Futures, Options, and Swaps

1
Futures, Options, and Swaps

• Fin 288

2
Derivatives

• Basic Definition
• Any Asset whose value is based upon (or derived
  from) an underlying asset.
• The performance of the derivative is dependent
  upon the performance of the underlying asset.

3
The Derivative Debate Positives

• Derivative securities have the potential to allow
  both financial firms and non-financial firms to
  greatly decrease risk and increase the efficiency
  of markets. Example of possible benefits include
  the ability to decrease interest rate risk,
  decrease price risk, decrease transaction costs,
  increase the efficiency of markets, provide
  investors with new non replicatable products, and
  increase information availability.

4
The Derivative Debate Negatives

• Use of derivatives has resulted in some dramatic
  financial losses
• Financial Firms (loss) Allied Irish Bank (700
  Million), Barings Bank (1 Billion), Daiwa Bank
  (gt 1 Billion), Kidder Peabody (350 Million),
  LTCM (4 Billion), Midland Bank (50 Million),
  National Westminister Bank ( 130 Million)
• Non Financial Firms (Loss) Allied Lyons (150
  Million), Hammersmith and Fulham (600 million),
  MG (1.8 Billion), Orange County (2 Billion),
  Shell (1 Billion), Sumitomo (2 Billion)

5
The Derivative DebateOverview

• Warren Buffett
• We view them as time bombs, both for the parties
  that deal in them and the economic system.
• Derivatives are financial weapons of mass
  destruction, carrying dangers that while now
  latent, are potentially lethal.
• Alan Greenspan-
• Although the benefits and costs of derivatives
  remain the subject of great spirited debate, the
  performance of the economy and the financial
  system in recent years suggests that those
  benefits have materially exceeded the costs.

6
The Derivative Debate

• To fully understand the benefits and risks of
  using derivative requires an understanding of the
  products available and the markets in which they
  trade.
• In class we will focus on the most popular and
  common forms of derivative products Futures,
  Options, and Swaps. We will also focus on the
  use of derivatives to manage risk and look at
  what caused the large individual losses outlined
  above.

7
Two Myths Concerning Derivatives

• Derivative Securities are a recent development
• The large losses associated with derivative
  securities indicate that derivative securities
  are the equivalent of gambling.

8
Myth 1

• Derivative Securities are a recent development
• Truth
• Derivative contracts can be traced back as far as
  2000 B.C. in India and also appeared in Ancient
  Greece where contracts similar to options were
  traded on olives during the winter prior to the
  spring harvest.

9
Brief History of Derivatives Markets

• 1100s Forward contracts were used by Flemish
  traders who gathered -- a letter de faire-
  forward contract specifying delivery at a later
  date
• 1600s
• Japan -- Cho-ai-mai (Rice Trade on Book)
  Essentially futures contracts on rice designed to
  manage the volatility in rice prices caused by
  weather, warfare and other risks.
• Netherlands -- formal futures markets developed
  to trade tulip bulbs in 1636
• Options also appeared in Amsterdam during the
  1600s

10
Brief History Continued

• 1700s trading in options began in the US and
  in England, but the exchanges were perceived as
  being dishonest
• 1863 -- Confederacy issued 20 year bonds
  denominated in French francs and convertible to
  cotton (a dual currency cotton indexed bond)

11
Brief History Continued.

• Organized Exchanges in US
• Chicago Board of Trade
• Established in 1848 to bring farmers and
  merchants together. Futures Contracts were first
  traded on the CBOT in 1865. Developed the first
  standard contract
• Chicago Mercantile Exchange
• Started as the Chicago Produce Exchange in 1874
  for trade in perishable agricultural products.
  In 1919 it became the Chicago Mercantile Exchange
  (CME). Introduced a contract for SP 500 futures
  in 1982.
• NYMEX 1872 KCBOT 1876

12
Brief History Continued

• Early 1900s Put and Call Dealers Association
  formed to bring together buyers and sellers of
  options, however the organization did not
  establish a secondary market and there were no
  contract guarantees.
• 1970s The uncertainty associate with the
  economic environment created an increase in the
  design of new derivative products designed to
  manage risk, and interest in options increased.

13
Brief History continued

• 1973 The Chicago Board of Trade forms the Chicago
  Board of Options Exchange (CBOE).
• Early 1980s The daily volume of trading on
  options exchanges is greater than the daily
  trading volume of the underlying assets. Options
  on major indexes and options on futures are
  developed.

