The 26 references with contexts in paper Christopher F Baum, Paola Zerilli, Liyuan Chen (2018) “Stochastic volatility, jumps and leverage in energy and stock markets: evidence from high frequency data” / RePEc:boc:bocoec:952

1
Ait-Sahalia Y., Fan J., and Li Y. (2013) The Leverage E§ect Puzzle: Disentangling Sources of Bias at High Frequency. NBER Working Paper No.17592.
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  1. In-text reference with the coordinate start=6041
    Prefix
    We also show that introducing jumps improves only the ability of modeling the behaviour of the volatility for the crude oil futures market. 2 2 Literature review Traditionally, the termleverage e§ectindicates the negative correlation between asset returns and changes in their volatility (see
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    Ait-Sahalia et al. (2013)
    Suffix
    for an extensive literature review). The interpretation of this e§ect is very intuitive if we think that events that have a negative impact on Önancial markets would eventually cause an increase in volatility.

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    Prefix
    There are two possible economic interpretations for this empirical property: 1) when asset returns fall, the Örm becomes more levered as the market value of their debt increases compared to the market value of their equity, making the stock riskier and therefore increasing its volatility (see Black (1976)); 2) when volatility increases, future prices fall (see
    Exact
    French et al. (1987)). Bekaert and Wu (2000) and Ait-Sahalia et al. (2013)
    Suffix
    study di§erent possible interpretations. The latter authors Önd that the leverage e§ect in high frequency data is not statistically signiÖcant over short periods, but become negative and statistically signiÖcant over long periods.

5
Artzner, P., Delbaen, F., Eber, J. and Heath, D. (1999). Coherent measures of risk. Mathematical Finance, 9(3), 203-228.
Total in-text references: 1
  1. In-text reference with the coordinate start=42086
    Prefix
    Despite its popularity, an obvious and distinctive limitation of theV aRapproach is that it only speciÖes the maximum one can lose at a given risk level, but provides no indication for how much more thanV aRone can lose if extreme tail events happen. This may lead to an equivalentV aRestimate for two di§erent positions, though they have completely di§erent risk exposures.
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    Artzner et al. (1999)
    Suffix
    proposed the concept of coherent risk measure, which has become the paradigm of risk measurement. A good alternative is conditional Value-at-Risk (CV aR), which is a coherent risk measure and retains the beneÖts ofV aRin terms of the capability to deÖne quantiles of the loss distribution.

7
Baum C. F. and Zerilli P. (2016), Jumps and stochastic volatility in crude oil futures prices using conditional moments of integrated volatility, Energy Economics, Volume 53, January 2016, Pages 175ñ181.
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  1. In-text reference with the coordinate start=2359
    Prefix
    of York, York YO10 5DD, UK, paola.zerilli@york.ac.uk and lc844.york@gmail.com 1 Introduction The study of volatility in crude oil and natural gas markets and its interaction with returns (leverage) has a broad range of Önancial impacts both from an hedging point of view and also for forecasting purposes. The main limitation of using daily data is that volatility is not observable (see
    Exact
    Bollerslev and Zhou (2002) and Baum and Zerilli (2016)).
    Suffix
    As suggested by Zhou (1996), the availability of high-frequency data has opened up new possibilities in estimating volatility. Tick-by-tick data provide an almost continuous observation of the return series, making the daily volatility observable so that it can be studied in great detail.

  2. In-text reference with the coordinate start=18857
    Prefix
    X t-k-s-t (x(s)dN(-s)) 2 12 Barndor§-Nielsen and Shephard (2004) proposed the Realized Bipower Variation as a consistent estimate of integrated volatility component in the presence of jumps: BV(t;k;n) =-2 Pn-k i=2 \f \fr t-k+ikn;1n -\f \f \f \f \fr t-k+ (i-1)k n; 1 n <\f \f \f RV(t;k;n)-BV(t;k;n)-!QV(t;k)-IV(t;k) QV(t;k)-IV(t;k) = X t-k-s-t (x(s)dN(-s)) 2 asn-!1 A similar approach was used in
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    Baum and Zerilli (2016).
    Suffix
    In this section, we are going to introduce the three models that are going to be estimated and compared in terms of ability to Öt the data, risk measurement and out of sample performance: the Stochastic Volatility model (SV), the Stochastic Volatility model with jumps (SVJ) and the Stochastic Volatility model with leverage (SVL). 13 4.1 Stochastic Volatility model (SV) We model the returns on cru

