Energy Derivatives
New Developments and Challenges
Alexander Eydeland
Morgan Stanley
New players in energy derivatives
markets
• Traditional users of energy derivatives:
energy producers, marketers and endusers.
• Main objective: to hedge energy exposure
• New players: “investors” - banks,
institutional investors, hedge funds
Increased interest in commodity-linked
products: the investors point of view
• spectacular returns in the last few years
• diversification
– historically commodity returns are weakly correlated
with equity or fixed income products and can be used
as a separate asset class (Gorton and Rouwenhorst,
2004)
– protection against inflation caused by economic
growth
– commodities are correlated with non-economic
drivers: weather, environmental issues, supply
constraints, etc.
Increased interest in commodity-linked
products: the issuer point of view
• Frequently the products can be split into
several components that can be used as a
long-term hedge of existing commodity
market risks - a useful feature particularly
when the markets are illiquid
Example 1. Product: Energy commodity-linked bond.
Issuer: Credit Suisse, 1998. Time maturity: 10 years.
•
At redemption, holder receives par, In addition, holder receives
semi-annual coupon. Each coupon is calculated according to the
formula:
Coupon = .73 x Percent_GainNYMEX_WTI
•
In this formula the coupon is calculated using percentage gain of the
NYMEX WTI contract during the coupon period, provided that this
gain is positive. For example, if during the coupon period the
NYMEX WTI contract moves up from $50 to $55 per barrel, coupon
payment on $1000 par bond will be .73*(.1)*1000 or $73. Next
coupon would be determined using a new base price of $55.
Example 2. Product: Energy commodity-linked note.
Issuer: Canadian Imperial Bank, 1998. Time to maturity: 5 years.
•
The note payment is determined by the price of the underlying
basket consisting of a weighted combination of the light sweet crude
and natural gas. If the basket price drops, the note holder receives
par at maturity. If it increases, holder receives
Par x (1 + 1.1 x Percent_GainBasket)
•
If the basket price moves from $10 to $11 the holder of $1000 par
bond receives $1000*(1+1.1*.1) = $1110
Example 3. Product: Commodity-linked note.
Issuer: Sao Paolo IMI, 1998. Time to maturity: 5 years.
•
Underlying index: a basket of petroleum, copper, gold, aluminum
and zinc. Holder is guaranteed 17% gain even if the price of the
basket drops. At maturity, holder is paid
Par x (1 + 1.2 x Percent_GainBasket)
•
If the basket price has moved from $100 to $120 holder receives
$1240
• There are similar products involving energy
commodities; mostly, oil products or natural gas (rarely,
electricity)
New Developments: Increased volume and
complexity
Examples:
•
The issuer guarantees that the sum of all coupons is greater than a
specified percentage value. If the value is not reached over the life
of the product, the deficit is compensated at maturity.
•
Coupon dependent on the history of commodity prices during the
coupon period, and not just on one price at the coupon payment
day. For example, it may depend on the sum of all previous coupon
payments.
•
Various deal interruption condition can be included such as note call
provisions, or stipulations that the product will be terminated when
commodity prices reach specified levels.
Frequent feature: use of baskets of instruments as an
underlying index
Baskets:
•
may consist entirely of energy commodities
•
may include, in addition to energy commodities, other commodities,
such as metals
•
may be combination of commodities with practically any other group
of indexes
•
we often witness products dependent on combination of crude,
natural gas, metals, SP500, Treasury yields, LIBOR, etc.
•
Creation of these baskets has become progressively easier in recent
years with popularization of the Goldman-Sachs Commodity Index
(GSCI) and its various sub-indexes
Hybrid Products
• Depend on several market/non-market drivers
• We interested in hybrid products which are
exposed to at least one commodity
• Pricing requires analysis of correlation structure
(in addition to volatility)
Hybrid Products: Examples
• Price/Price – spark spread options, crack spread options
• Price/Volume – load following deals
• Price/Temperature products
• Basket products – Rainbow options, Himalayan options
• Interest rates/FX/Equity contingent commodity products
– swaps, swaptions
• Credit/Commodity products – cds linked to commodity
price
Spark Spread Options
• Tolling deals
– call on power with strike price dependent on the cost of fuels,
emission and variable costs = option on spread between power
prices and prices of fuels and emission
– basket of correlated commodity products (three or four products
in the basket)
– objectives:
• power operator will guarantee stable cash flows stream (option
premium) typically from an institution with higher credit rating
• power plant operator may also use these options to hedge against
adverse power and fuel market movements
• marketers use these options to financially replicate power plant
operation without taking on operational and other risks associated
with running the plant
Tolling Deals: Examples
• Unit Contingent Toll with Callback on High Gas
– Standard Toll: Buyer has the right to call for power. When the
right is exercised the buyer pays the cost:
Number MWh x Price of 1MMBtu of NG x Heat Rate + costs
– Callback: Seller has the right not to deliver power during not
more than 10% of all hours of the year (if a specified unit is
forced out)
• Tolling Deal with Limited Number of Start-ups during the
year - complex path-dependent option
• Tolling deals with fuel substitution option
Challenges: Correlation Structure
• Correlation has a complex term structure: seasonality,
dependence on time to maturity
• “Correlation smile”: in Black-Scholes-type models used
to price complex spread options correlation parameters
may depend on underlying prices
• Example: Correlation vs Power_price/NG_price
Price/Volume Products
• Swing options
• Load following contracts
– receiving fixed payments
– paying costs of serving the load: Price x Load
• Challenges:
– Potentially strong non-linearity (if the correlation is high)
– Complex correlation structure
– Inability to hedge all risks, particularly, risks associated with load
fluctuations and load shape dynamics
– Need new approaches to valuation
Basket Products
• Options on basket price
– basket components may include crude, NG, equity indices,
bonds, etc.