14
Myth 2

• The large losses associated with derivative
  securities indicate that Derivative Securities
  are the equivalent of gambling.
• Truth
• Many of the losses were the result of poor
  operational oversight, excessive speculation, a
  lack of risk limits, and poor understanding of
  markets (especially liquidity risk).

15
The Derivative DebateLarge Losses and Market
Efficiency

• Alan Greenspan-
• Even the largest corporate defaults in history
  (WorldCom and Enron) and the largest sovereign
  default in history (Argentina) have not
  significantly impaired the capital of any major
  financial intermediary
• Warren Buffett-
• In the energy and utility sectors, companies
  used derivatives and trading activities to report
  great earnings until the roof fell in when
  the actually tried to convert the derivatives
  related receivables on the balance sheets into
  cash. Mark to Market then turned out to truly
  be mark to myth

16
Legitimate Questions about Derivatives

• What are the intended economic benefits and
  risks?
• Has the rapid growth in use of derivatives
  increased the possibility of systematic risk?
• Has there been a concentration of risk due to a
  limited number of dealers?
• Does Regulation do a good job of monitoring and
  limiting derivative related risk?
• What happened in the cases of the large losses?

17
Economic Benefits of Derivatives

• Risk Management given the link to the
  underlying asset a derivative can be used to
  decrease or increase the risk of owning the
  underlying asset
• Price and Informational Discovery since many
  claims are contingent on future events derivative
  markets can provide information about the markets
  perception of the future.

18
Economic Benefits Continued

• Operational Advantages generally derivative
  markets have lower transaction costs and greater
  liquidity compared to the spot market.
  Additionally they allow easier short sales
  helping to complete the market.
• Market Efficiency - Spot market prices are
  sometimes not consistent with assets true
  economic value and arbitrage opportunities exist.
  Derivatives help eliminate arbitrage and
  increase price efficiency.

19
Some Financial Risks

• Legal Risk
• Default Risk
• Liquidity Risk
• Market Risk
• However all financial assets bear most of these
  risks.

20
Other Risks

• Ability to increase leverage via use of
  derivatives can cause increased risk when the
  derivative security is used incorrectly. Sources
  of this possible problem include
• Excess optimism about forecasting ability
• Excessive speculation instead of risk management
• Poor understanding of security being traded
• Lack of liquidity in the market

21
Growth of Derivative Use

• Has the rapid growth in use of derivatives
  increased the possibility of systematic risk?
• This question is especially relevant for the
  banking sector which of course spills over to the
  entire financial sector.

22
Notional value

• Approximate Market Capitalization of the Wilshire
  5000 (represents 98 of equities traded in US)
  13.6 Trillion
• Approximate size of outstanding debt in all fixed
  income markets 23.5 Trillion
• The notional value of derivative securities held
  by commercial banks in the US as of Sept 30, 2004
  84 Trillion

23
Increase in Derivative use by Commercial banks
24
Concentration Risk

• 5 banks account for 95 of the total notional
  amount of derivatives with more than 99 of the
  total held by the largest 25 banks.
• Over-the-Counter contracts comprise 92 of the
  total notional holding and only 8 are exchange
  traded increasing credit risk and liquidity
  risk.
• During the third quarter of 2004 banks charged
  off 91 million from derivatives and total past
  due contracts were at 41 million

25
Size of the Market and Concentration Risk

• Notional value is a very misleading measure of
  risk since the represent the value of the
  underlying security, not necessarily the value
  that may be lost in the event of a bad outcome.
• However, this also makes it very difficult if not
  impossible to estimate the actual amount of risk
  that is present especially since such a large
  percentage are over the counter instruments.

26
The Derivative DebateConcentration Risk

• Alan Greenspan
• One development that gives me and others some
  pause is the decline in the number of major
  derivative dealers and its potential implications
  for market liquidity and for concentration of
  counterparty risk
• Warren Buffett-
• Large mounts of risk, particularly credit risk
  have become concentrated in the hands of
  relatively few dealers, who in addition trade
  excessively with each other.

27
Regulation

• Does Regulation do a good job of monitoring and
  limiting derivative related risk?
• There has been increased reporting requirements
  relating to derivative securities for both
  financial and non-financial firms, increasing
  transparency.
• The amount of off balance sheet securities has
  come under increased scrutiny in the banking
  sector.