8
Bekaert, G.,Wu, G., (2000). Asymmetric volatility and risk in equity markets. Review of Financial Studies 13, 1ñ42.
Total in-text references: 1
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    Prefix
    There are two possible economic interpretations for this empirical property: 1) when asset returns fall, the Örm becomes more levered as the market value of their debt increases compared to the market value of their equity, making the stock riskier and therefore increasing its volatility (see Black (1976)); 2) when volatility increases, future prices fall (see
    Exact
    French et al. (1987)). Bekaert and Wu (2000) and Ait-Sahalia et al. (2013)
    Suffix
    study di§erent possible interpretations. The latter authors Önd that the leverage e§ect in high frequency data is not statistically signiÖcant over short periods, but become negative and statistically signiÖcant over long periods.

9
Berkowitz, J. (2001). Testing density forecasts, with applications to risk management. Journal of Business & Economic Statistics, 19(4), 465-474.
Total in-text references: 1
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    Prefix
    Nevertheless, formal backtesting methods can be found in literature, such as the most commonly used approach zero-mean residual test by McNeil and Frey (2000) which rely on bootstrapping or one sampletprinciple, censored Gaussian method by
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    Berkowitz (2001) and
    Suffix
    the functional delta approach by Kerkhol and Melenverg 40 (2004)2. However, applying these methods tend to be di¢ cult and overly complex. The application of these methods is based upon the realization of speciÖc conditions, hence it is possible to backtestCV aRonly under speciÖc circumstances.

11
Black, F., (1976). Studies on stock price volatility changes. Proceedings of the 1976 Meeting of the American Statistical Association, Business and Economic Statistics, pp. 177ñ181.
Total in-text references: 1
  1. In-text reference with the coordinate start=6564
    Prefix
    There are two possible economic interpretations for this empirical property: 1) when asset returns fall, the Örm becomes more levered as the market value of their debt increases compared to the market value of their equity, making the stock riskier and therefore increasing its volatility (see
    Exact
    Black (1976));
    Suffix
    2) when volatility increases, future prices fall (see French et al. (1987)). Bekaert and Wu (2000) and Ait-Sahalia et al. (2013) study di§erent possible interpretations. The latter authors Önd that the leverage e§ect in high frequency data is not statistically signiÖcant over short periods, but become negative and statistically signiÖcant over long periods.

12
Bollerslev, T. and Zhou H. (2002), Estimating Stochastic Volatility Di§usion
Total in-text references: 5
  1. In-text reference with the coordinate start=2359
    Prefix
    of York, York YO10 5DD, UK, paola.zerilli@york.ac.uk and lc844.york@gmail.com 1 Introduction The study of volatility in crude oil and natural gas markets and its interaction with returns (leverage) has a broad range of Önancial impacts both from an hedging point of view and also for forecasting purposes. The main limitation of using daily data is that volatility is not observable (see
    Exact
    Bollerslev and Zhou (2002) and Baum and Zerilli (2016)).
    Suffix
    As suggested by Zhou (1996), the availability of high-frequency data has opened up new possibilities in estimating volatility. Tick-by-tick data provide an almost continuous observation of the return series, making the daily volatility observable so that it can be studied in great detail.

