using markov models in r to understand the lifecycle of exchange-traded...
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Using Markov Models in R to Understand theLifecycle of Exchange-traded Derivatives
Grant Cavanaugh(Presenter)
Ph.D. CandidateAgricultural EconomicsUniversity of [email protected]
Michael PenickSenior Economist
US Commodity Futures Trading Commission
R/Finance Chicago: May 18 2013
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NOTE
THIS PRESENTATION DOES NOT REFLECT THE OPINIONS
OF THE CFTC THE ANALYSIS PRESENTED HERE IS BASED ON PUBLICLY AVAILABLE DATA
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My dissertation
What is the chance that exchange-traded El Nino derivatives willtake off?
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Lets not neglect base rates
What is the chance that any exchange-traded derivatives will takeoff?
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The basic methodology
1. Get aggregate stats on annual trading volumes from aninstitutional database (futures, options, cleared swaps)
2. Add in Mike Penicks work on futures going back to 1954(volumes for some of the contracts in the database cut outabruptly)
3. Put volume in terms of levels (basically, log 10 rounded downwith separate level for 0 values)
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The basic methodology cont.
Now ask: given the state that a contract is in this year (year t),
what is the probability that it will go to each of the other possiblestates (i.e. those state we see in the sample) next year (year t+1)?
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The basic methodology cont.
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The basic methodology cont.
In more mathematical terms:
Volume levelyear t+1 |Volume levelyear t Categorical()
Dirichlet(x vol level 0, x vol level 1, . . . , x vol level 108 ) (1)
I estimated this using the Bayesian Gibbs sampling programMartyn Plummers JAGS (using R package rjags )
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The basic methodology cont.
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The basic methodology cont.
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The basic methodology cont.
If you run this routine on different grouping of contracts you cansee how the rise and fall of trading volumes varies:
across timeacross exchanges*on individual exchanges across time*across product subgroup*
*In full paper, not this presentation.
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The traditional story
Few contracts have/will ever take off.
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0.00
0.25
0.50
0.75
1.00
0e+00 2e+08 4e+08 6e+08Annual volume
E m p
i r i c a
l C D F
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0.5
0.6
0.7
0.8
0.9
1.0
0.5
0.6
0.7
0.8
0.9
1.0
0.5
0.6
0.7
0.8
0.9
1.0
0.5
0.6
0.7
0.8
0.9
1.0
0.5
0.6
0.7
0.8
0.9
1.0
0.5
0.6
0.7
0.8
0.9
1.0
0.5
0.6
0.7
0.8
0.9
1.0
1 9 5 0 ' s
1 9
6 0 ' s
1 9 7 0 ' s
1 9 8 0 ' s
1 9 9 0 ' s
2 0 0 0 ' s
2 0 1 1
0e+00 1e+06 2e+06 3e+06 4e+06 5e+06An n u a l vol ume
E m p
i r i c a l
C D F
1960
1970
1980
1990
2000
2010Year
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ECDFs tell us. . .
Trading volume grew steadily less concentrated between the 1950sand 1990s (perhaps with some retrenchment between the 1980s
and 1990s.)That trend reversed sharply in the 2000s, with the annual ECDFsapproaching a right angle.
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One likely cause. . .
Innovation exploded during the 2000s.