28
The Derivative Debate Regulation

• Warren Buffett
• There is no central bank assigned to the job of
  preventing the dominoes from toppling in
  insurance or derivatives. (total return swaps )
  and other kinds of derivatives severely curtail
  the ability of regulators to curb leverage and
  get their arms around the risk profiles of banks,
  insurers and other financial institutions.

29
The Derivative Debate Regulation

• Alan Greenspan
• Except where market discipline is undermined by
  moral hazard owing for example to federal
  guarantees of private debt, private regulation
  generally is far better at constraining excessive
  risk taking than is government regulation.

30
This Class.

• Our goal is to explain the functioning of
  derivative markets in detail and then introduce
  how they can be used by business to manage both
  financial and non-financial risk.

31
Basic Types of Derivative Contracts

• Forward Contracts
• Agreement between two parties to purchase and
  sell something at a later date at a price agreed
  upon today
• Futures Contract
• Same idea as a forward, but the contract trades
  on an exchange and the counter party is not set.

32
Basic Types of Derivative Contracts

• Options Contract - Agreement that gives the
  holder the right, but not the obligation, to buy
  or sell a security in the future as a designated
  price. the
• Swaps Contract An agreement between two
  entities to exchange cash flow streams based upon
  a prearranged formula.

33
Other Derivatives

• Options on futures The right to buy or sell a
  futures contract at a later date
• Swaption The option to enter into a swap at a
  future date
• Collateralized Mortgage Obligation (CMO) A
  mortgage backed security where investors are
  divided into classes and there are rules
  outlining the repayment of principal to each
  class.
• Indexed currency option notes Bonds where the
  amount received but the holder at maturity varies
  with an exchange (usually a foreign
  exchange rate)
• Credit, Weather, Electricity and other derivative
  classes

34
Forward Contracts

• Agreement between two parties to purchase (and
  sell) something at a later date at a price agreed
  upon today.
• Legal contract where both parties have the
  obligation to either buy or sell a specific
  product in the future at the designated price.
  Largest risk is the risk of default.

35
Payoff on Forward Contracts

• Long Position
• Agreeing to buy a specified amount (The Contract
  Size) of a given commodity or asset at a set
  point in time in the future (The Delivery Date)
  at a set price (The Delivery Price)
• Payoff
• The payoff will depend upon the spot (Cash) price
  at the delivery date.
• Payoff Spot Price Delivery Price

36
Example

• Assume you have agreed to buy 1,000,000 in 3
  months at a rate of 1 1.6196
• Spot Rate Spot Delivery Price Payoff
• 1.65 1.65-1.61960.0304 30,400
• 1.6169 1.6196-1.61960 0
• 1.55 1.55-1.61960.0696 -69,600

37
Example Graphically
Payoff
.0304
1.6196
1.650
Spot Price
1.55
-.0696
38
Payoff Short Position

• Agreeing to sell a specified amount (The Contract
  Size) of a given commodity or asset at a point of
  time in the future (The Delivery Date) at a set
  price (The Delivery Price).
• Payoff on Short position
• Since the position is profitable when the price
  declines the payoff becomes
• Payoff The Delivery Price The Spot Price

39
Long vs. Short

• For a long position to exist (someone agreeing to
  buy) there must be an offsetting short position
  (someone agreeing to sell).
• Assume that you held the short position for the
  previous example
• sell L 1,000,000 in 3 mos at a rate of L1
  1.6196
• Spot Rate Spot Delivery Price Payoff
• 1.65 1.6196-1.65-0.0304 -30,400
• 1.6169 1.6196-1.61960 0
• 1.55 1.6196-1.55 0.0696 69,600

40
Example Graphically
Payoff
.0304
1.6196
1.650
Spot Price
1.55
-.0696
41
Zero Sum Game

• The contract and many other derivative securities
  are often referred to as a zero sum game
• In the contract above the combined profit of the
  long and short position is zero. One party gains
  and the other looses by an equal amount.

