1.  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.  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: o “Oil prices jump after OPEC fails to increase production quotas” Los Angles Time (06/08/2011) o “Oil prices jump $2 after US leads air strikes on Libya” BBC news (03/21/2011)

5.  Let P t denote price at time t  If P t 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.  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.  GARCH Jump-diffusion (GJD) process: (6)  Maximum Likelihood Estimation:  With respect to the parameter space

8. 1. Pure Diffusion (PD): 2. Mixed Jump Diffusion (JD): 3. GARCH Diffusion (GPD): 4. GARCH Jump Diffusion (GJD)

9.  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. Parameters PDJDGPDGJD μ 0.4010.901 * 0.645 0.630 σ 8.877 *** 6.958 ***.. κ.. 15.349 *** 16.044 *** α.. 0.211 *** 0.040 β..0.560 *** 0.668 *** λ. 0.109. 0.30 θ.-4.588.-1.910 δ.16.133 ***.19.420 **

11. Parameters PDJDGPDGJD μ 0.0170.078 *** 0.0250.067 ** σ 2.629 *** 1.807 ***.. κ..0.088 *** 0.145 *** α..0.098 *** 0.004 *** β..0.892 *** 0.955 *** λ.0.121 ***. 0.074 *** θ.-0.510 **.-0.698 ** δ.5.4130 ***.6.143 ***

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