation of international equity markets. The Journal of Finance, 56(2), pp.649-676.
Longin, F.M. (1996). The asymptotic distribution of extreme stock market returns. Journal of business, pp.383-408.
Loretan, M., & Phillips, P.C.B. (1994). Testing the covariance stationarity of heavy-tailed time series: An overview of the theory with applications to several financial datasets. Journal of empirical finance, 1(2), pp.211-248.
Mey, J. de. (2003). The aftermath of September 11: The impact on and systemic risk to insurance industry. The Geneva Papers and Insurance, 28(1), pp.65-70.
Neftci, S.N. (2000). Value at risk calculations, extreme events, and tail estimation. The Journal of Derivatives, 7(3), pp.23-37.
Nippani, S., & Bathala, C. T. (2008). The impact of the asian tsunami on the affected countries' stock markets. The Icfai Journal of Applied Finance, 14(5), pp.44-56.
Orstry, J.D. (1998). Financial market contagion in the Asian crisis. IMF Worknig Paper.
Pickands III, J. (1975). Statistical inference using extreme order statistics. The Annals of Statistics, pp.119-131.
Saha, M., & Bhunia, A. (2012). How far India has gone down the road towards financial integration with US since subprime crisis? An Econometric Analysis.
Straetmans, S.T.M., Verschoor, W.F.C., & Wolff, C.C.P. (2008). Extreme US stock market fluctuations in the wake of 9/11. Journal of Applied Econometrics, 23(1), pp.17-42.
Wu, C. (2000). International trade relations and the contagious effects of the Asian financial crisis. Review of Pacific Basin Financial Markets and Policies, 3(3), pp.367-399.
Ye, W., Liu, X., & Miao, B. (2012). Measuring the Subprime Crisis Contagion: Evidence of Change Point Analysis of Copula Functions. European Journal of Operational Research.