Transcript Jump Testing - Duke University

Seasonal Variance in Corn
Futures
Caleb Seeley
4/16/08
Motivation
• Does the seasonal nature of corn
production have an impact on corn futures
prices?
• Will jumps in corn prices be impacted by
the seasonal production cycle?
Remaining Corn Stocks
12,000.00
10,000.00
Millions of Bushels
8,000.00
2001
2002
2003
6,000.00
2004
2005
2006
4,000.00
2,000.00
0.00
Sept.-Nov.
Dec.-Feb.
Mar.-May
Quarter
Jun.-Aug.
Total Corn Disappearance
4,000.00
3,500.00
3,000.00
Millions of Bushels
2,500.00
2001
2002
2003
2,000.00
2004
2005
2006
1,500.00
1,000.00
500.00
0.00
Sept.-Nov.
Dec.-Feb.
Mar.-May
Quarter
Jun.-Aug.
Motivation
• Corn is planted in the spring and harvested in
the early October. The crop is stored in October,
and used over the course of the next year.
• Prior to the harvest of corn, the remaining stocks
from the previous year have almost been
completely used up.
• Will examine corn futures prices at 5 minute
intervals over 25 years (1983-2007) to see how
this impacts volatility of corn futures prices.
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
• Jump Test from BN-S (2005)
Background Mathematics Part 3
• Tri-Power Quarticity
• Z-statistic – used .999 significance level (3.09)
Realized Semi-Varience
• Semi-variance taken from Barndorff-Nielsen,
Kinnebrock, Shephard (2008)
• Realized semi-variance is the sum of squared
negative returns (where 1 is the indicator
function that the return is negative) :
Results
• Average RV = .0001002
• Average BV = .000151
• Annualized RV = 17.03%
• Annualized BV = 15.89%
• Jump Days: 372 (5.8%)
Standard Error: .000369
• Both monthly and weekly realized variance and
bipower-variation exhibit same pattern.
• Likely causes of increased volatility may also
cause price increases eg: drought, crop disease
• Does Semi-Variance suggest this is the case?
Monthly RSV
Weekly RSV
Results
• No, SV and Upward-Variance exhibit an
identical pattern to RV and BV
• Do the patterns in RV and BV impact
jumps on a seasonal basis?
RV-BV/RV
• Standard Error: .00813273
RV-BV/RV
Conclusions
• Distinct pattern in yearly volatility:
– As corn stocks dwindle and in preparation for
next years harvest corn price volatility rises to
a peak in July.
• This pattern is observed in both RV and
BV suggesting that it is part of the
continuous portion of volatility, NOT the
jump portion.
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%)
Jumps By Month
Jan:
Feb:
Mar:
Apr:
May:
June:
July:
Aug:
Sep:
Oct:
Nov:
Dec:
38
32
34
26
22
29
37
34
23
27
29
34
Jumps Per Month
40
35
30
25
Jumps
•
•
•
•
•
•
•
•
•
•
•
•
20
15
10
5
0
1
2
3
4
5
6
7
Month
8
9
10
11
12
Conclusions
• Jumps are not much more prevalent in the
summer than any other season.
• Suggests that the volatility rises due to known,
predicted events.
– Weather catastrophes and low corn stocks are known
to occur during summer months.
• Thus the continuous volatility increases as the
corn stocks dwindle as prices become more
susceptible to any shock