• Rainbow or Best-of basket products
– pays the best annual return of the basket components
• Himalayan option
– every year pays the return of the best performing basket
component and then this component is removed from the basket
• Challenges:
– Finding distribution of basket prices
– How to construct the volatility structure of the basket from the
volatility structures of the individual components?
Commodity-contingent interest rate/equity
products
• Commodity-contingent interest rate swap
– floating leg - LIBOR
– “fixed” leg - fixed rate multiplied by the number of days
(expressed as a fraction of the payment period) during which
crude or other commodity prices are above a certain level
• Commodity-contingent interest rate swaption (typically,
Bermudan style)
• Bermudan-style commodity-contingent guaranteed
minimum coupon knock-out option
– Pays coupon dependent on the commodity price levels at the
payment time
– Disappears after the total coupon reaches a specified level
– If at the end of the deal the total value of paid coupons is less
than the specified value the last coupon pays the difference
Modeling challenges
• Test: terminal distributions of returns dPT PT at any
time T is normal - justification for the use of geometric
Brownian motion (GBM) as a modeling process
• SP500: distribution of returns is close to normal
Modeling Challenges
Power, NG and crude prices: normality must be rejected;
distribution has fat tails
Modeling Challenges
Crude: Fat tails of the distribution
Modeling Challenges
Distribution Parameters (A. Werner, Risk Management
in the Electricity Market, 2003)
Annual.
Volatility
Skewness
Kurtosis
Nord Pool
182%
1.468
26.34
NP 6.p.m.
238%
2.079
76.82
DAX
23%
0.004
3.33
Empirical characteristics of energy
commodities
• Implied volatility surface:
– implied volatility increases with time
– volatility depends on strike
In addition, for spread options we must consider
• Correlation surface:
– Correlation depends on time to expiration
– Correlation depends on time between contracts
– Correlation depends on “strike” (heat rate, in case of
spark spread options)
WTI futures implied volatility curve
Correlation between returns of Jan ’04 NYMEX WTI futures
contract and Feb’04 - Jun’05 WTI contracts
Volatility has “smiles”, “smirks”, and “frowns”
Stochastic Volatility (Heston, 1993)
Volatility is a random variable
dPt
= μ dt + v(t ) dW1
Pt
dv ( t ) = κ (θ − v ( t ) ) dt + σ v(t ) dW2
E ( dW1 dW2 ) = ρ dt
price process
volatility process
Stochastic volatility process generates more
realistic price distributions
Tails of CDF for terminal distributions generated by
stochastic volatility process and by GBM
New Developments
• Levy Stable Processes (for review see Boyarchenko
and Levendorskii, 2002 )
• Levy Processes with Stochastic Volatility: CGMY
model (Carr, Geman, Madan, Yor, 2003)
• Regime-switching models
Historic Power Prices vs. GBM paths
Hybrid Power Price Model
Power is a function of principal drivers
1. Demand
2. Fuel Prices
3. Outages
Hybrid Power Price Model
(Eydeland, Wolyniec, 2001)
PT = α1sgen (DT ; T ,UT , ΩT (α2λ ) , ET ,VOMT ,α3CT )
Model uses fundamental and market data
• sgen - function determined by technical characteristics of
all power plants (efficiency, operational constraints, etc.)