  2. In-text reference with the coordinate start=11725
    Prefix
    We focus on the role of volatility as a measure of variability and uncertainty of futures returns and we examine the impact of the leverage e§ect between futures returns and their variance. In our investigation, we use the moment conditions derived from the stochastic variance as proposed by
    Exact
    Bollerslev and Zhou (2002) and Garcia et al. (2011).
    Suffix
    3 Data The raw data used in this study are 10-minute aggregations of natural gas, crude oil and S&P500 futures contract transactions-level data provided by TickData, Inc. Industry analysts have noted that to avoid market disruptions, major participants 5 in the natural gas futures market roll over their positions from the near contract to the next-near contract over several days before the near c

  3. In-text reference with the coordinate start=16152
    Prefix
    ret WTI 0.00 0.01 -1.64 1.73 0.23 -0.09 7.33 Table 2:Descriptive Statistics for the daily futures realised variance 20012016 mean median min max stdev skew kurt fut rv SP500 0.00 0.00 0.00 0.32 0.01 12.75 258.67 fut rv NG0.06 0.02 0.00 5.86 0.19 19.15 495.16 fut rv WTI 0.03 0.01 0.00 2.68 0.08 20.95 648.12 4 Estimation method Following
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    Bollerslev and Zhou (2002),
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    who use continuously observed futures prices on oil, we build a conditional moment estimator for stochastic variance models based on matching the sample moments ofRealized Variancewith population moments of 10 Table 3: Test Statistics and P-values for daily futures returns KSmirnov p-val SFrancia p-valQp-val fut ret SP5000.0870.000 14.078 0.000 156.575 0.000 fut ret NG0.0560.000 11.640

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    Prefix
    It is the parameter of the Poisson counting process that takes values: 1when an extreme event happens 0otherwise The main moment conditions used for the SV speciÖcation, are augumented using two additional moment conditions. From
    Exact
    Bollerslev and Zhou (2002)
    Suffix
    Appendix Bpage 62(B:14)a§ects all the moment conditions (impact of jumps) At time(t;t+ 1) e1Jt;t+1=E[RVt;t+1jGt]-RVt;t+1 =E[BPt;t+1jGt] +--2xdt-RVt;t+1 since E[RVt;t+1jGt] =E[BPt;t+1jGt] +--2xdt 18 and e2Jt;t+1=E RV2t;t+1 \f \fGt -RV2t;t+1 =E BP2t;t+1 \f \fGt + 2--2xE RV2t;t+1 \f \fGt dt---4xdt-RV2t;t+1 They are then augmented using appropriate functions of the past values of the realised variance

  5. In-text reference with the coordinate start=59536
    Prefix
    In this Appendix we also show the expressions of 2 additional moment conditions that have the main purpose of modelling the leverage e§ect: we have not used them in our results as, when tested, these moment conditions did not add any relevant information to the available set and therefore they revelead to be redundant in this case. 8.1 Residual 1 From
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    Bollerslev and Zhou (2002),
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    page 56Appendix A.1equation(A:3) 51 e1t+1;t+2=E[Vt+1;t+2jGt]-Vt+1;t+2 =-E[Vt;t+1jGt] +\f-Vt+1;t+2 whereVt+1;t+2is therealised varianceandGtis the information set. dt=T-t=t+ 1-t= 1 =t+ 2-(t+ 1) = 1 -=e-\f=>(1--) a= 1 (1--) = \f -> b=>(1-a) =>\f 8.2 Residual 2 E V2t+1;t+2 \f \fGt =H1-E V2t;t+1 \f \fGt +I-E[Vt;t+1jGt] +J e2t+1;t+2=E V2t+1;t+2 \f \fGt -V2t+1;t+2 =H1-E V2t;t+1 \f \fGt +I-E[Vt;t+1jGt]

14
Casassus, J., Collin-Dufresne, P., (2005). Stochastic convenience yield implied from commodity futures and interest rates. Journal of Finance, Vol. 60, No. 5, 56 2283-2331.
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    In this paper, we employ a stochastic volatility model in order to 4 analyze the uncertainty of S&P500, natural gas and crude oil futures returns. The empirical analysis makes use of high-frequency (tick-by-tick) data from the futures markets, aggregated to 10-minute intervals during the trading day.
    Exact
    Schwartz (1997), Schwartz and Smith (2000), and Casassus and Collin-Dufresne (2005)
    Suffix
    propose multi-factor models for energy prices where returns are only a§ected by Gaussian shocks, but they constrain volatility to be constant. Pindyck (2004) examines the volatility of energy spot and futures prices, estimating the standard deviation of their Örst di§erences.

