臺灣博碩士論文加值系統

本篇論文將實現變幅（realized range）概念應用在風險值模型中，利用Martens and van Dijk (2007) 所提出的修正誤差方法，並使用MEM（Multiplicative Error Model）來預測下一期的波動性，得到實現變幅基礎下的風險值模型。此外，本研究也利用常態分配假設下的變異數-共變異數法（variance-covariance method），以及厚尾性質的極值理論 （extreme value theory）兩種不同假設的風險值模型來一起做比較。在實證上，以標準普爾500（S&P 500）指數與那斯達克（Nasdaq）指數的高頻率資料作為研究對象，進行實現變幅、報酬與變幅基礎下的風險值模型在風險值的預測能力比較。實證結果顯示，以實現變幅為基礎下的風險值模型表現優於其他的風險值模型。

This paper investigates the concept of realized range into the Value-at-Risk estimation. We follow the bias-correction method of Martens and van Dijk (2007) and use MEM model（Multiplicative Error Model）to forecast volatility and VaR estimation. In addition, we apply two different VaR methods to make the comparison: Variance-covariance method and Extreme value theory. In empirical research, we use the intra-day data of S&P 500 and Nasdaq Index to compare the forecast ability of VaR with realized range, daily return and daily range data. The comparing result shows that realized-range-based VaR model performs better than other models.

中文摘要 i
ABSTRACT ii
謝辭 iii
TABLE OF CONTENTS iv
Ⅰ. INTRODUCTION 1
Ⅱ. PREVIOUS RESEARCH 4
2.1. VOLATILITY MODELS 4
2.2. VAR MODELS 6
2.3. EXTREME VALUE THEORY 8
Ⅲ. MODEL 11
3.1. CONDITIONAL VOLATILITY MODELS 11
3.2. ESTIMATING TAIL INDEX 16
3.3. EVALUATING VALUE-AT-RISK 20
3.4. COMPARISON OF VALUE-AT-RISK MODELS 23
IV. RESULTS 29
4.1. DATA 29
4.2. DESCRIPTIVE STATISTICS 29
4.3. EMPIRICAL ANALYSIS 31
V. CONCLUSION 38
REFERENCES 39

