 1

AbantoValle, C. A., Bandyopadhyay, D., Lachos, V.H. and Enriquez, I. (2010). Robust Bayesian analysis of heavytailed stochastic volatility models using scale mixtures of normal distributions.Computational Statistics&Data Analysis, 54(12), 28832898.
(check this in PDF content)
 2

Aloui, C. and Mabrouk, S. (2010). ValueatRisk estimations of energy commodities via longmemory, asymmetry and fattailed GARCH models.Energy Policy, 38(5), 23262339.
(check this in PDF content)
 3

Artzner, P., Delbaen, F., Eber, J. and Heath, D. (1999). Coherent measures of risk.
(check this in PDF content)
 4

Mathematical Finance, 9(3), 203228.
(check this in PDF content)
 5

Basel Committee on Banking Supervision. 1996a. Amendment to the Capital Accord to incorporate market risks. Bank for International Settlements, Basel.
(check this in PDF content)
 6

Basel Committee on Banking Supervision. 1996b. Supervisory framework for the use of backtesting in conjunction with the internal models approach to market risk capital requirements. Publication No. 22, Bank for International Settlements, Basel.
(check this in PDF content)
 7

Breidt, F. J., Crato, N. and De Lima, P. (1998). The detection and estimation of long memory in stochastic volatility.Journal of Econometrics, 83(1), 325348.
(check this in PDF content)
 8

Cappuccio, N., Lubian, D. and Raggi, D. (2004). MCMC Bayesian estimation of a skew
(check this in PDF content)
 9

GED stochastic volatility model.Studies in Nonlinear Dynamics&Econometrics, 8(2).
(check this in PDF content)
 10

Chai, J., Guo, Jue., Gong L. and Wang S. Y. (2011). Estimating crude oil price ’Value at Risk’ using the BayesianSVSGT approach.Systems EngineeringTheory&Practice, 31(1).
(check this in PDF content)
 11

Chan, J. C. (2013). Moving average stochastic volatility models with application to inflation forecast.Journal of Econometrics, 176(2), 162172.
(check this in PDF content)
 12

Chan, J. C. (2017). The stochastic volatility in mean model with timevarying parameters: An application to inflation modeling.Journal of Business&Economic Statistics, 35(1), 1728.
(check this in PDF content)
 13

Chan, J. C. and Grant, A. L. (2016a). Modeling energy price dynamics: GARCH versus stochastic volatility.Energy Economics, 54, 182189.
(check this in PDF content)
 14

Chan, J. C. and Grant, A. L. (2016b). On the observeddata deviance information criterion for volatility modeling.Journal of Financial Econometrics, 14(4), 772802.
(check this in PDF content)
 15

Chan, J. C. and Grant, A. L. (2016c). Fast computation of the deviance information criterion for latent variable models.Computational Statistics&Data Analysis, 100, 847859.
(check this in PDF content)
 16

Chan,J. C. and Hsiao,C. Y.L. (2013).Estimation of Stochastic Solatility
(check this in PDF content)
 17

ModelswithHeavyTailsandSerialDependence.[Online].Availableat https://papers.ssrn.com/sol3/papers.cfm?abstractid=2359838[Accessed27October 2017].
(check this in PDF content)
 18

Chen, C. W., Gerlach, R. and Wei, D. (2009). Bayesian causal effects in quantiles: Accounting for heteroscedasticity.Computational Statistics&Data Analysis, 53(6), 19932007.
(check this in PDF content)
 19

Chen, Q., Gerlach, R. and Lu, Z. (2012). Bayesian ValueatRisk and expected shortfall forecasting via the asymmetric Laplace distribution.Computational Statistics&Data Analysis, 56(11), 34983516.
(check this in PDF content)
 20

Chib, S., Nardari, F. and Shephard, N. (2002). Markov chain Monte Carlo methods for stochastic volatility models.Journal of Econometrics, 108(2), 281316.
(check this in PDF content)
 21

Christoffersen, P. F. (1998). Evaluating interval forecasts.International Economic Review, 841862.
(check this in PDF content)
 22

Diebold, F. X. and Mariano, R. S. (1995). Comparing predictive accuracy.Journal of Business and Economic Statistics, 13, 253263.
(check this in PDF content)
 23

Fan, Y., Zhang, Y. J., Tsai, H. T. and Wei, Y. M. (2008). Estimating Value at Riskof crude oil price and its spillover effect using the GEDGARCH approach.Energy Economics, 30(6), 31563171.
(check this in PDF content)
 24

Hollander, M. and Wolfe, D. A. (1999).Nonparametric Statistical Methods. 2nd edn. New York: John Wiley.
(check this in PDF content)
 25