15
Chan, J. and A. Grant (2016). "On the Observed-Data Deviance Information Criterion for Volatility Modeling", Journal of Financial Econometrics, 14, 4, 772802.
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    Prefix
    The latter authors Önd that the leverage e§ect in high frequency data is not statistically signiÖcant over short periods, but become negative and statistically signiÖcant over long periods. In recent years, the commodity price literature has shown that there is evidence of leverage e§ects in various energy markets. More speciÖcally,
    Exact
    Chan and Grant (2016),
    Suffix
    considering lower frequency (weekly) commodity returns conclude that SV models (with an MA component) are able to replicate the main features of the data more e¢ ciently than GARCH models. At the same time, they Önd a signiÖcant negative leverage e§ect in crude oil spot markets.

16
Chen, L., Zerilli P. and Baum C. (2018) "Leverage e§ects and stochastic volatility in spot oil returns: A Bayesian approach with VaR and CVaR applications" Energy Economics íin pressí. Christo§ersen, P. F. (1998). Evaluating interval forecasts. International Economic Review, 841-862.
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    Prefix
    From an econometric point of view, the employment of intraday data leads to the estimation of the structural parameters of the stochastic volatility models using simple moment conditions tailored to Öt all the relevant empirical features of energy and stock index returns. In terms of hedging strategies in the crude oil market, it has been shown (see
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    Chen, Zerilli and Baum (2018))
    Suffix
    that the introduction of the leverage e§ect in the traditional SV model with normally distributed errors is capable of adequately estimating risk in a VaR and CVaR sense for conservative oil suppliers in both the WTI and Brent spot markets while it tends to overestimate risk for more speculative oil suppliers.

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    Prefix
    futures and speculative investors who are short futures would be better o§ not considering the leverage e§ect in order to have more precise forecasts of risk in a VaR sense. 45 46 47 48 7 Conclusions In this paper we estimate a Stochastic Volatility model using high frequency data on crude oil, natural gas and stock index (S&P500) futures. In terms of hedging strategies, it has been shown (see
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    Chen, Zerilli and Baum 2018),
    Suffix
    at lower frequencies and for crude oil spot returns, that the introduction of the leverage e§ect in the traditional SV model with Normally distributed errors is capable of adequately estimating risk (in a VaR and CVaR sense) for conservative oil suppliers in both the WTI and Brent markets while it tends to overestimate risk for more speculative oil suppliers.

19
Fan Y., Zhang Y., Tsai H., Wei Y. (2008) Estimating ëValue at Riskíof crude oil price and its spillover e§ect using the GED-GARCH approach, Energy Economics, Volume 30, Issue 6, Pages 3156-3171.
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  1. In-text reference with the coordinate start=7513
    Prefix
    At the same time, they Önd a signiÖcant negative leverage e§ect in crude oil spot markets. Kristoufek (2014) focuses on the leverage e§ect in commodity futures markets and provides an extensive literature review in this area.
    Exact
    Fan et al. (2008)
    Suffix
    estimate VaR of crude oil prices using a GED-GARCH approach with daily WTI and Brent prices spanning from 1987 to 2006. They Önd that this type of model speciÖcation does as well as the standard normal distribution at a 95% conÖdence level.

  2. In-text reference with the coordinate start=46440
    Prefix
    This test investigates if the failure rate is equal to the expected prescribed risk level and if the exceptions are independently distributed over time. The null hypothesis for this test is that the exceptions are independent and that the expected failure rate is equal to prescribed risk level. 6.1 Out-of-sample VaR and CVaR estimations As in
    Exact
    Fan et al. (2008) and
    Suffix
    Youssef at al. (2015), in this subsection, we test the forecasting ability of the SV and SVL models by computing the out-of-sample VaR 3Kupiecís (1995) approach is an unconditional test. On the other hand, we need to conditionally examine theV aRperformance under the time-varying volatility framework.

