New Trends in Energy Derivatives

1
New Trends in Energy Derivatives

• Alexander Eydeland
• Morgan Stanley

2
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
• protection against inflation caused by economic
  growth
• commodities are correlated with non-economic
  drivers weather, environmental issues, supply
  constraints, etc.

3
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

4
Examples Commodity-linked bonds

• At redemption, holder is paid par if the GSCI has
  fallen. If the the GSCI price has risen, holder
  receives par (1 a percentage gain in the
  GSCI)
• At redemption, holder receives
• 85 of par par (2 percentage rise in
  gold price)
• For example, if gold grows from 400 to 440
  then the holder of a 1000 par bond gets
  1000(.85) 1000 2(.1) 1050

5
Examples Commodity-linked bonds

• At redemption, holder receives par. In addition,
  holder receives semi-annual coupon. Those
  payments are .82 (percentage gain in the NYMEX
  WTI). Say the NYMEX WTI goes from 50/bbl to
  55/bbl, coupon payment on a 1000 par bond would
  be .82 (.1) (1000) or 82. Next coupon payment
  would be determined off a new base price of 55.

6
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)

7
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

8
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

9
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

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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

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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

12
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?

13
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

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Modeling challenges

• Test terminal distributions of returns
  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

15
Modeling Challenges

• Power, NG and crude prices normality must be
  rejected distribution has fat tails

16
Modeling Challenges

• Crude Fat tails of the distribution

17
Modeling Challenges

• Distribution Parameters (A. Werner, Risk
  Management in the Electricity Market, 2003)

18
Stochastic Volatility (Heston, 1993)

• Volatility is a random variable
• 
  price process
• 
  volatility process

19
Stochastic volatility process generates more
realistic price distributions

• Tails of CDF for terminal distributions generated
  by stochastic volatility process and by GBM

20
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

21
Historic Power Prices vs. GBM paths
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Hybrid Power Price ModelPower is a function of
principal drivers

• 1. Demand
• 2. Fuel Prices
• 3. Outages

23
Hybrid Power Price Model (Eydeland, Wolyniec,
2001)

• 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
• O - outages

24
Hybrid Model generates realistic paths
Actual prices vs. Modeled prices
25
Hybrid Model Analytical Approximation (Mahoney,
2004)

• Fuel Price
• ? (t) - seasonal factor
• Market Heat Rate
• Power Price

26
Hybrid Model (Mahoney, 2004)

27

• At t0 the value of the power plant at a future
  time T is computed as a conditional expectation
• Using characteristic function
• the value of the plant can be represented as

28
Correlation Risk

• Correlation structure is complex
• Term structure dependence on time to expiration,
  time interval between two contracts seasonality
• Sensitivity to correlation is high
• How to manage correlation risk?

29
Difficulties in managing correlation risk

• correlation is not traded
• historical data is poor
• data is nonstationary, markets are evolving

30
What are the alternatives?

• Structural models
• Correlation independent bounds
  super/sub-replication

31
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

32
References

• Boyarchenko, Svetlana and Sergei Levendorskii,
  Non-Gaussian Merton-Black-Scholes 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)
• Heston, Steven, A Closed-Form Solution for
  Options with Stochastic Volatility, Review of
  Financial Studies, Vol. 6, No. 2 (1993)
• Mahoney, Daniel, A New Spot Model for Power
  Prices, Preprint, 2004

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