Chapter 9 Derivatives

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Chapter 9Derivatives
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1. Terminology

• Stocks, bonds, etc., are direct claims on
  productive assets like factories, houses, etc.
  
• Derivatives are not direct claims on productive
  assets
  
• Rather they are contracts promising payoffs that
  depend on what happens in the future
  
• Often they derive their values from direct claims
  on productive assets hence their name

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2. Terminology

• In a real sense, derivatives are merely bets
  about the future that some parties make with
  other parties
  
• Direct claims involve immediate settlement i.e.
  the buyer pays the seller for it now and obtains
  it now in a spot transaction in a spot market
  
• With derivatives, settlement occurs when the
  event on which the bet was made actually occurs

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3. Terminology

• Transactions in derivatives are termed forward
  transactions
  
• Derivatives exist because they facilitate
  risk-sharing by permitting diversification and
  risk-shifting at very low cost
  
• The diversification occurs because parties with
  very different risks make bets with each other

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1. Example of Diversification

• On 3/1, a wheat farmer and a miller are uncertain
  about the price of wheat on 9/30
  
• On 9/30, the farmer will harvest and sell 500,000
  bushels, and the miller will buy 500,000 bushels
  
• The farmer bets that the price will be low the
  miller bets that it will be high

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2. Example of Diversification

• If the price is high
• The farmers crop sells for more, but she loses
  her bet.
  
• The miller must pay more for wheat, but she wins
  her bet.
  
• If the price is low
• The farmers crop sells for less, but she wins
  her bet.
  
• The miller can pay less for wheat, but she loses
  her bet.

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3. Example of Diversification

• If the bets are done properly, neither the farmer
  nor the miller bears any risk
  
• Their opposite exposures to risk from the
  uncertain price of wheat on 9/30 enable this
  complete diversification
  
• This process of diversification is called two-way
  hedging

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Risk-Shifting

• Risk-shifting occurs when a party exposed to risk
  (a hedger) makes a bet with a speculator more
  willing to bear the risk
  
• For example, a wheat farmer bets that the wheat
  price will be low while a Saudi Prince bets that
  it will be high.
  
• This is an example of one-way hedging.

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Futures

• A futures contract is an agreement that specifies
  that a commodity or financial instrument be
  delivered on an agreed-upon future date at an
  agreed-upon price
• Futures originated in grains, metals, and other
  commodities
  
• Most active current use futures in financial
  instruments like Treasury bills and bonds

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Some Facts about Futures

• Virtually all are traded on organized exchanges
• Most important exchanges Chicago Board of Trade
  (CBT) and the Chicago Mercantile Exchange (The
  Merc)
  
• Contracts are standardized, specifying exactly
  what and how much is to be delivered and when
  
• Example 5000 bushels of a certain kind and grade
  of wheat on certain fixed dates in June,
  September, etc.

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More Facts about Futures

• The exchanges eliminate risk by intermediating
  between the buyers and sellers of futures
  
• That is, buyers and sellers actually deal only
  with the exchange, not each other
  
• The exchanges guarantee performance of the
  contracts
  
• The exchanges protect themselves by requiring
  both sellers and buyers to post surety bonds in
  margin accounts
  
• Standardization and the elimination of default
  risk raise trading volumes, thereby enhancing
  liquidity

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1. Extended Example

• On 3/1, a farmer who will harvest and sell
  500,000 bushels of wheat on 9/30 hedges her
  position by selling 100 September wheat futures
  i.e. buying -100 September wheat futures. (Each
  future is for 5000 bushels.)
• On 3/1, a miller who will buy 500,000 bushels of
  wheat on 9/30 hedges her position by buying 100
  September wheat futures
  
• No cash changes hands between them
• The exchange requires both to deposit surety
  bonds in margin accounts say, 25,000 each

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2. Extended Example

• The futures price on Sep wheat futures is
  3/bushel, making the millers and farmers
  positions worth 1,500,000 and -1,500,000 (equal
  to ?100?5000bushels?3/bushel)
• On 3/2, the futures price falls to 2.98/bushel
• The millers and farmers positions are now worth
  1,490,000 and -1,490,000
  
