臺灣博碩士論文加值系統

本篇文章將採用長期記憶模型之一的HYGARCH模型，搭配1985年廣場協議後的日圓匯率期貨資料來估計日圓期貨匯率買入和放空部位的日報酬風險值，探討控管日圓匯率期貨在使用上的風險。為了更準確地計算風險值，本文採用常態分配、學生t分配以及偏態學生t分配來作模型估計以及風險值之計算。

本文實證的結果將有兩方面的貢獻：首先，實證結果顯示當我們採用厚尾分配估計風險值時，樣本內風險值的估計誤差會與信賴水準的高低呈正比的現象，證明在極端的風險值估計上，厚尾分配均有較佳的表現。其次，與其他使用HYGARCH模型研究日圓匯率的文章相較，本文在風險控管層面上所提供的偏態學生t分配，於估計風險值時，比起只考慮厚尾的對稱學生t分配將來得更為有效，其不但在估計誤差上較小，而且根據Kupiec檢定法，其在樣本內的風險值估計也有較好的表現。此外，本文也將多方證明此資料的偏態分配屬於右偏。

In order to manage the exposure of the dollar/yen futures returns with regarding the long memory behavior in volatility, we use the HYGARCH(1,d,1) model with the data after the Plaza Accord to compute daily Value-at-Risk (VaR) of long and short trading positions. To take into account the fat-tail situation in financial time series, we estimate the model under the normal, Student-t, and skewed Student-t distributions. The contribution of this article is twofold. First, the empirical results show that the bias of in-sample VaR increases as the confidence level increases when VaR is calculated with a fat-tail distribution. Second, we provide a better distribution, the skewed Student-t innovation, for estimating the HYGARCH model for the Japanese yen in respect of risk management because the bias under the skewed Student-t innovation is smaller than that under the Student-t distribution, and in-sample VaR of the models with a skewed Student-t distribution outperforms based on Kupiec test. In addition, we get the innovation skewed to the right through the in-sample VaR analysis.

1. Introduction 01
2. Data and Methodology 06
2.1 Data 06
2.2 Methodology 07
2.2.1 FIGARCH 07
2.2.2 HYGARCH 08
2.2.3 VaR 09
2.2.4 Kupiec Test 10
3. Empirical Result 12
3.1 Unit Root Tests and Stationarity Test 12
3.2 Long Memory in Volatility 12
3.3 Estimating the Models 13
3.4 In-Sample and Out-of-Sample VaRs Analyses 14
3.4.1 In-sample VaR computations 15
3.4.2 Out-of-sample VaR computations 16
4. Conclusions 18
References 19
Figures & Tables 23

1. Akaike, H. 1974, A new look at the statistical model indentification, IEEE Transactions on Automatic Control, AC-19,716-723.
2. Baillie, R.T., T. Bollerslev, and H.O. Mikkelsen, 1996, Fractionally integrated generalized autoregressive conditional heteroskedasticity, Journal of Econometrics, 74, pp.3-30.
3. Beine, M., A. Benassy-Quere, and C. Lecourt, 1999, The impact of foreign exchange interventions: New evidence from FIGARCH estimations, CEPII, document de travail, n° 99-14, pp.7-37.
4. Baine, M. and S. Laurent, 2000, Structural change and long memory in volatility: new evidence from daily exchange rates. In “Developments in forecast combination and portfolio choice” by Dunis, C., A. Timmermann and J. Moody (eds.). Wiley, New York.
5. Beine, M., S. Laurent, and C. Lecourt, 2002, Accounting for conditional leptokurtosis and closing days effect in FIGARCH models of daily exchange rates, Applied Financial Economics, 12, pp.589-600.
6. Bollerslev, T. and H.O. Mikkelsen, 1996, Modeling and pricing long- memory in stock market volatility, Journal of Econometrics, 73, pp.151-184.
7. Davidson J., 2004, Moment and Memory Properties of Linear Conditional Heteroscedasticity Models, and a New Model, Journal of Business & Economic Statistics, 22, 16-29.
8. de Vries, C.G..,1991, On the relation between GARCH and stable processes, Journal of Econometrics, 48, pp.313-324
9. Dickey, D.A., and W.A. Fuller, 1979, Distribution of the estimators for autoregressive times series with a unit root, Journal of the American Statistical Association, Vol.74, pp.427-431.
10. Ding, Z., C.W.J. Granger, and R.F. Engle, 1993, A long memory property of stock market returns and a new model, Journal of Empirical Finance, 1, pp 83-106.
11. Ding, Z. and C.W.J. Granger, 1996, Modeling volatility persistence of speculative returns: A new approach, Journal of Econometrics, 73, pp.185-215.
12. Doornik, A., G. Draisma, and M. Ooms, 2001, Introduction to Ox, version 3, Timberlake Consultants Ltd.
13. Engle, R.F., 1982, Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation, Econometrica, 50, pp. 987-1007.
14. Engle, R.F. and T. Bollerslev, 1986, Modeling the persistence of conditional variance, Econometric Reviews, 5, pp.1-50.
15. Gray, S.F., 1996, Modeling conditional distribution of interest rates as a regime-switching process, Journal of Financial Economics, 42, 27-62
16. Gupta, A., and B. Liang, 2005, Do hedge funds have enough capital? A value-at-risk approach, Journal of Econometrics, 77, pp.219-253.
17. Hamilton, J.D. and R. Susmel, 1994, Autoregressive conditional heteroskedasticity and changes in regime, Journal of Econometrics, 64, pp.307-333
18. Inui, K., M. Kijima, and A. Kitano, 2003, VaR is subject to a significant positive bias, working paper.
19. Jorian, P., 2000, Risk management lessons from long term capital management, European Financial Management, 6, pp.277-300.
20. Jorian, P., 2001, Value At Risk: The new benchmark for managing financial risk, second ed. McGraw-Hill Publication, New York.
21. Kupiec, P., 1995, Techniques for verifying the accuracy of risk measurement models, Journal of Derivatives, 2, pp.174-184.
22. Kwiaowski, D., P.C.B. Phillips, P. Schmidt, and Y. Shin, 1992, Testing the null hypothesis of stationarity against the alternative of a unit root: How sure are we that economic time series have a unit root? Journal of Econometrics, 54, pp.159-178.
23. Li, X., Q. Xu, 2006, Assessing tail-related risks in Asian emerging equity markets, working paper.
24. Ljung, G., and G.. Box, 1978, On a measure of lack of fit in time series models, Biometrika, 65, pp.297-303.
25. Lo, A.W., 1991, Long term memory in stock market prices, Econometrica, 59, pp.1279-1313.
26. Philips, P.C.B. and P. Perron, 1988, Testing for a unit root in time series regression, Biometrika, 75, pp.335-346.
27. Sarantis, N., 1999, Modeling nonlinearities in real effective exchange rates, Journal of International Money and Finance, 18, pp.27-45.
28. Schmidt, P., 1990, Dickey-Fuller tests with drift, Advances in Econometrics, 8, pp.161-200
29. West, K.D., H.J. Edison, and D. Cho, 1993, A utility-based comparison of some model of exchange rate volatility, Journal of International Economics, 35, pp.23-45