In contrast to financial markets, volume risk is as important as price risk. → It
takes several forms. −volumetric options (financially traded or embedded in
supply.
Fundamentals of Commodities Spot and Forward / Futures Markets
Hélyette Geman Professor of Finance Birkbeck University of London & ESCP- EAP
m ai -9 oc 1 m t-91 ar sao 92 ût ja 92 nv -9 ju 3 in no 93 v9 av 3 r-9 se 4 pt fé 94 vr -9 ju 5 ildé 95 cm 95 ai -9 oc 6 m t-96 ar sao 97 ût ja 97 nv -9 ju 8 in no 98 v9 av 8 rse 9 9 pt -9 9
180
160
140
120
100
80
60
GSCI TR DJ-AIGCITR
Growth of $100: 1991-9991
ar s00 ju in -0 se 0 pt -0 dé 0 cm 00 ar s01 ju in -0 se 1 pt -0 dé 1 cm 01 ar s02 ju in -0 se 2 pt -0 dé 2 cm 02 ar s03 ju in -0 se 3 pt -0 dé 3 cm 03 ar s04
m
Commodities as a Desirable Investment as of early 2000
190
170
150
130
110
90
GSCI TR DJ-AIGCITR
Growth of $100: 2000-2004
DJ-AIG Energy - January 2002 to July 2006 450 400 350 300 250 200 150 100 50 1
3
5
7
9
11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57
DJ-AIG Energy Sub-index
Is Mean Reversion Dead? Geman 2005, JAI
DJ- AIG Index Jan 2006- Nov 2008
CRB Index Jan 2006 – Nov 2008
Major Commodity Exchanges NYMEX (New York, 1872)
Crude oil (WTI), natural gas, heating oil, propane, unleaded gasoline
IPE (1980)/ICE (2005)
Crude oil (Brent), natural gas
Nordpool, EEX, APX, Powernext, Electricity GMX, OMEL …. London Metal Exchange (London, Aluminum, copper, nickel, tin, lead and 1877), COMEX silver London Bullion Exchange, CBOT
Gold and silver
CBOT (Chicago, 1850)
Corn, soybean, wheat, rice
CME (Chicago, 1898)
Pork bellies, beef, lumber
Dubai Exchange
Middle East Crude oil, gold, wheat
IMEX (Qatar)
Liquid Natural Gas (LNG)
Commodity Prices: A shift of Paradigm → The price of a commodity −is not the present value of future cashflows −nor the expected value (under the right probability measure) of the final payoff → It is fundamentally driven by supply and demand Quantity
Demand
Supply
Q° P°
Supply
Demand Price
Elastic supply and demand
Short-term inelastic supply and demand
→ Another key quantity is the available inventory at the date of analysis, worldwide or in a given region. This inventory has in particular a major impact on price volatility (see Geman-Nguyen 2005) → In contrast to financial markets, volume risk is as important as price risk → It takes several forms −volumetric options (financially traded or embedded in supply contracts) −uncertainty on oil reserves may generate a downward jump on the stock of an oil company
Comparative Moves of WTI and Brent Crude Prices
A very unusual situation related to US inventory
Commodities and Numéraire
→ Most commodities are denominated in US dollars → During the recent decline of the dollar, some OPEC members considered the possibility of using as a "numéraire" the arithmetic average of the dollar and the euro → Maybe the right way of thinking is to use the commodity (e.g., a barrel of oil) as the numéraire when managing an energy derivatives portfolio! → Gold has partly been playing this rule for decades
Shipping and Freight → Two types of freight Dry bulk: Capesize, Panamax, Handymax Tankers: Suez-Aframax → Major actors in the spot and forward markets: Cargill, Louis Dreyfus, Total, Shell, Deutsche Bank, Morgan Stanley → Trading activity Baltic Exchange (London), used to offer Futures contracts, now only forwards Imarex (Oslo), provides daily quotes on maritime shipping LCH-Clearnet (London) Nymex (New York), very active for dry bulk
Freight Derivatives Market Basics of FFAs → An FFA (Forward Freight Agreement) is a contract to buy or sell the price of freight for a specific cargo route over a defined future period → It is based on a defined voyage or time charter → It is financially settled, the settlement being based on the spot market index (typically the average of the last 7 days in expiration month or the monthly average) as assessed by the Baltic Exchange or Platt's
