Chapter 5
Energy Derivatives: Structures
and Applications
(Book Review)
Zhao, Lu (Matthew)
Dept. of Math & Stats, Univ. of Calgary
January 24, 2007
“Lunch at the Lab” Seminar
Outline
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Exchange Traded Instruments
Swaps
Caps, Floors and Collars
Swaptions
Compound Options – Captions and Floptions
Spread and Exchange Options
Path Dependent Options
1 Introduction
Exotic Options
• More complicated payoff structures than
standard derivatives
• Known as second generation, or sometimes
path-dependent options
• Trade over-the-counter (almost)
2 Exchange Traded Instruments
• New York Mercantile Exchange (NYMEX)
Futures and American style futures options on oil,
gas and electricity; crack spread options
• Chicago Board Options Exchange (CBOE)
Electricity futures and options
• Sydney Futures Exchange and Nordic Electricity
Exchange
Electricity futures
3 Swaps
• First energy swaps were traded in October 1986
(Chase Manhattan Bank vs. Cathay Pacific
Airways and Koch Industries, oil-indexed price
swap)
• Swaps are also known as Contracts-forDifferences or Fixed-for-Floating contracts
• Used to lock in a fixed price for a certain
predetermined but not necessarily constant
quantity
3.1 Vanilla Swap
• An agreement in which counterparties exchange a
floating energy price for a fixed energy price
• Example
Buyer: an oil producer
Swap provider: an oil refiner
• A swap would allow them to buy forward their
anticipated oil consumption based on current oil
forward prices
• Vanilla swaps can be priced directly off the
forward energy curve since the appropriate
portfolio of forward deals is an exact hedge of the
swap. Therefore, the payoff at each reset date is
the same as for a forward contract
• A vanilla swap is usually viewed as a weighted
average of the forwards underlying the swap with
weights being the discount rates to each of the
swap settlement dates
• The value of a vanilla swap
3.2 Variable Volume Swap
• This contract is identical to a vanilla swap
except that the underlying quantity or
volume is not known in advance
• The variability of the volume must be
modeled in order to price contracts (detailed
in Chapter 7)
3.3 Differential Swap
• Similar to vanilla swaps except that the
counterparties exchange the difference between
two different floating prices for a fixed price
differential
• Example
A refiner’s probability depends on the market price
differential of the raw commodity and the refined
products and a differential swap allows a refiner to
lock in their refining margin at the fixed price
• A differential swap is a portfolio of forward
differential contracts with maturity dates
corresponding to the settlement dates underlying
the differential swap
• The value is given by
3.4 Margin or Crack Swap
• A specific form of differential swap in
which the fixed price payer receives the
difference between the market price
differential of the raw commodity and the
refined products in appropriate fractions and
the fixed price
3.5 Participation Swap
• Similar to a vanilla swap in that the fixed price payer is
fully protected when prices rise above the agreed fixed
price but they participate in a certain percentage of savings
if prices fall.
• Example
A participation swap for gasoil at a fixed price of $150 per
ton with a participation of 50%
a) If the gasoil price is $160 per ton, the fixed price payer
received $10 per ton;
b) If the gasoil price is $140 per ton, the fixed price payer
only pay the provider $5 per ton
3.6 Double-Up Swap
• The fixed price payer can achieve a better swap
price than the market price but in return the swap
provider has the option to double the volume
before the pricing period starts
• The fixed price payer is exposed to the risk that if
swap prices fall the fixed price receiver will
exercise the right to double the swap volume
3.7 Extendable Swap
• Similar to the double-up swap except that
the swap provider has the option to extend
the period of the swap for a predetermined
period
4 Caps, Floors and Collars
• Caps provide price protection for the buyer
above a predetermined level for a
predetermined period of time
• Floors guarantee the minimum price that
will be paid or received at a predetermined
level
• A collar is a combination of a long position
in a cap and a short position in a floor
• A generic cap can be viewed as a portfolio of
standard European call options with strike prices
equal to the cap level and maturity dates equal to
the settlement dates of the cap
• Value of a standard cap is given by
• Similarly, a generic floor is a portfolio of European
put options with strike prices equal to the floor
level and maturity dates equal to the settlement
dates of the floor
• Value of a floor is given by
• Collars are typically used by energy buyers
who wish to hedge against price increases
and wish to use the premium on short floors
to pay for the cap protection
• The strike prices of the cap and floor can be
set to yield a collar at zero cost
5 Swaptions
• A swaption is a European option on an energy
swap
• A call option on the swap, also called a payer
swaption, with strike price K and time to maturity
T, provides the holder of the option the right to
enter into a swap, paying the fixed price K and
receiving the floating energy spot price
• A put option on a swap, or receiver swaption,
gives the purchaser of the option the right to sell a
swap or receive the fixed price K and pay the
floating price
• The payoff to the payer swaption as
• The value of the payer swaption is
• If physical settlement considered
Payoff
• Value
6 Compound Options-Captions
and Floptions
• An option which allows its holder to
purchase or sell another option for a fixed
price is called a compound option
• A caption is an option on a cap and a
floption is an option on a floor
• These instruments are options on portfolios
of options and no simple analytical
formulae exist
7 Spread and Exchange Options
7.1 Calendar Spreads
• If the futures contracts are written on the same
underlying energy, but with different maturity
dates, then the option is often referred to as a
calendar spread option
• Payoff to a European call spread option with
strike K and maturity T as
• Value of the calendar spread option
7.2 Crack Spreads
• If the futures contracts underlying the option are
written on two separate energies, then the option is
often referred to as a crack spread option. The
maturity of the futures contracts can be on the
same date or different dates
• Options of this type are often used by companies
who are exposed to the difference in price between
two different energies
• Payoff
• Value
7.3 Exchange Options
• Provide a payout which is based on the relative
performance of two energy prices
• Two types:
a) out-performance options’ payoff
b)
8 Path Dependent Options
8.1 Asian Options-Average Price and Average
Strike
• Asian options are options whose final payoff is
based in some way on the average level of an
energy price during some or all of the life of the
option
• In general, the main use of Asian options is
hedging an exposure to the average price over a
period of time
8.2 Barrier Options
• Barrier options are standard options that either
cease to exist or only come into existence if the
underlying price crosses a predetermined level –
the barrier
• Analytical formulae exist for the basic barrier
options in the Black-Scholes-Merton world under
the assumption that the crossing of the barrier is
continuously checked. For discretely fixed barrier
options we need to use numerical techniques to
evaluate prices
8.3 Lookback Options-Fixed
Strike and Floating Strike
• The payout of lookback options is a function of
the highest or lowest price at which the underlying
asset trades over some period during the life of the
option. For this reason, they are occasionally
referred to as hindsight options
• Analytical formulae exist for the standard
lookback options in a Black-Scholes-Merton
world when the maximum or minimum is checked
continuously, but numerical techniques must be
used for discretely fixed examples
8.4 Ladder and Cliquet Options
• Ladder options have a predefined set of
levels such that if the underlying price
crosses a particular level it locks in a
minimum payoff equal to the difference
between the level crossed and the strike
price
• Cliquet options have a predefined set of
dates at which the underlying price is
observed and they payoff the maximum of
the differences between these fixings and
the predefined strike price for a call or the
maximum of the differences between the
predefined strike price and the fixings for a
put
9 Summary
• Exotic options are almost common place in
the energy markets compared with other
markets
• The high volatility exhibited by many
energy commodities and the fact that they
have been embedded in many energy
contracts for a long time has led to a ready
acceptance for these kinds of derivatives
THE END
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