42
Contract Goals

• The goal of the contract is to decrease risk,
  assume that you had to pay L1,000,000 in 3 months
  for the shipment of an input. You are afraid
  that the price will increase and you will pay a
  higher price.
• Similarly the other party may be afraid that the
  price will decrease (maybe they are receiving a
  payment in 3 months).
• Both parties can hedge by entering into the
  forward agreement however after the 3 months,
  one party will actually be worse off compared
  to not hedging

43
Determining the delivery price

• The delivery price will be determined by the
  participants expectations about the future price
  and their willingness to enter into the contract.
  (Todays spot price most likely does not equal
  the delivery price).
• What else should be considered?
• They should both also consider the time value of
  money
• Storage costs especailly if the asset is a
  commodity

44
Future and Forward contracts

• Both Futures and Forward contracts are contracts
  entered into by two parties who agree to buy and
  sell a given commodity or asset (for example a T-
  Bill) at a specified point of time in the future
  at a set price.

45
Futures vs. Forwards

• Future contracts are traded on an exchange,
  Forward contracts are privately negotiated
  over-the-counter arrangements between two
  parties.
• Both set a price to be paid in the future for a
  specified contract.
• Forward Contracts are subject to counter party
  default risk, The futures exchange attempts to
  limit or eliminate the amount of counter party
  default risk.

46
Other Forward Contract Risks

• One goal of the negotiation is to specify exactly
  the type, quantity, and means of delivery of the
  underlying asset.
• The chance that an asset different than
  anticipated might be delivered should be
  eliminated by the contract.
• Futures contracts attempt to account for this
  problem via standardization of the contract.

47
Futures Contracts

• Long Position Agreeing to purchase a specified
  amount of a given commodity or asset at a point
  in time in the future at a set price (the futures
  price)
• Short Position Agreeing to sell a specified
  amount of a given commodity or asset at a point
  of time in the future for a set price (the
  futures price).

48
Option Contracts

• The first difference between an option and a
  future (or forward) contract is that the holder
  of the option has the right to buy or sell a
  product but is not obligated to do so. They have
  the choice to not exercise the option.
• The second main difference is that the holder of
  the option pays an initial price for the right to
  buy or sell.

49
Option Terminology

• Call Option the right to buy an asset at some
  point in the future for a designated price.
• Put Option the right to sell an asset at some
  point in the future at a given price

50
Option Terminology

• Expiration Date The last day the option can be
  exercised (American Option) also called
  the strike date, maturity, and exercise date
• Exercise Price The price specified in the
  contract
• American Option Can be exercised at any time up
  to the expiration date
• European Option Can be exercised only on the
  expiration date

51
Option Terminology

• Long position Buying an option
• Long Call Bought the right to buy the asset
• Long Put Bought the right to sell the asset
• Short Position Writing or Selling the option
• Short Call - Agreed to sell the other party the
  right to buy the underlying asset, if the other
  party exercises the option you deliver the asset.
  
• Short Put - Agreed to buy the underlying asset
  from the other party if they decide to exercise
  the option.

52
Risk to the Writer of the Option

• The writer of the call option accepts all of the
  risk since the buyer will not exercise if there
  would be a loss.

53
Call Option Profit

• Call option as the price of the asset increases
  the option is more profitable.
• Once the price is above the exercise price
  (strike price) the option will be exercised
• If the price of the underlying asset is below the
  exercise price it wont be exercised you only
  loose the cost of the option.
• The Profit earned is equal to the gain or loss on
  the option minus the initial cost.

54
Profit Diagram Call Option(Long Call Position)

• Profit
• Spot Price
• Cost

S-X-C
S
X
55
Example Naked Call Option

• Assume that you can purchase a share of stock in
  one month with an exercise price of 100.
• Assume that the option is currently at the money
  (the current price of the stock is also 100) and
  selling for 3.
• What are the possible payoffs if you bought the
  option and held it until maturity?

56
Five possible results

• The price of the stock at maturity of the option
  is 100. The buyer looses the entire purchase
  price, no reason to exercise.
• The price of the stock at maturity is less than
  100. The buyer looses the 3 option price and
  does not exercise the option.

57
Five Possible Results continued

• The price of the stock at maturity is greater
  than 100, but less than 103. The buyer will
  exercise the option and recover a portion of the
  option cost.
• The price of the stock is equal to 103. The
  buyer will exercise the option and recover the
  cost of the option.
• The price of the stock is greater than 103. The
  buyer will make a profit of S-100-3.

58
Profit Diagram Call Option(Long Call Position)

• Profit
• Spot Price
• -3

S-100-3
S
103
100
59
Profit Diagram Call Option(Short Call Position)

• Profit
• Spot Price

S
X
CX-S
60
Put option payoffs

• The writer of the put option will profit if the
  option is not exercised or if it is exercised and
  the spot price is less than the exercise price
  plus cost of the option.
• In the previous example the writer will profit as
  long as the spot price is less than 103.
• What if the spot price is equal to 103?