Andersen, T., Bollerslev, T., Diebold, F., and Labys, P. (2001), The distribution of realized exchange rate volatility, Journal of the American Statistical Association, 96, 42-55.
Andersen, T., Bollerslev, T., Diebold, F., and Labys, P. (2003), Modeling and forecasting realized volatility, Econometrica, 71, 579-625.
Barndorff-Nielsen, O., and Shephard, N. (2002), Econometric analysis of realised volatility and its use in estimating stochastic volatility models, Journal of the Royal Statistical Society Series, 64, 253-280.
Berkowitz, J., and O’brien, J. (2002), How accurate are Value-at-Risk models at commercial banks, Journal of Finance, 57, 1093-1111.
Bollerslev, T. (1986), Generalized autoregressive conditional heteroscedasticity, Journal of Econometrics, 31, 307-327.
Bollerslev, T., Chou, R., and Kroner K. (1992), ARCH modeling in finance: A review of the theory and empirical evidence, Journal of Econometrics, 52, 5–59.
Brooks, C. (2002), Introductory Econometrics for Finance, Cambridge.
Chou, R. (2005), Forecasting financial volatilities with extreme values: The conditional autoregressive range (CARR) model, Journal of Money, Credit and Banking, 37, 561-582.
Christensen, K., and Podolskij, M. (2007), Realized range-based estimation of integrated variance, Journal of Econometrics, 141, 323-349.
Christoffersen, P. (1998), Evaluating interval forecasts, International Economic Review, 39, 841-862.
Christoffersen, P., Hahn, J., and Inoue, A. (2001), Testing and comparing Value-at-Risk measures, Journal of Empirical Finance, 8, 325-342.
Corrado, C., and Truong, C. (2007), Forecasting stock index volatility: Comparing implied volatility and the intraday high-low price range, Journal of Financial Research, 30, 201-215.
Dacorogna, M., Muller, U., Pictet, O., and de Vries, C. (1995), The distribution of extremal foreign exchange rate returns in extremely large data sets, Tinbergen Institute Discussion Paper, 70-95.
Danielsson, J., and de Vries, C. (2000), Value-at-Risk and extreme returns, Annales d'Économie et de Statistique, 60, 239-270.
Duffie, D., and Pan, J. (1997), An overview of value at risk, Journal of Derivatives, 4, 7-49.
Engel, J., and Gizycki, M. (1999), Conservatism, accuracy and efficiency: Comparing Value-at-Risk models, Working paper 2, Australian Prudential Regulation Authority.
Engle, R. (1982), Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation, Econometrica, 50, 987-1008.
Engle, R. (2002), New frontiers for ARCH models, Journal of Applied Econometrics, 17, 425–446.
Engle, R. and Manganelli, S. (2004), CAViaR: Conditional Autoregressive Value at Risk by Regression Quantiles, Journal of Business & Economic Statistics, 22, 367-381.
Giot, P., and Laurent, S. (2004), Modeling daily Value-at-Risk using realized volatility and ARCH type models, Journal of Empirical Finance, 11, 379-398.
Hall, P. (1990), Using the bootstrap to estimate mean squared error and select smoothing parameter in nonparametric problems, Journal of Multivariate Analysis, 32, 177-203.
Hansen, P., and Lunde, A. (2006), Realized variance and market microstructure noise, Journal of Business and Economic Statistics, 24, 127-218.
Hartz, C., Mittnik, S., and Paolella, M. (2006), Accurate value-at-risk forecasting based on the normal-GARCH model, Computational Statistics & Data Analysis, 51, 2295-2312.
Hendricks, D. (1996), Evaluation of Value-at-Risk models using historical data, Federal Reserve Bank of New York Economic Policy Review, 2, 36-69.
Hill, B. (1975), A simple general approach to inference about the tail of a distribution, The Annals of Statistics, 3, 1163-1174.
Huisman, R., Koedijk, K., Kool, C., and Palm, F. (2001), Tail-index estimates in small samples, Journal of Business and Economic Statistics, 19, 208-216.
Huisman, R., Koedijk, K., and Pownall, R. (1998), VaR-x: Fat tails in financial risk management, Journal of Risk, 1, 47-62.
Jansen, D., and de Vries, C. (1991), On the frequency of large stock returns: Putting booms and busts into perspective, Review of Economics and Statistics, 73, 18-24.
Jorion, P. (2000), Value at Risk, McGraw Hill, New York.
Jorion, P. (2007), Financial Risk Manager Handbook, fourth edition, John Wiley & Sons.
Kearns, P. and Pagan, A. (1997), Estimating the density tail index for financial time series, Review of Economics and Statistics, 79, 171-175.
Koedijk, K., Schafgans, M., and de Vries, C. (1990), The tail index of exchange rate returns, Journal of International Economics, 29, 93-108.
Kupiec, P. (1995), Techniques for verifying the accuracy of risk measurement models, Journal of Derivatives, 3, 73-84.
Lanne, M. (2006), A mixture multiplicative error model for realized volatility, Journal of Financial Econometrics, 4, 594-616.
Longin, F. (1996), The asymptotic distribution of extreme stock market returns, Journal of Business, 69, 383-408.
Lopez, J. (1999), Methods for evaluating Value-at-Risk estimates, Federal Reserve Bank of San Francisco Economic Review, 2, 3-39.
Martens, M., van Dijk, D. (2007), Measuring volatility with the realized range, Journal of Econometrics, 138, 181-207.
McNeil, A., and Frey, R. (2000), Estimation of tail-related risk measures for heteroscedastic financial time series: An extreme value approach, Journal of Empirical Finance, 7, 271-300.
Neftci, S. (2000), Value at Risk calculations, extreme events, and tail estimation, Journal of Derivatives, 7, 23-37.
Parkinson, M. (1980), The extreme value method for estimating the variance of the rate of return, Journal of Business, 53, 61-65.
Pownall, R., and Koedijk, K. (1999), Capturing downside risk in financial markets: The case of the Asian Crisis, Journal of International Money and Finance, 18, 853-870.