Hung, J.C., Lee, M.C. and Liu, H.C. (2008). Estimation of valueatrisk for energy commodities via fattailed GARCH models.Energy Economics, 30(3), 11731191.
(check this in PDF content)
 26

Koopman, S. J. and Hol Uspensky, E. (2002). The stochastic volatility in mean model: empirical evidence from international stock markets.Journal of Applied Econometrics, 17(6), 667689.
(check this in PDF content)
 27

Kotz, S., Kozubowski, T. and Podgorski, K. (2001).The Laplace distribution and generalizations: a revisit with applications to communications, economics, engineering, and finance.New York: Springer Science & Business Media.
(check this in PDF content)
 28

Kristoufek, L. (2014). Leverage effect in energy futures.Energy Economics, 45, 19.
(check this in PDF content)
 29

Kupiec, P. H. (1995). Techniques for verifying the accuracy of risk measurement models.
(check this in PDF content)
 30

The Journal of Derivatives, 3(2), 7384.
(check this in PDF content)
 31

Lardic, S. and Mignon, V. (2008). Oil prices and economic activity: An asymmetric cointegration approach.Energy Economics, 30(3), 847855.
(check this in PDF content)
 32

Lehmann, E. L. (1974).Nonparametrics. New York: HoldenDay Inc. McGrawHill.
(check this in PDF content)
 33

Lopez, J. A. (1998). Testing your risk tests.Financial Survey, 1820.
(check this in PDF content)
 34

Lopez, J. A. (1999). Methods for evaluating ValueatRisk estimates.Federal Reserve Bank of San Francisco Economic Review, 2, 317.
(check this in PDF content)
 35

Louzis, D. P., XanthopoulosSisinis, S. and Refenes, A. P. (2014). Realized volatility models and alternative ValueatRisk prediction strategies.Economic Modelling, 40, 101116.
(check this in PDF content)
 36

Marimoutou, V., Raggad, B. and Trabelsi, A. (2009). Extreme value theory and value at risk: application to oil market.Energy Economics, 31(4), 519530.
(check this in PDF content)
 37

Papapetrou, E. (2001). Oil price shocks, stock market, economic activity and employment in Greece.Energy Economics, 23(5), 511532.
(check this in PDF content)
 38

Sarma, M., Thomas, S. and Shah, A. (2003). Selection of ValueatRisk models.Journal of Forecasting, 22, 337358.
(check this in PDF content)
 39

So, M. E. P., Lam, K. and Li, W. K. (1998). A stochastic volatility model with Markov switching.Journal of Business&Economic Statistics, 16(2), 244253.
(check this in PDF content)
 40

Takahashi, M., Omori, Y. and Watanabe, T. (2009). Estimating stochastic volatility models using daily returns and realized volatility simultaneously.Computational Statistics&Data Analysis, 53(6), 24042426.
(check this in PDF content)
 41

Wichitaksorn, N., Wang, J. J., Boris Choy, S. T. and Gerlach, R. (2015). Analyzing return asymmetry and quantiles through stochastic volatility models using asymmetric Laplace error via uniform scale mixtures.Applied Stochastic Models in Business and Industry, 31(5), 584608.
(check this in PDF content)
 42

Youssef, M., Belkacem, L. and Mokni, K. (2015). ValueatRisk estimation of energy commodities: A longmemory GARCHEVT approach.Energy Economics, 51, 99110.
(check this in PDF content)
 43

Yu, J. and Yang, Z. (2002). A class of nonlinear stochastic volatility models. Univ. of
(check this in PDF content)
 44

Auckland,Economics Working Paper, (229).
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 45

Zhao, S., Lu, Q., Han, L., Liu, Y. and Hu, F. (2015). A meanCVaRskewness portfolio optimization model based on asymmetric Laplace distribution.Annals of Operations Research, 226(1), 727739.
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A. Asymmetric Laplace distribution A random variableXis said to follow an Asymmetric Laplace Distribution if the characteristic function ofXcan be defined as: ψ(t) = 1
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B. VaR and CVaR derivation for oil supply and demand under SVALD For oil supply, we have: P(yt≤−V aRs,tΩt) =P ( yt−μ
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C. Derivation of the pdf of scaled ALD Consider a random variablezfollows the Asymmetric Laplace density function in equation (17) with mean and variance given by:15 E(z) =θ+ τ
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D. Derivation of scaled ALD as an SMU This part demonstrates the derivation of SALD as a scale mixture offU(εtθ−λκ 2σt √ 1+κ4
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Since Case (2): ∫∞ 0 √
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E. Derivation of full conditional distributions This part presents brief derivation of the full conditional distributions of model parameters and latent volatilities under the SMU of ALD. •For parameterδ, we have: f(δβ,σ2η,h,y)∝f(h1δ,β,σ2η)
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B Hence, we can obtain: δβ,σ2η,h,y∼N( B A
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