61
Put Option Profits

• Put option as the price of the asset decreases
  the option is more profitable.
• Once the price is below the exercise price
  (strike price) the option will be exercised
• If the price of the underlying asset is above the
  exercise price it wont be exercised you only
  loose the cost of the option.

62
Profit Diagram Put Option

• Profit
• Spot Price
• Cost

X-S-C
S
X
63
More Terminology

• In - the - money options
• when the spot price of the underlying asset for a
  call (put) is greater (less) than the exercise
  price
• Out - of - the - money options
• when the spot price of the underlying asset for a
  call (put) is less (greater) than the exercise
  price
• At the - money options
• when the exercise price and spot price are equal.

64
Swap Introduction

• An agreement between two parties to exchange cash
  flows in the future.
• The agreement specifies the dates that the cash
  flows are to be paid and the way that they are to
  be calculated.
• A forward contract is an example of a simple
  swap. With a forward contract, the result is an
  exchange of cash flows at a single given date in
  the future.
• In the case of a swap the cash flows occur at
  several dates in the future. In other words, you
  can think of a swap as a portfolio of forward
  contracts.

65
Mechanics of Swaps

• The most common used swap agreement is an
  exchange of cash flows based upon a fixed and
  floating rate.
• Often referred to a plain vanilla swap, the
  agreement consists of one party paying a fixed
  interest rate on a notional principal amount in
  exchange for the other party paying a floating
  rate on the same notional principal amount for a
  set period of time.
• In this case the currency of the agreement is the
  same for both parties.

66
Notional Principal

• The term notional principal implies that the
  principal itself is not exchanged. If it was
  exchanged at the end of the swap, the exact same
  cash flows would result.

67
An Example

• Company B agrees to pay A 5 per annum on a
  notional principal of 100 million
• Company A Agrees to pay B the 6 month LIBOR rate
  prevailing 6 months prior to each payment date,
  on 100 million. (generally the floating rate is
  set at the beginning of the period for which it
  is to be paid)

68
The Fixed Side

• We assume that the exchange of cash flows should
  occur each six months (using a fixed rate of 5
  compounded semi annually).
• Company B will pay
• (100M)(.025) 2.5 Million
• to Firm A each 6 months.

69
Summary of Cash Flows for Firm B

• Cash Flow Cash Flow Net
• Date LIBOR Received Paid Cash
  Flow
• 3-1-98 4.2
• 9-1-98 4.8 2.10 2.5 -0.4
• 3-1-99 5.3 2.40 2.5 -0.1
• 9-1-99 5.5 2.65 2.5 0.15
• 3-1-00 5.6 2.75 2.5 0.25
• 9-1-00 5.9 2.80 2.5 0.30
• 3-1-01 6.4 2.95 2.5 0.45

70
Swap Diagram

• LIBOR
• Company A Company B
• 5

71
Offsetting Spot Position
Assume that A has a commitment to borrow at a
fixed rate of 5.2 and that B has a commitment
to borrow at a rate of LIBOR .8

• Company A
• Borrows (pays) 5.2
• Pays LIBOR
• Receives 5
• Net LIBOR.2

• Company B
• Borrows (pays) LIBOR.8
• Receives LIBOR
• Pays 5
• Net 5.8

72
Swap Diagram

• Company A Company B
• The swap in effect transforms a fixed rate
  liability or asset to a floating rate liability
  or asset (and vice versa) for the firms
  respectively.

LIBOR
LIBOR.8
5.2
5
5.8
LIBOR .2
73
Options on Futures

• Options on futures are as popular or even more
  popular than on the actual asset.
• Options on futures do not require payments for
  accrued interest.
• The likelihood of delivery squeezes is less.
• Current prices for futures are readily available,
  they are more difficult to find for bonds.

74
Useful Concepts / Terminology

• The language of derivative markets can be
  confusing. Some basic principles apply to all of
  the markets and instruments that we will cover.

75
Risk Preferences

• Risk Loving vs. Risk Neutral vs. Risk Adverse
• Assume you are faced with two equally likely
  outcomes
• A gain of 10 and a loss of 5.
• How much would you be willing to pay to accept
  the risk of the possible loss?

