# The 14 references with contexts in paper Christopher F Baum, Paola Zerilli (2014) “Jumps and stochastic volatility in crude oil futures prices using conditional moments of integrated volatility” / RePEc:boc:bocoec:860

1
Alquist, Ron & Kilian, Lutz & Vigfusson, Robert J., (2011). ”Forecasting the Price of Oil,” CEPR Discussion Papers 8388, C.E.P.R. Discussion Papers.
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In the futures markets, returns exhibit heavy tails, autocorrelation, and volatility clustering, leading to significant challenges in modeling their first and second moments. Both the International Monetary Fund (IMF) and the Federal Reserve Board (see
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Alquist et al. (2011) and
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IMF 2005 p. 67; 2007, p. 42) use futures prices as the best available proxy for the market expectations of the spot crude oil price. Like many financial series, commodity futures prices are likely to exhibit random-walk behavior.

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Stochastic Volatility model (SV) We model the returns on futures on crude oil using the Heston (1993) model. For simplicity, we set the drift of the log price equal to zero.2This choice is consistent with
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Alquist et al. (2011)
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who find that a reasonable and parsimonious forecasting model for spot oil prices is the random walk without drift. 2As Bollerslev et al. (2002) suggest, a drift could be easily introduced in the futures returns equation. 7 dpt=dln(Ft) = √ VtdW1t dVt=κ(θ−Vt)dt+σ √ VtdW2t E(dW1tdW2t) = 0 In this model, there are two orthogonal Wiener processes,dW1tanddW2t, driving the evolution of returns and

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This experiment allows us to assess the structural stability of the model as within the shorter sample λ, the frequency of extreme events, is significantly different from zero. 10 5.3. Does leverage matter? As suggested by
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Alquist et al. (2011),
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there is no reason why oil producers should be concerned about the volatility of the price of oil. The data seem to suggest that there is no connection between the shocks affecting futures prices and the shocks affecting the corresponding volatility.

6
Bernanke, B.S. (1983), Irreversibility, Uncertainty, and Cyclical Investment, Quarterly Journal of Economics, 98, 85-106.
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1. In-text reference with the coordinate start=6491
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Larsson and Nossman (2011) find evidence for stochastic volatility and jumps in both returns and volatility daily spot prices of WTI crude oil from 1989 to 2009. The role of volatility as a measure of uncertainty of oil price futures is 2 stressed by
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Bernanke (1983), Pindyck (1991) and
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Kellogg (2010) who show that this measure of uncertainty is extremely relevant for firms’ investment decisions. Our contribution lies in the use of the information on volatilty of oil futures returns provided by high frequency, intra-day data while focusing on the role of volatility as measure of variability and uncertainty of oil price forecasts. 3.

7
Bollerslev, T. and H. Zhou (2002), Estimating Stochastic Volatility Diffusion Using Conditional Moments of Integrated Volatility, Journal of Econometrics, 109, 33-65.
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The high frequency data allows us to test various models for oil futures returns using a straightforward Generalized Method of Moments (GMM) estimator that matches sample moments of the realized volatility to the corresponding population moments of the integrated volatility in the spirit of
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Bollerslev and Zhou (2002).
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These models are then compared, in terms of overall fit of the data and forecast accuracy statistics, over the full sample. The model with stochastic volatility and jumps is also tested over a subsample (January 2006–December 2012) to address structural stability (as in 1 Andersen, Benzoni and Lund (2002)).

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The Box–Pierce portmanteau (orQ) test for white noise rejects its null for both series. The daily returns series exhibits significant ARCH effects at 1, 5, 10 and 22 lags, while no evidence of ARCH effects is found in the realized volatility series. 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 volatility jump-diffusion models based on matching the sample moments of 4 realized volatility with population moments of integrated volatility.