Baltic Indices
→ The Baltic Handymax Index (BHMI), the Baltic Panamax Index (BPI) and the Baltic Capesize Index (BCI) are calculated from average rates on major routes, both voyage and timecharter, as assessed by a panel of brokers → The Baltic Dry Index (BDI) is the average of the BHMI, BPI and BCI. It provides a good general indicator of movement in the dry bulk market and continues the time series of the Baltic Freight Index (BFI) which was introduced in 1985
Freight Dry - Bulk Market → The Baltic Capesize Index (BCI) reached an absolute maximum (level 9000) in January 2005, then experienced a huge drop later that year: −5125 Oct 15 −4637 Nov 15 −3385 Dec 15 −3018 Jan 15, 06 → The annual volatility is of the order of 110% → Both spikes and volatility make this market similar to the electricity market
Baltic Capesize Index
Baltic Panamax Index
Baltic Dry Index January 2001 - April 2008
Theory of Storage Kaldor (1939), Working (1949), Brennan (1958)
Three fundamentals results: → The convenience yield accounts for the benefit that accrues to the holder of the physical commodity but not to the holder of the futures contract. It is represented as an implicit dividend → The volatility of the commodity spot price is high when inventory is low → The volatility of Futures contracts decreases with the maturity: "Samuelson effect"
The Convenience Yield (continued) → It is the "comfort" provided by holding the spot commodity → Owning the commodity allows to reduce costs and delays in delivery (Kaldor) to satisfy an unexpected rise in demand (Brennan) to secure the continuity of production (Kaldor) → The convenience yield is all the higher as inventory is low → It is positively correlated to the spot price of the commodity → It accrues to the holder of the physical commodity but not to the holder of a derivative contract
Spot-Forward Relationship for a Storable Commodity Under no arbitrage
⎤ ⎡ f T (t ) = S(t ) ⎢ 1 + r ( T − t ) + c( T − t ) − y1 ( T − t ) ⎥ 123 123 1 424 3 ⎥ ⎢ ⎣⎢ cos t of financing cos t of storage implicit dividend ⎥⎦
If we define a convenience yield net of cost of storage
f T (t ) = S(t )[1 + (r − y ) ( T − t )] Or in continuous time
f T (t ) = S(t ) e ( r − y )( T −t ) as long as r and y are constant over the period (t, T)
Correlation Spot-Futures (Nordpool)
Correlation spot price - first nearby
Crude Oil Matthew Simmons, Twilight in the Desert → "Sooner or later, the worldwide use of oil must peak because oil, like the other two fossils - coal and natural gas - is non renewable" → Over the past 30 years, daily oil consumption has risen by approximately 33 million barrels, Asia accounting for more than half of this growth in demand → Current consumption levels suggest that the world's oil supply should last until around 2045 → The world's largest producers are Saudi Arabia (13% of world production), Russia (12%), the United States (7%), Iran (6%) and China (5%) → The Gulf of Mexico region provides about 29% of the US oil production, hence the disruption created by the long shutdown of many oil rigs after hurricanes Katrina and Rita in summer 2005
Brent Crude Oil – April 2007 to March 2009
NYMEX WTI Crude Oil - April 2007 to March 2009
The Forward Curve → The set {FT (t) , T > t} is the forward curve prevailing at date t for a given commodity in a given location → It is the fundamental tool when trading commodities, as spot prices may be unabservable and options illiquid → The shape of the forward curve is at any date t in a one-to-one mapping with the convenience yield y