• The farmers position improves in value by
  10,000 the millers improves by -10,000

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3. Extended Example

• The exchange credits the farmers margin account
  with 10,000 and debits the millers for 10,000

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4. Extended Example

• The exchange may now ask the miller to deposit
  more in her margin account and if she doesnt,
  sell her position to someone else
  
• That is how the exchange protects itself
• The farmer and miller made bets the farmer won
  and the miller lost between 3/1 and 3/2
  
• But they have offsetting losses and gains on
  wheat and are therefore hedged
  
• The farmer lost 10,000 on the wheat net 0
• The miller gained 10,000 on the wheat net 0

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5. Extended Example

• Typically, both would liquidate their positions
  before 9/30no one wants to make or take delivery
  with the exchange
  
• The farmer does so by buying 100 contracts
• (-100100 0)
• The miller does so by selling 100 contracts
• (100-100 0)
• The exchange then closes their margin accounts
  and mails them checks for their original surety
  bond cumulative capital gain any additions to
  their margin accounts any withdrawals
  interest earned

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Futures Prices

• Minute by minute, futures prices are determined
  so that of contracts bought sold
  
• Equal are betting spot price of wheat on 9/1
  will be and
• The futures price must approach the spot price
  that will prevail on 9/1 as date approaches 9/1
  
• Speculators help make futures price expected
  9/1 spot price
  
• Speculators also enhance liquidity

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Example FFR Futures

• On 2/21/06, the price of the Feb futures contract
  on 30-day federal funds was 95.50, implying that
  the funds rate was then expected to average
  10095.50 4.50 in Feb, the Feds target for
  it.
• The price of the Apr futures contract was 95.25,
  implying the fed funds rate was then expected to
  average 10095.25 4.75 in Apr.
  
• The FOMC was to meet on 3/27-28/06.
• We can conclude that on 2/21/06 the market
  expected FOMC to raise the target to 4.75 at
  that meeting.

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1. Options

• An options contract is a right to buy or sell a
  given asset at an agreed-upon price on or before
  an agreed-upon future date
  
• The right to buy is termed a call option
• The right to sell is termed a put option
• Key feature of options they are rights, not
  obligations
  
• The owner of an option need not exercise it and
  therefore never does if shed lose by doing so

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2. Options

• The strike price (or exercise price) is the
  agreed-upon price in the option contract
  
• The expiration date is the agreed-upon last date
  on which the option can be exercised
  
• The premium is the price that the buyer pays the
  seller for the option

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Options Are Bets

• The buyers of a call option are betting that the
  assets price will exceed the strike price by
  more than the premium
  
• The sellers are betting the opposite

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1. Trading of Options

• Over-the-counter markets
• Exchanges such as CME, NYSE, AMEX
• The most widely traded options stock indices,
  futures on stock indices, interest-rate futures,
  currencies, futures on currencies, a few large
  companies
• Exchange options are sold in anonymous markets in
  which buyers and sellers deal with the exchange,
  not each other

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2. Trading of Options

• Sellers provide surety bonds that must be
  deposited into margin accounts at the exchange
  
• But not the buyers because they have no
  obligation on which to default
  
• Sellers of options must add funds to their margin
  accounts whenever P changes enough to put the
  exchange at risk.
  
• If not, the exchange sells out the positions and
  refunds the balance in the margin accounts.

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Intrinsic Value

• Intrinsic value of an option is what its owner
  would receive if she exercised it immediately
  
• Example 1. Intrinsic value Max(0,PS) of a
  call option with strike price S on an asset with
  price P.
  
• Example 2. Intrinsic value Max(0,SP) for the
  analogous put option

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Intrinsic Value of a Call Option
P
S
time
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Intrinsic Value of a Put Option
P
S
S
S
time
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Pricing Options

• An options premium (price) is never less than
  its intrinsic value because the option can always
  be exercised to obtain its intrinsic value.
  