• D - demand
• U - fuel(s) used
• Ω - outages
Hybrid Model generates realistic paths
Actual prices vs. Modeled prices
Risks
• Quantifiable risks
–
–
–
–
–
–
–
–
•
market/price risk
credit/default risk
modeling/valuation risk
financing/financial risk
operations risk
volumetric risk
business continuity risk
environmental risk
Source: Committee of Chief Risk Officers
(CCRO), 2002
• Non-quantifiable risks
–
–
–
–
–
–
–
strategic risk
operational risk
staffing/organization risk
regulatory risk
political risk
technological risk
legal risk
Managing market price risk
Two methods of risk reduction
•
•
Diversification
Hedging
Hedging in the perfect world
V = f (F )
V - option value
F - price of a tradable instrument (for
example, futures price)
f - option pricing formula (for example,
Black-Scholes)
Hedging in the perfect world
Delta Hedging:
Combine long position in one option
and short position in Δ futures
∂V
Δ =
∂F
Hedging in the perfect world
Change in option value vs. change in hedge value
Hedging = risk reduction
Reduction of the uncertainty of the future cash flows
Energy deals and assets =
spread options
• Power plants, tolling contracts = spark
spread options
• Gas storage = calendar spread options
• Transmission lines, pipelines, transmission
right contracts = geographical spread
options
Power Plant
• In the simplest case (immediate response
to price changes, one fuel -- natural gas),
the plant cash flow at time T:
T
CF = ∑ C ⋅ max( Pt − HR ⋅ Gt − VOM ,0)
t =0
–
–
–
–
C -- capacity
HR -- heat rate
P T and GT are power and nat. gas prices at time T
VOM -- variable costs
Hedging spread options in the perfect
world
• What is needed for valuation and hedging?
– Joint distribution
– Evolution processes for power and fuel prices
– Cashflow function
– Sufficient amount of tradable hedge instruments
(futures, forwards, options)
Hedging in energy markets: real world
• Mismatch in asset/hedge maturities: long maturity of assets
vs. short maturity of hedges
• Mismatch in granularity: fine (daily, hourly) granularity of
assets vs. coarse (monthly, quarterly) granularity of hedges
• Mismatch in underlying commodity, “dirty” hedges.
– For example, fuel contracts in one location are used to
hedge exposure in other locations
Hedging in energy markets: real world
• Liquidity constraints:
– Price may depend on the volume
– Execution time may depend on the volume
– Wider bid/ask spreads
– Higher hedging costs
– distributions are hard to calibrate because of
biases due to liquidity constraints
• implication: different hedging strategies may
produce different option values
Hedging in energy markets: short and
medium term
• Hedge instruments are available although the
set of hedges is not complete and mismatches
persist
• Consequently, hedges are “dirty” resulting in
residual cashflow variance
• Liquidity, in general, is not a problem for medium
size deals
• Possible to follow the “perfect world” hedging
methodology
Hedging in energy markets: short and
medium term
• Problems in defining the right evolution
process
– empirical power price data shows mean
reversion, spikes, high kurtosis, regime
switching; processes difficult to calibrate due
to lack of data and its non-stationarity
Hedging in energy markets: short and
medium term
How is the joint distribution defined?
– Typically, by supplying correlation coefficient implicitly assuming
that the joint distribution belongs to the elliptic family of
distributions
– The correlation coefficient is computed using historical data
•
Problem: correlation coefficient between power and natural gas (or
oil) is not a constant; it has structure. Taking average will
overestimate the option and miscalculate hedges
Hedging in energy markets: short and
medium term
• Other issues:
– Standard approach will have difficulties
incorporating structural changes of the stack
or demand
– Unlike cashflows of financial products, the
cashflows of energy assets are determined by
complex operating strategies: dispatch
strategy for power plants or
injection/withdrawal strategy for gas storage
Alternative Method: Hybrid Model for Power
Prices
PT = α1sgen (DT ; T ,UT , ΩT (α2λ ) , ET ,VOMT ,α3CT )
Model uses fundamental and market data
• sgen - function determined by technical characteristics of
all power plants (efficiency, operational constraints, etc.)
