Cayton, Peter Julian A. and Mapa, Dennis S. (2012): Time-varying conditional Johnson SU density in value-at-risk (VaR) methodology.
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Stylized facts on financial time series data are the volatility of returns that follow non-normal conditions such as leverage effects and heavier tails leading returns to have heavier magnitudes of extreme losses. Value-at-risk is a standard method of forecasting possible future losses in investments. A procedure of estimating value-at-risk using time-varying conditional Johnson SU¬ distribution is introduced and assessed with econometric models. The Johnson distribution offers the ability to model higher parameters with time-varying structure using maximum likelihood estimation techniques. Two procedures of modeling with the Johnson distribution are introduced: joint estimation of the volatility and two-step procedure where estimation of the volatility is separate from the estimation of higher parameters. The procedures were demonstrated on Philippine-foreign exchange rates and the Philippine stock exchange index. They were assessed with forecast evaluation measures with comparison to different value-at-risk methodologies. The research opens up modeling procedures where manipulation of higher parameters can be integrated in the value-at-risk methodology.
|Item Type:||MPRA Paper|
|Original Title:||Time-varying conditional Johnson SU density in value-at-risk (VaR) methodology|
|Keywords:||Time Varying Parameters; GARCH models; Nonnormal distributions; Risk Management|
|Subjects:||G - Financial Economics > G1 - General Financial Markets > G12 - Asset Pricing ; Trading Volume ; Bond Interest Rates
C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C53 - Forecasting and Prediction Methods ; Simulation Methods
G - Financial Economics > G3 - Corporate Finance and Governance > G32 - Financing Policy ; Financial Risk and Risk Management ; Capital and Ownership Structure ; Value of Firms ; Goodwill
C - Mathematical and Quantitative Methods > C2 - Single Equation Models ; Single Variables > C22 - Time-Series Models ; Dynamic Quantile Regressions ; Dynamic Treatment Effect Models ; Diffusion Processes
|Depositing User:||Dennis S. Mapa|
|Date Deposited:||26. Jan 2012 23:14|
|Last Modified:||14. Apr 2015 16:59|
Bangko Sentral ng Pilipinas (2006), Circular No. 538: Revised Risk-Based Capital Adequacy Framework, BSP Regulations.
Basel Committee on Banking Supervision (1996), Supervisory Framework for the Use of “Backtesting” in Conjunction with the Internal Models Approach to Market Risk Capital Requirements, Bank for International Settlements.
Basel Committee on Banking Supervision (2004), International Convergence of Capital Measurement and Capital Standards, Bank for International Settlements.
Berman, S. M. (1964), “Limiting theorems for the maximum term in stationary sequences,” in Annals of Mathematical Statistics, Vol. 35, pp. 502–516.
Bollerslev, T. (1986), “Generalized Autoregressive Conditional Heteroscedasticity,” in Journal of Econometrics, Vol. 31, pp. 307-327.
Bollerslev, T., and J. M. Wooldridge (1992), “Quasi-Maximum Likelihood Estimation and Inference in Dynamic Models with Time-Varying Covariances,” in Econometric Reviews, Vol. 11, pp. 143-172.
Box, G. E. P. ; G. M. Jenkins, and G. C. Reinsel (1994), Time Series Analysis: Forecasting and Control, 3rd Ed., USA: Prentice Hall.
Cayton, P. J. A.; D. S. Mapa, and M. T. Lising (2010). “Estimating Value-at-Risk (VaR) using TiVEx-POT Models,” in Journal of Advanced Studies in Finance, Vol. I (2), pp. 152-170.
Chatterjee, S.; A. S. Hadi, and B. Price (2000), Regression Analysis by Example, 3rd Ed., USA: John Wiley & Sons, Inc.
Christoffersen P. (1998), “Evaluating Interval Forecast,” in International Economic Review, Vol. 3(4): 841-862.
Christoffersen, P. and D. Pelletier (2003), “Backtesting Value-at-Risk: A Duration-Based Approach”. CIRANO Scientific Series.
Coles, S. (2001). An Introduction to Statistical Modeling of Extreme Values. New York : Springer-Verlag.
Danielsson, J.; and C. G. de Vries (1997), “Tail Index and Quantile Estimation with Very High Frequency Data,” in Journal of Empirical Finance, Vol. 4, pp. 241-257.
Davison, A. C., and Smith, R. L. (1990), “Models for exceedances over high thresholds,” (with discussion), in Journal of the Royal Statistical Society, Series B, Vol. 52, pp. 393–442.
Engel, J. and M. Gizycki (1999), “Conservatism, Accuracy and Efficiency: Comparing Value-at-Risk Models,” Australian Prudential Regulation Authority, Reserve Bank of Australia, Working Paper 2.
Engle, R. F. (1982), “Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation,” in Econometrica, Vol. 50, No. 4, pp. 987-1007.
Fallon, E. C.; and J. A. Sarmiento-Sabogal (2003), “Is Historical VAR a Reliable Tool for Relative Risk Measurement in the Colombian Stock Market?: An Empirical Analysis Using the Coefficient of Variation” A Working Paper of the Pontificana Universidad Javeriana, Bogota, Colombia.
Hansen, B. E. (1994), “Autoregressive Conditional Density Estimation,” in International Economic Review, Vol. 35, No. 3, pp. 705-730.
Harvey, C. R.; and A. Siddique (1999), “Autoregressive Conditional Skewness,” in Journal of Financial and Quantitative Analysis, Vol. 34, No. 4, pp. 465-487.
Johnson, N. L. (1949), “Systems of frequency curves generated by methods of translation,” in Biometrika, Vol. 36, pp. 149–176.
Jondeau, E.; S. Poon, and M. Rockinger (2007), Financial Modeling under Non-Gaussian Distributions. London: Springer-Verlag.
Jondeau, E.; and M. Rockinger (2001), “Gram-Charlier densities,” in Journal of Economic Dynamics and Control, Vol. 25, pp. 1457-1483.
Jorion, P. (2007), Value at Risk: The New Benchmark for Managing Financial Risk, 3rd Ed., USA: McGraw-Hill.
Longerstaey, J.; and M. Spencer (1996), RiskMetrics™ – Technical Document. USA: J. P. Morgan/Reuters.
Longin, F. M. (2000), “From Value at Risk to Stress Testing: The Extreme Value Approach,” in Journal of Banking and Finance, Vol. 24, pp. 1097-1130.
McNeil, A.J., 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.
Pickands, J. (1975), “Statistical inference using extreme order statistics,” in Annals of Statistics, Vol. 3, pp. 119–131.
Rockinger, M.; and E. Jondeau (2001), “Entropy Densities with Applications to Autoregressive Skewness and Kurtosis,” A Working Paper of the Direction Generale des Etudes et des Relations Internationales, Direction des Etudes Economiques et de la Recherche, NER # 79.
Smith, R. L. (1999), “Measuring risk with extreme value theory,” working paper, Department of Statistics, University of North Carolina at Chapel Hill.
Suaiso, Jose Oliver (2009). “Measuring Market Risk using Extreme Value Theory (EVT).” The Philippine Review of Economics, Vol. XLVI, No. 2, December 2009, pp. 91-121.
Tsay, R. S. (2002), Analysis of Financial Time Series, John Wiley & Sons.
Yan, J. (2005), “Asymmetry, Fat-tail, and Autoregressive Conditional Density in Financial Return Data with Systems of Frequency Curves,” Working Paper in Department of Statistics and Actuarial Science, University of Iowa, USA.
Zakoian, J. (1994), “Threshold heteroskedastic models,” in Journal of Economic Dynamics and Control, Vol. 18(5), pp. 931-955.