8
Casassus, J., Collin-Dufresne, P., (2005). Stochastic convenience yield implied from commodity futures and interest rates. Journal of Finance, Vol. 60, No. 5, 2283-2331. 14
Total in-text references: 1
1. In-text reference with the coordinate start=5238
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Key findings include the importance of both jumps and stochastic volatility in oil futures returns and the apparent unimportance of leverage as a modeled component. The wider applicability of this method of estimation to other markets is outside the scope of this paper, but an interesting topic for future research. 2. Review of the literature
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Schwartz (1997), Schwartz and Smith (2000), Casassus and Collin-Dufresne (2005)
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propose multi-factor models for energy prices where returns are only affected by Gaussian shocks only, but constrain volatility to be constant. Pindyck (2004) examines the volatility of energy spot and futures prices, estimating the standard deviation of their first differences.

10
Heston, S., (1993). A closed-form solution for options with stochastic volatility with applications to bond and currency options. Review of Finanacial Studies 6, 327–343.
Total in-text references: 1
1. In-text reference with the coordinate start=12466
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As we discuss below, there is no empirical support for leverage, in that the parameter expressing the effect of leverage is never significantly different from zero. Thus, we present here our findings from the SV and SVJ models. 5.1. Stochastic Volatility model (SV) We model the returns on futures on crude oil using the
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Heston (1993)
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model. For simplicity, we set the drift of the log price equal to zero.2This choice is consistent with Alquist et al. (2011) who find that a reasonable and parsimonious forecasting model for spot oil prices is the random walk without drift. 2As Bollerslev et al. (2002) suggest, a drift could be easily introduced in the futures returns equation. 7 dpt=dln(Ft) = √ VtdW1t dVt=κ(θ−Vt)dt

11
Kilian, Lutz (2009) “Not All Oil Price Shocks Are Alike: Disentangling Demand nd Supply Shocks in the Crude Oil Market.” American Economic Review 99, no. 3: 1053–69.
Total in-text references: 1
1. In-text reference with the coordinate start=2307
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Crude oil, as a key global commodity, has experienced considerable price level variation in the boom preceding the global financial crisis in 2008 and the ensuing Great Recession. A major oil price shock in 2008 was caused by constraints on the production of crude oil paired with low elasticity of demand (for details, see Hamilton (2009) and
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Kilian (2009)).
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This shock, while being caused by fundamentals, was clearly exacerbated by financial speculation and ‘financialization’ of commodities. Variation in oil price levels has been accompanied by wide variations in the volatility of returns.

12
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=6246
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Vo (2009) estimates a multivariate stochastic volatility model using daily data on the West Texas Intermediate (WTI) crude oil futures contracts traded on the NYMEX and finds that stochastic volatility plays an important role.
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find evidence for stochastic volatility and jumps in both returns and volatility daily spot prices of WTI crude oil from 1989 to 2009. The role of volatility as a measure of uncertainty of oil price futures is 2 stressed by Bernanke (1983), Pindyck (1991) and Kellogg (2010) who show that this measure of uncertainty is extremely relevant for firms’ investment decisions.

13
Pindyck, R.S. (1991), Irreversibility, Uncertainty and Investment, Journal of Economic Literature, 29, 1110-1148.
Total in-text references: 1
1. In-text reference with the coordinate start=6491
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Larsson and Nossman (2011) find evidence for stochastic volatility and jumps in both returns and volatility daily spot prices of WTI crude oil from 1989 to 2009. The role of volatility as a measure of uncertainty of oil price futures is 2 stressed by
Exact
Bernanke (1983), Pindyck (1991) and
Suffix
Kellogg (2010) who show that this measure of uncertainty is extremely relevant for firms’ investment decisions. Our contribution lies in the use of the information on volatilty of oil futures returns provided by high frequency, intra-day data while focusing on the role of volatility as measure of variability and uncertainty of oil price forecasts. 3.

14
Pindyck, R. S. (2004), Volatility and commodity price dynamics. Journal of Futures Markets, 24: 1029–1047.
Total in-text references: 1
1. In-text reference with the coordinate start=5469
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Review of the literature Schwartz (1997), Schwartz and Smith (2000), Casassus and Collin-Dufresne (2005) propose multi-factor models for energy prices where returns are only affected by Gaussian shocks only, but constrain volatility to be constant.
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Pindyck (2004)
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examines the volatility of energy spot and futures prices, estimating the standard deviation of their first differences. Askari and Khrichene (2008) fit jump-diffusion models to futures on Brent crude oil.