20
French, K. R., Schwert, G. W., Stambaugh, R. F., (1987). Expected stock returns and volatility, Journal of Financial Economics 19, 3ñ29.
Total in-text references: 1
  1. In-text reference with the coordinate start=6632
    Prefix
    There are two possible economic interpretations for this empirical property: 1) when asset returns fall, the Örm becomes more levered as the market value of their debt increases compared to the market value of their equity, making the stock riskier and therefore increasing its volatility (see Black (1976)); 2) when volatility increases, future prices fall (see
    Exact
    French et al. (1987)). Bekaert and Wu (2000) and Ait-Sahalia et al. (2013)
    Suffix
    study di§erent possible interpretations. The latter authors Önd that the leverage e§ect in high frequency data is not statistically signiÖcant over short periods, but become negative and statistically signiÖcant over long periods.

21
Garcia R., Lewis M., Pastorello S. and Renault E. (2011) Estimation of objective and risk-neutral distributions based on moments of integrated volatility, Journal of Econometrics 160 (2011) 22ñ32.
Total in-text references: 3
  1. In-text reference with the coordinate start=11725
    Prefix
    We focus on the role of volatility as a measure of variability and uncertainty of futures returns and we examine the impact of the leverage e§ect between futures returns and their variance. In our investigation, we use the moment conditions derived from the stochastic variance as proposed by
    Exact
    Bollerslev and Zhou (2002) and Garcia et al. (2011).
    Suffix
    3 Data The raw data used in this study are 10-minute aggregations of natural gas, crude oil and S&P500 futures contract transactions-level data provided by TickData, Inc. Industry analysts have noted that to avoid market disruptions, major participants 5 in the natural gas futures market roll over their positions from the near contract to the next-near contract over several days before the near c

  2. In-text reference with the coordinate start=29521
    Prefix
    This main moment condition is then augmented using past realizations of the returns and the variance as instruments (see the Appendix for more details). Additional details about the moment conditions and more speciÖcally about the equations for the leverage e§ect can be found in
    Exact
    Garcia et al. (2011).
    Suffix
    As shown in Tables 20, 22, 24 all the moment conditions are in accordance with the data and the overall HansenísJstatistic indicates that the overidentifying restrictions are valid. As shown in Tables 19, 21, 23 all estimated parameters of the model are very precisely estimated (-is signiÖcant at 10% level for WTI) and take on sensible values from an analytical perspective. 26 We Önd that stochast

  3. In-text reference with the coordinate start=60410
    Prefix
    2-1 e-2-B= -<2 > >(1-2-) + > 2(-+ 5) (--1) C=--2 (1--) =--a--2 D= -2> 2(1--) 2 =a2----2-> 52 H1 =-2 G1 =\f2 I= 1 a2(C+ 2-\f) + ---2 (2ab+A) a N= a2 D+\f2 +\f(2ab+A) + 1--2 -b2+B -J=-bI+N 8.3 Residual 3 Residuals 3 to 5 are built in order to deal with the leverage aspect as they focus on the relationship between futures returns and their variance. This moment condition derives from the paper by
    Exact
    Garcia et al. (2011)
    Suffix
    page 32 top equation in Box I: e3t+1;t+2= E[pt;t+1Vt+1;t+2jGt]-b a -pt;t+1Vt;t+1 Considering the relationship between the population varianceVtand the realised varianceVt;t+1 E[Vt;t+1jFt] =aVt+b Vt= E[Vt;t+1jFt]-b a Ab+ab2-aB-(A-2ab)E[Vt;t+1jFt] +aE V2t;t+1 \f \fFt V2t= a3 E[pt;t+1Vt;t+1jGt] = --e-(E[Vt;t+1jGt]-+>(e--k-1)) = --e-> E[Vt;t+1jGt]-b a -+>(e--k-1) E[pt;t+1Vt+1;t+2jGt]-b a 53 e3t+1;t+2=

26
Heston, S., (1993). A closed-form solution for options with stochastic volatility with applications to bond and currency options. Review of Finanacial Studies 6, 57 327ñ343.
Total in-text references: 1
  1. In-text reference with the coordinate start=19380
    Prefix
    models that are going to be estimated and compared in terms of ability to Öt the data, risk measurement and out of sample performance: the Stochastic Volatility model (SV), the Stochastic Volatility model with jumps (SVJ) and the Stochastic Volatility model with leverage (SVL). 13 4.1 Stochastic Volatility model (SV) We model the returns on crude oil, natural gas and S&P500 futures using the
    Exact
    Heston (1993)
    Suffix
    model, setting the leverage e§ect equal to zero at the beginning. dpt=dln(Ft) = p VtdW1t dVt=-(>-Vt)dt+p VtdW2t dW1tdW2t= 0 In this model, there are two orthogonal Wiener processes,dW1tanddW2t, driving the evolution of returns and volatility.

