Seasonal Variance among Light Sweet Crude and Corn Futures Caleb Seeley 3/16/08

Introduction Examine Light Sweet Crude futures prices at 5 minute intervals over 20 years (1987-2007) Examine Corn futures prices at 5 minute intervals over 25 years (1982-2007) Begin by looking for significant jumps and then continue by examining variance monthly and weekly Using Bardorff-Nielson and Shephard model of jump testing.

Background Mathematics Realized Variation: Realized Bi-Power Variation:

Background Mathematics Part 2 The relative jump is defined: RJt = (RVt – BVt) / RVt In order to studentize the RJt one needs to estimate the integrated quarticity

Background Mathematics Part 3 Tri-Power Quarticity Z-statistic – used .999 significance level (3.09)

Oil Price 92-07

Crude Results Average RV = .00030825 Average BV = .00029271 Annualized RV = 27.87% Annualized BV = 27.16% Jump Days = 81 (1.54%)

Results from 1992-2007 RV 27.54% BV 26.97% Jumps: 61 (1.52%)

RV BV 92-07

Results Winter Jumps:17 (21%) Spring Jumps:27 (33%) Summer Jumps:17 (21%) Fall Jumps:20 (25%) Warm Weather Jumps:44 (54%) Cold Weather Jumps:37 (46%)

RV BV by month

RV-BV by moth

RV BV by week

RV-BV by week

Corn Results Average RV = .0001002 Average BV = .000151 Annualized RV = 17.03% Annualized BV = 15.89% Jump Days: 372 (5.8%)

Seasonal Jumps Winter Jumps: 105 (28.2%) Spring Jumps: 78 (20.97%) Summer Jumps: 101(27.15%) Fall Jumps: 88 (23.66%) Warm Weather Jumps: 193 (51.88%) Cold Weather Jumps: 179 (48.12%)

Sp RVBV

Rvbv month

Rv bv week

Rv-bv month

Rv-bv week