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Jump Processes in the Market for Crude Oil

Jump Processes in the Market for Crude Oil. An Empirical Investigation. Jump Processes in the Market for Crude Oil Neil A. Wilmot Assistant Professor Department of Economics University of Minnesota Duluth & Charles F. Mason H.A. True Chair in Petroleum and Natural Gas Economics

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Jump Processes in the Market for Crude Oil

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  1. Jump Processes in the Market for Crude Oil An Empirical Investigation

  2. Jump Processes in the Market for Crude Oil Neil A. Wilmot Assistant Professor Department of Economics University of Minnesota Duluth & Charles F. Mason H.A. True Chair in Petroleum and Natural Gas Economics Department of Economics & Finance University of Wyoming

  3. Introduction • Stochastic element to natural resource prices • Changes in oil prices continue to catch both experts and consumers by surprise (Wirl, 2008) • Continuous stochastic process are inadequate: • “Oil prices jump after OPEC fails to increase production quotas” Los Angles Time (06/08/2011) • “Oil prices jump $2 after US leads air strikes on Libya”BBC news (03/21/2011)

  4. Distribution of Price Returns

  5. Discontinuities in the Price • Let Pt denote price at time t • If Pt follows a geometric Brownian motion process, then gives the pure diffusion (PD) model (1) • The jump component is modeled as a Poisson driven process q, where (2)

  6. Data Generation Mechanism • The mixed jump-diffusion (JD) process is given as (3) • Alternatively, to incorporate a time-varying process, a GARCH(1,1)(GPD) framework is employed, (4)where (5)

  7. Maximum likelihood • GARCH Jump-diffusion (GJD) process: (6) • Maximum Likelihood Estimation: • With respect to the parameter space

  8. Model Assumptions • Pure Diffusion (PD): • Mixed Jump Diffusion (JD): • GARCH Diffusion (GPD): • GARCH Jump Diffusion (GJD)

  9. Data and its Properties • Data: WTI Spot, Brent Spot, WTI Futures • Prior to the parameter estimation, the data was investigated for nonstationarity utilizing LM unit root tests that allow for the presence of structural breaks

  10. Parameter Estimates: Monthly (WTI) Spot

  11. Parameter Estimates: Daily (WTI) Spot

  12. Conclusions • Likelihood Ratio Tests • Supports the presence of jumps relative to the pure diffusion process • Importance of time-varying volatility • Structural Break Sub-Periods • Results support the previous conclusions • Temporal aggregation • Greater aggregation tends to ‘wash out’ jumps

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