76
Risk Preferences

• Risk Neutral If you are willing to pay 2.50,
  you are willing to pay a fair price to accept
  the risk. (If you repeated the event over and
  over on average you would receive your 2.50)
• Risk Averse If you are willing to pay less than
  2.50 lets say 2.00, you are risk averse. The
  .50 represents a risk premium, the additional
  return you expect to earn for accepting the risk.
  The lower the amount you are willing to pay the
  more risk averse you are.

77
Short Selling

• The investor is selling an asset that he / she
  does not want.
• This is accomplished by borrowing an asset from a
  broker and selling it. The anticipation is that
  the price of the asset will decline. The
  investor is obligated to buy back the asset in
  the future and return it to the broker.
• Short selling of derivatives is much simpler than
  short selling stock. Often selling short can
  offset risk in other positions.

78
Risk Preferences

• In pricing derivative products we often will
  assume that the participants are risk neutral.
  In other words the value of the securities
  represent their fair price

79
Risk and Return

• Generally, increased risk results in increase
  return.
• Based on the idea of a risk free rate which is
  the return you require on an investment with a
  guaranteed payoff.
• In derivative markets the value of the assets
  will often be priced based on the use of a risk
  free rate. In a perfect world the derivative
  contract would eliminate the risk associated with
  the fluctuation in the underlying asset.
  Therefore the combination of the two provides a
  risk free return and provide a return comparable
  to the risk free rate.

80
Market Efficiency

• Market efficiency occurs when the price of an
  asset reflects it true economic value. You can
  think of this as the theoretical fair value of
  the asset (think about the CAPM providing a fair
  value).
• A good portion of the class is placed on valuing
  derivatives, just like valuing of assets you have
  done in other classes. The value or price of the
  derivative will assume that markets are efficient.

81
Types of Traders

• Hedger - A participant in a derivatives
  transaction who is attempting to decrease the
  risk associate with a spot position by taking the
  opposite position in a derivatives market.
• Speculator- Unlike hedgers speculators are
  attempting to profit from the future movement of
  the market.

82
Arbitrageurs

• Participants who can lock in an immediate profit
  by simultaneously entering into transactions in
  two or more markets.
• A basic assumption throughout the course is that
  arbitrage opportunities do not exist. The basis
  for this argument is that if they did exist, the
  laws of supply and demand will quickly eliminate
  them as participants attempt to take advantage of
  the opportunity the quicker arbitrage
  opportunities leave the market the more efficient
  the market is.

83
Arbitrage and the Law of one price

• Assume you have two stocks A and B. There are
  two possible outcomes one month from now.
• If the first outcome occurs Stock A is worth 100
  and Stock B is worth 50
• If the second outcome occurs, Stock A is worth
  80 and stock B is worth 40.
• From the example it looks like one share of stock
  A is worth two shares of stock B. In other words
  by buying two shares of stock B today you should
  be able to get the same outcome as one share of
  stock A.

84
Law of one Price

• What if stock A is selling for 85 today and B is
  selling for 39
• You could sell short stock A and receive 85 use
  the proceeds to buy two shares of B (total cost
  78) and have a positive cash flow of 7. In one
  month you could sell your two shares of B and buy
  one of A returning it to the broker -- You are
  ahead the 7 plus any interest you received.

85
Market Reaction

• If this condition existed the price of stock B
  would increase (everyone buys it) the price of A
  would decrease (everyone is short selling it).
• The two prices would move until the opportunity
  no longer exists. This is sometimes referred to
  as the law of one price (the arbitrage
  opportunity must be eliminated quickly)

86
The Law of One Price

• Assuming the law of one price is correct
• Investors will prefer more wealth to less
• If two investment opportunities have the same
  outcome they must have the same price
• An investment that produces the same return in
  all states is risk free and should earn the risk
  free rate.
• Investors will prefer an opportunity if it
  produces a higher return in at least one state
  and equivalent returns in all other states.

87
Storage, Delivery, and Settlement

• Storing an asset entails risk since the spot
  price of the commodity fluctuates. This risk can
  be eliminated through the use of derivatives,
  implying that in the absence of storage costs the
  investment should earn the risk free rate.
• Similarly since at expiration the contract is
  identical to a spot transaction the mechanism for
  delivery of a commodity and settlement of the
  contract (via delivery or cash) plays a key role
  in determining the price of the derivative.