28
Kristoufek, L. (2014) Leverage e§ect in energy futures, Energy Economics, Volume 45, September 2014, Pages 1ñ9.4.
Total in-text references: 4
  1. In-text reference with the coordinate start=7379
    Prefix
    More speciÖcally, Chan and Grant (2016), considering lower frequency (weekly) commodity returns conclude that SV models (with an MA component) are able to replicate the main features of the data more e¢ ciently than GARCH models. At the same time, they Önd a signiÖcant negative leverage e§ect in crude oil spot markets.
    Exact
    Kristoufek (2014)
    Suffix
    focuses on the leverage e§ect in commodity futures markets and provides an extensive literature review in this area. Fan et al. (2008) estimate VaR of crude oil prices using a GED-GARCH approach with daily WTI and Brent prices spanning from 1987 to 2006.

  2. In-text reference with the coordinate start=8168
    Prefix
    Youssef et al. (2015) 3 evaluate VaR and CVar for crude oil and gasoline markets using a long memory GARCH-EVT approach. Their Öndings and backtesting exercise show that crude oil markets are characterized by asymmetry, fat tails and long range memory. In the commodity price literature,
    Exact
    Kristoufek (2014) and Nomikos and Andriosopoulos (2012),
    Suffix
    using daily data, Önd aninverse leverage e§ectin the natural gas market: a positive correlation coe¢ cient. Larsson and Nossman (2011) Önd evidence for stochastic volatility and jumps in both returns and volatility daily spot prices of WTI crude oil from 1989 to 2009.

  3. In-text reference with the coordinate start=8495
    Prefix
    In the commodity price literature, Kristoufek (2014) and Nomikos and Andriosopoulos (2012), using daily data, Önd aninverse leverage e§ectin the natural gas market: a positive correlation coe¢ cient. Larsson and Nossman (2011) Önd evidence for stochastic volatility and jumps in both returns and volatility daily spot prices of WTI crude oil from 1989 to 2009. See
    Exact
    Kristoufek (2014)
    Suffix
    for an extensive literature review on the leverage e§ect in commodity markets. We contribute to the current debate by testing for the existence of the leverage e§ect when considering a near-continuous observation of the processes with the ability to study their volatility in great detail because of the use of high frequency futures returns in the S&P500, natural gas and crude oil markets and by st

  4. In-text reference with the coordinate start=30381
    Prefix
    More speciÖcally, we Önd signiÖcant evidence of aleverage e§ectfor S&P500 and crude oil markets: a negative shock to returns increases volatility in these markets. In contrast, we Önd evidence ofinverse leverage e§ectfor the natural gas market (in line with
    Exact
    Kristoufek (2014)).
    Suffix
    27 Table 19:GMM estimates for SVL model for the S&P500 futures: 09/2001ñ06/2016 0.0424--(2.92) > 0.00649--(5.55) 0.249--(17.96) -0.379--(-11.29) N3704 t statistics in parentheses -p<0:10;--p<0:05;---p<0:01 28 29 Table 21:GMM estimates for SVL model for the Natural Gas futures: 09/2001ñ06/2016 0.760--(3.45) > 0.0460--(5.60) 0.925--(3.49) 0.201--(4.57) N3708 t statistics in parentheses -p<0:10;--p<0

29
Kupiec, P. H. (1995). Techniques for verifying the accuracy of risk measurement models. The Journal of Derivatives, 3(2), 73-84.
Total in-text references: 2
  1. In-text reference with the coordinate start=45273
    Prefix
    methodologies as well as their implementations at di§erent circumstances can refer to Wimmerstedt (2015). 41 the indicator function which is deÖned as: Downside:It= 1if yt<-V aRd;t 0if yt-V aRu;t Upside:It= 1if yt> V aRu;t 0if yt-V aRd;t Furthermore, there are three formal tests based on the above criteria to backtest theV aRestimates. The unconditional coverage test (LRuc), proposed by
    Exact
    Kupiec (1995),
    Suffix
    is to examine whether the null hypothesisH0:FR=-can be satisÖed. A good performance of theV aRmodel should be accompanied by an accurate unconditional coverage, that is, the failure rate is statistically expected to be equal to the prescribedV aRlevel-.

