 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 Department of Economics & Finance University of Wyoming

 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)

 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)

 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)

 GARCH Jump-diffusion (GJD) process: (6)  Maximum Likelihood Estimation:  With respect to the parameter space

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

 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

Parameters PDJDGPDGJD μ * σ *** ***.. κ *** *** α *** β *** *** λ θ δ *** **

Parameters PDJDGPDGJD μ *** ** σ *** ***.. κ *** *** α *** *** β *** *** λ *** *** θ ** ** δ *** ***

 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