The oil market as a World Market
→ Seasonality is not significant since tankers are rerouted to satisfy a surge of demand in a given region → The representation of the spot price as a geometric Brownian motion is less questionable since it has indeed been increasing in average → It is in the context of this crucial commodity that Brennan and Schwartz (1985), Gibson and Schwartz (1990) remarkably introduced in the valuation of derivative contracts the economic concept of
convenience yield → Gabillon (1991) shows the role of the convenience yield in explaining the role of oil forward curves
10/30/2007
7/10/2007
3/20/2007
11/28/2006
8/8/2006
4/18/2006
12/27/2005
9/6/2005
5/17/2005
1/25/2005
10/5/2004
6/15/2004
2/24/2004
11/4/2003
7/15/2003
3/25/2003
12/3/2002
8/13/2002
4/23/2002
1/1/2002
WTI Oil Prices Jan 2002 - Oct 2007
120
100
80
60
40
20
0
c9 av 5 rao 96 ût -9 dé 6 c9 av 6 rao 97 ût -9 dé 7 c9 av 7 rao 98 ût -9 dé 8 c9 av 8 rao 99 ût -9 dé 9 c9 av 9 rao 00 ût -0 dé 0 c0 av 0 r ao -01 ût -0 dé 1 c0 av 1 r ao -02 ût -0 dé 2 c0 av 2 r ao -03 ût -0 dé 3 c0 av 3 r ao -04 ût -0 dé 4 c0 av 4 r-0 5
dé
Spread of the Oil Forward Curve - Dec 1995 / Dec 2005
Crude Oil Price Spread 29th Versus 1st
6
4
2
0
-2
-4
-6
-8
-10
-12
-14
Price Spread 29th Versus 1st
ar
s06 ju il0 no 6 vm 06 ar s07 ju il0 no 7 v m -0 7 ar s08 ju il0 no 8 vm 08 ar s09 ju il0 no 9 vm 09 ar s10 ju il1 no 0 v m -1 0 ar s11 ju il1 no 1 vm 11 ar s12 ju il1 no 2 vm 12 ar s13 ju il1 no 3 v m -1 3 ar s14 ju il14
m
Forward Price
Oil Forward Curve - March 2006 (Bid and Ask) Forward Curv e
68,37
67,37
66,37
65,37
64,37
63,37
62,37
Maturity
WTI Forward Bid WTI Forward Offer
Back to Backwardation in September 2007 80
78
76
74
72
70
68 M1
M5
M9
M13
M17
M21
M25
M29
M33
M37
M41
M45
M49
M53
M57
M61
Crude Oil Future curve (17/11/2008) 85
80
75
70
65
60
55
50
1/2/2009
9/2/2008
5/2/2008
1/2/2008
9/2/2007
5/2/2007
1/2/2007
9/2/2006
5/2/2006
1/2/2006
9/2/2005
5/2/2005
1/2/2005
9/2/2004
5/2/2004
1/2/2004
9/2/2003
5/2/2003
1/2/2003
9/2/2002
5/2/2002
1/2/2002
9/2/2001
5/2/2001
1/2/2001
NYMEX First Nearby – Jan 2001 to Jan 2009 NYMEX Oil Near Month Contract Prices (Jan 2001-Jan 2009)
$160.00
$140.00
$120.00
$100.00
$80.00
$60.00
$40.00
$20.00
$0.00
References H. Geman and S. Kourouvakalis (2008) "A Lattice-Based Method for Pricing Electricity Derivatives under the Geman-Roncoroni Model", Applied Mathematical Finance S. Borovkova and H. Geman (2007) "Seasonal and Stochastic Effects in Commodity Forward Curves", Review
of Derivatives Research H. Geman and A. Roncoroni (2006) "Understanding the Fine Structure of Electricity Prices", Journal of
Business H. Geman (2005) "Energy Commodity Prices: Is Mean Reversion Dead", Journal of Alternative Investments H. Geman and S. Ohana (2006) "Inventory, Reserves and Price volatility in Oil and Natural Gas Markets“,Energy Economics H. Geman (2005) "Commodities and Commodity Prices: Pricing and Modelling for Agriculturals, Metals and Energy", Wiley Finance H. Geman and V. Nguyen (2005) "Soybean inventory and forward curves dynamics", 2005, Management
Science H. Geman and M. Yor (1993) "An Exact Valuation for Asian Option", Mathematical Finance A. Eydeland and H. Geman (1999) "Fundamentals of Electricity options" in Energy Price Modelling, Risk Books H. Geman and O. Vasicek (2001) "Forwards and Futures on Non Storable Commodities", RISK H. Geman (2002) "Pure Jump Lévy Processes for Asset Price Modelling", Journal of Banking and Finance H. Geman (2003) "DCF versus Real Option for Pricing Energy Physical Assets" Conference of the International Energy Agency - Paris - March 2003
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