  2. In-text reference with the coordinate start=45562
    Prefix
    A good performance of theV aRmodel should be accompanied by an accurate unconditional coverage, that is, the failure rate is statistically expected to be equal to the prescribedV aRlevel-. The method proposed by
    Exact
    Kupiec (1995)
    Suffix
    is capable to test the overestimates or underestimates of aV aRmodel. It does not, however, consider whether the exceptions are scattered or if they appear in clusters3. In order to examine whether the V aRviolations are serially uncorrelated over time, Christo§ersen (1998) proposes the independent likelihood ratio test (LRind).

30
Larsson, K. and Nossman, M., (2011), Jumps and stochastic volatility in oil prices: Time series evidence, Energy Economics vol. 33, issue 3, pages 504-514.
Total in-text references: 1
  1. In-text reference with the coordinate start=8332
    Prefix
    In the commodity price literature, Kristoufek (2014) and Nomikos and Andriosopoulos (2012), using daily data, Önd aninverse leverage e§ectin the natural gas market: a positive correlation coe¢ cient.
    Exact
    Larsson and Nossman (2011)
    Suffix
    Önd evidence for stochastic volatility and jumps in both returns and volatility daily spot prices of WTI crude oil from 1989 to 2009. See Kristoufek (2014) for an extensive literature review on the leverage e§ect in commodity markets.

31
Mason, C. and Wilmot, N. (2014), Jump processes in natural gas markets, Energy Economics, 46, issue S1, p. S69-S79.
Total in-text references: 1
  1. In-text reference with the coordinate start=10665
    Prefix
    Schwartz (1997), Schwartz and Smith (2000), and Casassus and Collin-Dufresne (2005) propose multi-factor models for energy prices where returns are only a§ected by Gaussian shocks, but they constrain volatility to be constant. Pindyck (2004) examines the volatility of energy spot and futures prices, estimating the standard deviation of their Örst di§erences.
    Exact
    Mason and Wilmot (2014)
    Suffix
    investigate the potential presence of jumps in two key daily natural gas prices: the spot price at the Henry Hub in the US, and the spot price for natural gas at the National Balancing Point in the UK.

32
McNeil, A. J. and Frey, R. (2000). Estimation of tail-related risk measures for heteroscedastic Önancial time series: an extreme value approach. Journal of Empirical Finance, 7(3), 271-300.
Total in-text references: 1
  1. In-text reference with the coordinate start=42907
    Prefix
    Although theCV aRapproach has been widely used for risk analysis, the implementation of backtesting forCV aRmodels is much harder than forV aRmodels. Nevertheless, formal backtesting methods can be found in literature, such as the most commonly used approach zero-mean residual test by
    Exact
    McNeil and Frey (2000)
    Suffix
    which rely on bootstrapping or one sampletprinciple, censored Gaussian method by Berkowitz (2001) and the functional delta approach by Kerkhol and Melenverg 40 (2004)2. However, applying these methods tend to be di¢ cult and overly complex.

33
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    Youssef et al. (2015) 3 evaluate VaR and CVar for crude oil and gasoline markets using a long memory GARCH-EVT approach. Their Öndings and backtesting exercise show that crude oil markets are characterized by asymmetry, fat tails and long range memory. In the commodity price literature,
    Exact
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    Suffix
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35
Pindyck, R. S. (2004), Volatility and commodity price dynamics. Journal of
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    examines the volatility of energy spot and futures prices, estimating the standard deviation of their Örst di§erences. Mason and Wilmot (2014) investigate the potential presence of jumps in two key daily natural gas prices: the spot price at the Henry Hub in the US, and the spot price for natural gas at the National Balancing Point in the UK.