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0
1000
2000
3000
1960 1970 1980 1990 2000 2010Year
D e r i v a
t i v e s
i n s a m p
l e
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vol 0, year t+1 vol 1's, t+1 vol 10's, t+1 vol 100's, t+1 vol 1000's, t+1 vol 10^4's, t+1 vol 10^5's, t+1 vol 10^6's, t+1 vol 10^7's, t+1 vol 10^8's, t+1
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0.59
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1960
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1980
1990
2000
2010
1950
1960
1970
1980
1990
20002010
1950
1960
1970
1980
1990
2000
2010
1950
1960
1970
1980
1990
2000
2010
1950
1960
1970
1980
1990
2000
2010
v o
l 0 , y e a
r t
v o
l 1 ' s
, t
v o
l 1
0 ' s
, t
v o
l 1
0 0
' s
, t
v o
l 1
0 0 0
' s , t
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0 . 5 0
0 . 7 5
1 . 0 0
0 . 0 0
0 . 2 5
0 . 5 0
0 . 7 5
1 . 0 0
0 . 0 0
0 . 2 5
0 . 5 0
0 . 7 5
1 . 0 0
0 . 0 0
0 . 2 5
0 . 5 0
0 . 7 5
1 . 0 0
0 . 0 0
0 . 2 5
0 . 5 0
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0 . 0 0
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0 . 0 0
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1 . 0 0
0 . 0 0
0 . 2 5
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D e c a d e
F 0 0
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From 0 to 0
vol 0, year t+1
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0.53
0.6
0.89
0.93
0.82
0.7
0.46
1950
1960
1970
1980
1990
2000
2010
v ol 0
, y e a
r t
0.00 0.25 0.50 0.75 1.00
Pr(yearonyear move)
D e c a d e
F i l di it t d bl di it
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From single digits to double digits
vol 10's, t+1
q
q
q
q
q
q
q
0.21
0.09
0.14
0.03
0.02
0.2
0.15
1950
1960
1970
1980
1990
2000
2010
v o
l 1 ' s
, t
0.00 0.25 0.50 0.75 1.00
Pr(yearonyear move)
D e c a d e
F d bl digit t 100
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From double digits to 100s
vol 100's, t+1
q
q
q
q
q
q
q
0.31
0.08
0
0.05
0.13
0.27
0.11
1950
1960
1970
1980
1990
2000
2010
v o
l 1 0
' s , t
0.00 0.25 0.50 0.75 1.00
Pr(yearonyear move)
D e c a d e
From 100s to 1 000s
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From 100s to 1,000s
vol 1000's, t+1
q
q
q
q
q
q
q
0.09
0.06
0.29
0.15
0.12
0.22
0.1
1950
1960
1970
1980
1990
2000
2010
v ol 1
0 0
' s , t
0.00 0.25 0.50 0.75 1.00
Pr(yearonyear move)
D e c a d e
From 1 000s to 10 000s
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From 1,000 s to 10,000 s
vol 10^4's, t+1
q
q
q
q
q
q
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0.11
0.11
0.12
0.14
0.17
0.18
0.1
1950
1960
1970
1980
1990
2000
2010
v o
l 1 0 0 0
' s , t
0.00 0.25 0.50 0.75 1.00
Pr(yearonyear move)
D e c a d e
What should we take from this?
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What should we take from this?
Contracts at low levels of trading are more exible than in the past.
More readily move up to trading in the thousands.Low trading is no longer the death sentence it once was.