15
Schwartz, E. S., (1997). The stochastic behavior of commodity prices: Implications for valuation and hedging. Journal of Finance, Vol. 52, No. 3, 923-973.
Total in-text references: 1
1. In-text reference with the coordinate start=5238
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Key findings include the importance of both jumps and stochastic volatility in oil futures returns and the apparent unimportance of leverage as a modeled component. The wider applicability of this method of estimation to other markets is outside the scope of this paper, but an interesting topic for future research. 2. Review of the literature
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Schwartz (1997), Schwartz and Smith (2000), Casassus and Collin-Dufresne (2005)
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propose multi-factor models for energy prices where returns are only affected by Gaussian shocks only, but constrain volatility to be constant. Pindyck (2004) examines the volatility of energy spot and futures prices, estimating the standard deviation of their first differences.

16
Schwartz, E. S., Smith, J. E.,(2000). Short-term variations and longterm dynamics in commodity prices. Management Science, Vol. 47, No. 2, 893-911. 15
Total in-text references: 1
1. In-text reference with the coordinate start=5238
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Key findings include the importance of both jumps and stochastic volatility in oil futures returns and the apparent unimportance of leverage as a modeled component. The wider applicability of this method of estimation to other markets is outside the scope of this paper, but an interesting topic for future research. 2. Review of the literature
Exact
Schwartz (1997), Schwartz and Smith (2000), Casassus and Collin-Dufresne (2005)
Suffix
propose multi-factor models for energy prices where returns are only affected by Gaussian shocks only, but constrain volatility to be constant. Pindyck (2004) examines the volatility of energy spot and futures prices, estimating the standard deviation of their first differences.

17
Schwartz, E. S., Trolle, A., (2009). Unspanned stochastic volatility and the pricing of commodityderivatives. Review of Financial Studies, Vol. 22 (11): 4423-4461.
Total in-text references: 1
1. In-text reference with the coordinate start=5693
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Pindyck (2004) examines the volatility of energy spot and futures prices, estimating the standard deviation of their first differences. Askari and Khrichene (2008) fit jump-diffusion models to futures on Brent crude oil.
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Schwartz and Trolle (2009)
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propose a multifactor stochastic volatility model for pricing futures and options on light sweet crude oil trading on the NYMEX. Using daily data, they present evidence that taking account of stochastic volatility improves pricing, but they consider the inclusion of jumps to be less important.

20
Tukey, John W (1977). Exploratory Data Analysis. Addison-Wesley.
Total in-text references: 1
1. In-text reference with the coordinate start=15544
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All five estimated parameters 9 of the model are very precisely estimated and take on sensible values from an analytical perspective. In order to better motivate the concept of jumps in the futures returns process, we employ non-parametric methods to identify those periods when “extreme events” may have occurred. Following
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Tukey (1977),
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we consider extreme events to be those periods when the one-trading-day change in futures returns lay outside the bounds of the “adjacent values” of a conventional box plot. The adjacent values are defined using 1.5 times the inter-quartile range (IQR), or difference between the empirical 75th and 25th percentiles (p75, p25) of the series.

21
Vo, M. T., (2009). Regime-switching stochastic volatility: evidence from the crude oil market, Energy Economics, 31, 779-788. 16
Total in-text references: 1
1. In-text reference with the coordinate start=6014
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Schwartz and Trolle (2009) propose a multifactor stochastic volatility model for pricing futures and options on light sweet crude oil trading on the NYMEX. Using daily data, they present evidence that taking account of stochastic volatility improves pricing, but they consider the inclusion of jumps to be less important.
Exact
Vo (2009)
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estimates a multivariate stochastic volatility model using daily data on the West Texas Intermediate (WTI) crude oil futures contracts traded on the NYMEX and finds that stochastic volatility plays an important role.