• D - demand
• U - fuel(s) used
• Ω - outages
Hybrid method
• The benefits of the method:
– captures distribution properties (high kurtosis,
spikes, volatility and correlation structure)
– correlation is not an input
– matches market data
– allows incorporation of future structural
changes
Hedge efficiency
Back testing of hedging
Managing other risks
• Credit risk - credit derivatives
• Operational risk - insurance
• Demographic, economic growth risks contractual clauses
• All this increases the cost of risk
management; these costs should be taken
into consideration at the valuation stage
References
•
•
•
•
•
Boyarchenko, Svetlana and Sergei Levendorskii, Non-Gaussian Merton-BlackScholes Theory, World Scientific, 2002
Eydeland, Alexander and Krzysztof Wolyniec, Energy and Power Risk
Management: New Developments in Modeling, Pricing and Hedging, Wiley,
2002
Carr, Peter and Helyette Geman, Dilip Madan, Marc Yor, Stochastic Volatility for
Levy Processes, Mathematical Finance, Vol. 13, No. 3 (2003)
Rouwenhorst, K. Geert and Gorton, Gary B., "Facts and Fantasies about
Commodity Futures" (February 28, 2005). Yale ICF Working Paper
Heston, Steven, A Closed-Form Solution for Options with Stochastic Volatility,
Review of Financial Studies, Vol. 6, No. 2 (1993)
Disclosures
The information herein has been prepared solely for informational purposes and is not an offer to buy or sell or a solicitation of an offer to buy or sell any security or instrument or to participate in any trading
strategy. Any such offer would be made only after a prospective participant had completed its own independent investigation of the securities, instruments or transactions and received all information it
required to make its own investment decision, including, where applicable, a review of any offering circular or memorandum describing such security or instrument, which would contain material information
not contained herein and to which prospective participants are referred. No representation or warranty can be given with respect to the accuracy or completeness of the information herein, or that any future
offer of securities, instruments or transactions will conform to the terms hereof. Morgan Stanley and its affiliates disclaim any and all liability relating to this information. Morgan Stanley, its affiliates and
others associated with it may have positions in, and may effect transactions in, securities and instruments of issuers mentioned herein and may also perform or seek to perform investment banking services for
the issuers of such securities and instruments.
The information herein may contain general, summary discussions of certain tax, regulatory, accounting and/or legal issues relevant to the proposed transaction. Any such discussion is necessarily generic and
may not be applicable to, or complete for, any particular recipient's specific facts and circumstances. Morgan Stanley is not offering and does not purport to offer tax, regulatory, accounting or legal advice
and this information should not be relied upon as such. Prior to entering into any proposed transaction, recipients should determine, in consultation with their own legal, tax, regulatory and accounting
advisors, the economic risks and merits, as well as the legal, tax, regulatory and accounting characteristics and consequences, of the transaction.
Notwithstanding any other express or implied agreement, arrangement, or understanding to the contrary, Morgan Stanley and each recipient hereof are deemed to agree that both Morgan Stanley and such
recipient (and their respective employees, representatives, and other agents) may disclose to any and all persons, without limitation of any kind, the U.S. federal income tax treatment of the securities,
instruments or transactions described herein and any fact relating to the structure of the securities, instruments or transactions that may be relevant to understanding such tax treatment, and all materials of any
kind (including opinions or other tax analyses) that are provided to such person relating to such tax treatment and tax structure, except to the extent confidentiality is reasonably necessary to comply with
securities laws (including, where applicable, confidentiality regarding the identity of an issuer of securities or its affiliates, agents and advisors).
The projections or other estimates in these materials (if any), including estimates of returns or performance, are forward-looking statements based upon certain assumptions and are preliminary in nature. Any
assumptions used in any such projection or estimate that were provided by a recipient are noted herein. Actual results are difficult to predict and may depend upon events outside the issuer’s or Morgan
Stanley’s control. Actual events may differ from those assumed and changes to any assumptions may have a material impact on any projections or estimates. Other events not taken into account may occur
and may significantly affect the analysis. Certain assumptions may have been made for modeling purposes only to simplify the presentation and/or calculation of any projections or estimates, and Morgan
Stanley does not represent that any such assumptions will reflect actual future events. Accordingly, there can be no assurance that estimated returns or projections will be realized or that actual returns or
performance results will not be materially different than those estimated herein. Any such estimated returns and projections should be viewed as hypothetical. Recipients should conduct their own analysis,
using such assumptions as they deem appropriate, and should fully consider other available information in making a decision regarding these securities, instruments or transactions. Past performance is not
necessarily indicative of future results. Price and availability are subject to change without notice.
The offer or sale of securities, instruments or transactions may be restricted by law. Additionally, transfers of any such securities, instruments or transactions may be limited by law or the terms thereof.
Unless specifically noted herein, neither Morgan Stanley nor any issuer of securities or instruments has taken or will take any action in any jurisdiction that would permit a public offering of securities or
instruments, or possession or distribution of any offering material in relation thereto, in any country or jurisdiction where action for such purpose is required. Recipients are required to inform themselves of
and comply with any legal or contractual restrictions on their purchase, holding, sale, exercise of rights or performance of obligations under any transaction. Morgan Stanley does not undertake or have any
responsibility to notify you of any changes to the attached information.
With respect to any recipient in the U.K., the information herein has been issued by Morgan Stanley & Co. International Limited, regulated by the U.K. Financial Services Authority. THIS
COMMUNICATION IS DIRECTED IN THE UK TO THOSE PERSONS WHO ARE MARKET COUNTERPARTIES OR INTERMEDIATE CUSTOMERS (AS DEFINED IN THE UK
FINANCIAL SERVICES AUTHORITY’S RULES).
ADDITIONAL INFORMATION IS AVAILABLE UPON REQUEST.