vol 0, year t+1 vol 1's, t+1 vol 10's, t+1 vol 100's, t+1 vol 1000's, t+1 vol 10^4's, t+1 vol 10^5's, t+1 vol 10^6's, t+1 vol 10^7's, t+1 vol 10^8's, t+1
q
0 05q
0q
0 01q
0 04q
0 25q
0 56q
0 1q
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0q
02010
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0.01
0.01
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0.85
0.7
0.58
0.61
0.71
0.61
0.56
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0.12
0.11
0.05
0.07
0.09
0.17
0.22
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0.1
0.07
0.09
0.1
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0.84
0.83
0.84
0.7
0.81
0.72
0.67
q
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0.77
0.15
0.04
0.08
0.05
0.08
0.19
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0.83
0.94
0.8
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0.81
0.78
q
q
q
q
q
q
q
0.02
0.02
0.02
0.17
0.02
0.02
0.07
q
q
q
q
q
q
q
0
0
0
0
0
0
0
q
q
q
q
q
q
0
0
0
0
0
0
0
q
q
q
q
q
q
q
0
0
0
0
0
0
0
q
q
q
q
q
q
q
0
0
0.02
0.05
0.02
0.09
0.02
q
q
q
q
q
q
q
0.74
0.74
0.74
0.81
0.91
0.92
0.93
q
q
q
q
q
q
q
0.02
0.02
0.02
0.02
0.84
0.08
0.06
q
q
q
q
q
q
0
0
0
0
0
0
0
q
q
q
q
q
q
q
0
0
0
0
0
0
0
q
q
q
q
q
q
q
0
0
0
0
0
0
0
q
q
q
q
q
q
q
0.01
0.01
0.01
0
0.04
0.04
0
q
q
q
q
q
q
q
0.92
0.92
0.92
0.92
0.14
0.92
0.94
1950
1960
1970
1980
1990
2000
1950
1960
1970
1980
1990
2000
2010
1950
1960
1970
19801990
2000
2010
1950
1960
1970
1980
1990
2000
2010
1950
1960
1970
1980
1990
2000
2010
v o
l 1
0 ^ 4 ' s
, t
v o
l 1
0 ^
5 ' s
, t
v o
l 1
0 ^
6 ' s
, t
v o
l 1
0 ^ 7 ' s
, t
v o
l 1
0 ^
8 ' s
, t
0 . 0 0
0 . 2 5
0 . 5 0
0 . 7 5
1 . 0 0
0 . 0 0
0 . 2 5
0 . 5 0
0 . 7 5
1 . 0 0
0 . 0 0
0 . 2 5
0 . 5 0
0 . 7 5
1 . 0 0
0 . 0 0
0 . 2 5
0 . 5 0
0 . 7 5
1 . 0 0
0 . 0 0
0 . 2 5
0 . 5 0
0 . 7 5
1 . 0 0
0 . 0 0
0 . 2 5
0 . 5 0
0 . 7 5
1 . 0 0
0 . 0 0
0 . 2 5
0 . 5 0
0 . 7 5
1 . 0 0
0 . 0 0
0 . 2 5
0 . 5 0
0 . 7 5
1 . 0 0
0 . 0 0
0 . 2 5
0 . 5 0
0 . 7 5
1 . 0 0
0 . 0 0
0 . 2 5
0 . 5 0
0 . 7 5
1 . 0 0
D e c a d e
What should we take from this?
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What should we take from this?
The additional exibility for low volume contracts coincided with
some erosion of the probability of progressing to higher volumelevels.
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vol 0, year t+1
q
q
q
q
q
q
q
0.01
0.01
0.03
0.05
0.05
0.04
0.05
1950
1960
1970
1980
1990
2000
2010
v o
l 1 0
^ 4 ' s
, t
0.00 0.25 0.50 0.75 1.00Pr(yearonyear move)
D e c a d e
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Netting out the changes
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Netting out the changes
What is more important from the standpoint of a new contract?The substantially increased exibility from low levels of
volume?The smaller fall in the probability of progressing to higherlevels of volume?
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q
q
q
q
q
q
q
1960
1980
2000
1e+05 1e+06Expec te d volume a fter 10 years
D e c a d e
Conclusions
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Markets have become more concentrated in any given year.But, contracts are more likely to rise up from low levels of trading.On balance, expected trading level after ten years remained inthe middle of the historical range.So, despite remarkable rates of innovation, the prospects forthe marginal innovation have not eroded.
Conclusions - from the full article
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Based on our reading of the NYMEX:this decadal changes in derivative lifecycles were driven by theswitch to electronic trading rather than exchange consolidation
In general:variations in expected year ten trading volumes were largerdecade to decade than from exchange to exchange or producttype to product type
Final thought - the iTune-ization of derivatives markets?
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g
Paradigm shift in marginal cost structure of a good withelastic demand. (Supply effect)New technologies allow for ubiquitous access to that good.
(Demand effect)The market rewards specialty products more than in the past;and, blockbusters are as large/larger than theyve ever beenbefore. . . but some of this change came at the expense of babyblockbusters.
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