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    In this paper, we employ a stochastic volatility model in order to 4 analyze the uncertainty of S&P500, natural gas and crude oil futures returns. The empirical analysis makes use of high-frequency (tick-by-tick) data from the futures markets, aggregated to 10-minute intervals during the trading day.
    Exact
    Schwartz (1997), Schwartz and Smith (2000), and Casassus and Collin-Dufresne (2005)
    Suffix
    propose multi-factor models for energy prices where returns are only a§ected by Gaussian shocks, but they constrain volatility to be constant. Pindyck (2004) examines the volatility of energy spot and futures prices, estimating the standard deviation of their Örst di§erences.

39
Schwartz, E. S., Smith, J. E.,(2000). Short-term variations and long-term dynamics in commodity prices. Management Science, Vol. 47, No. 2, 893-911.
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    In this paper, we employ a stochastic volatility model in order to 4 analyze the uncertainty of S&P500, natural gas and crude oil futures returns. The empirical analysis makes use of high-frequency (tick-by-tick) data from the futures markets, aggregated to 10-minute intervals during the trading day.
    Exact
    Schwartz (1997), Schwartz and Smith (2000), and Casassus and Collin-Dufresne (2005)
    Suffix
    propose multi-factor models for energy prices where returns are only a§ected by Gaussian shocks, but they constrain volatility to be constant. Pindyck (2004) examines the volatility of energy spot and futures prices, estimating the standard deviation of their Örst di§erences.

45
Wimmerstedt, L. (2015). Backtesting Expected Shortfall: The Design and Implementation of Di§erent Backtests. [Online]. Available at http://www.diva-portal.org/smash/record.jsf?pid=diva2$n%$3A848996$n&$dswid=1158 [Accessed 10 December 2017].
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  1. In-text reference with the coordinate start=44905
    Prefix
    aRs andFRV aRdas follows: FRV aRd= 1 T XT t=1 It(yt<-V aRd;t) FRV aRu= 1 T XT t=1 It(yt> V aRu;t) whereV aRd;tandV aRu;tare the estimatedV aRsfor downside and upside risk at time t for a given conÖdence interval,Tis the number of observations andIt(-)is 2A comprehensive discussion of variousCV aRbacktesting methodologies as well as their implementations at di§erent circumstances can refer to
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    Wimmerstedt (2015).
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    41 the indicator function which is deÖned as: Downside:It= 1if yt<-V aRd;t 0if yt-V aRu;t Upside:It= 1if yt> V aRu;t 0if yt-V aRd;t Furthermore, there are three formal tests based on the above criteria to backtest theV aRestimates.

46
Youssef M., Belkacem L., Mokni K. (2015) Value-at-Risk estimation of energy commodities: A long-memory GARCHñEVT approach, Energy Economics, Volume 51, Pages 99-110.
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    They Önd that this type of model speciÖcation does as well as the standard normal distribution at a 95% conÖdence level. They also test and Önd evidence for asymmetric leverage e§ects without modelling them directly.
    Exact
    Youssef et al. (2015)
    Suffix
    3 evaluate VaR and CVar for crude oil and gasoline markets using a long memory GARCH-EVT approach. Their Öndings and backtesting exercise show that crude oil markets are characterized by asymmetry, fat tails and long range memory.

47
Zhou, Bin (1996) High-Frequency Data and Volatility in Foreign-Exchange Rates, Journal of Business & Economic Statistics, Vol. 14, No. 1 (Jan., 1996), pp. 45-52 59
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    york@gmail.com 1 Introduction The study of volatility in crude oil and natural gas markets and its interaction with returns (leverage) has a broad range of Önancial impacts both from an hedging point of view and also for forecasting purposes. The main limitation of using daily data is that volatility is not observable (see Bollerslev and Zhou (2002) and Baum and Zerilli (2016)). As suggested by
    Exact
    Zhou (1996),
    Suffix
    the availability of high-frequency data has opened up new possibilities in estimating volatility. Tick-by-tick data provide an almost continuous observation of the return series, making the daily volatility observable so that it can be studied in great detail.