• An options premium exceeds its intrinsic value
  by more,
  
• The longer the time until it expires
• The more variable the price of the underlying
  asset
  
• The higher the interest rate

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Effect of Intrinsic Value, Jan SP500 Index on
11/26/2008When P Was 888
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Effect of Expiration Date, SP500 Index with S
900 on 11/26/2008When P Was 888
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Effect of Variability, March Options,11/26/2008,
Intrinsic Value 0

• The Nasdaq100 index is more variable than the
  SP500 index.

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Effect of Expiration Date
P
S
time
0
T2
T1
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Effect of Variability

• Low Variability

• High Variability

P
P
S
S
time
time
T
0
0
T
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Illustration of Margin

• On 3/30, Mary sells 100 June call options on the
  SP500 with a strike price of 1100 when the SP
  index is 1115.
  
• The options premium is 30. She receives
  100x30, or 3000.
  
• She is required to put 5000, say, into a margin
  account.
  
• On 3/31, the index rises to 1125. The exchange
  may ask for more margin.
  
• On 4/1, the index falls to 1005. The exchange
  may let her withdraw some funds from her margin
  account.

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Standardization of Options

• Exchange-traded options are highly standardized
  only a few strike prices, expiration dates, and
  underlying assets are available
  
• Standardization, low transaction costs, and the
  intermediation of the exchange make these options
  highly liquid and generate large trading volumes

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Swaps

• A swap is an agreement between two or more
  parties to exchange specified sets of cash flows
  over a specified period of time.
  
• The three most common types of swaps are
• Interest-rate swaps
• Currency swaps
• Credit-default swaps
• Swaps are not traded on exchanges but rather are
  negotiated by the parties or by brokers.

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Interest-Rate Swaps

• We consider two parties, A and B.
• A is receiving cash flows that vary with the
  level of interest rates but would rather have a
  constant cash flow.
  
• B has the opposite situation.
• Each could hedge in the futures market, but those
  markets offer only short-term hedges.
  
• Instead, they swap their cash flows.

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1. Currency Swaps

• Party A has easier access to financial markets in
  one currency (say, US) than in another currency
  (say, Euros).
  
• Party B has the opposite situation.
• A lends US to B, and B lends Euros to A.
• The loans are equal at the initial exchange rate
  and have the same maturity date.

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2. Currency Swaps

• The interest and principal on the US loan are
  paid in US.
  
• The interest and principal on the Euro loan are
  paid in Euros.
  
• The interest rates on the loans are set at
  competitive levels.
  
• The currency swap benefits both parties by
  lowering their effective borrowing rates.

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1. Credit-Default Swaps

• A wants to hold the bonds of XYZ Corp but does
  not want to bear the default-risk.
  
• B agrees to pay A an agreed-upon amount if XYZ
  defaults on its bonds on or before some
  agreed-upon expiration date.
  
• In return, A agrees to pay B a fixed fee every
  quarter until the expiration date.
  
• In essence, credit-default swaps are a type of
  insurance policy.

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2. Credit-Default Options

• Much in the news recently.
• Many holders of bonds backed by subprime
  mortgages bought credit-default swaps.
  
• When the price of housing began falling and
  subprime mortgages began to default in large
  numbers, the sellers of these credit-default
  options found themselves in deep do-do.
• One big seller American Insurance Group, which
  received a giant bailout.

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3. Credit-Default Swaps

• World-wide, these swaps total about 70 trillion,
  more than world GDP.
  
• The large value reflects the tendency of sellers
  to offset their positions by buying
  credit-default options from some other party
  say, C.
• Long buy-sell chains can be generated A ? B ? C
  ? D ? ??? ? Z.
  
• If all of the positions were netted out, the
  total would be perhaps only a few trillion.

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Social Benefits of Derivatives

• Derivatives enable hedgers with opposite risks to
  diversify their risks away at very low
  transaction costs.
  
• They also enable hedgers to shift risk from
  themselves to speculators more willing to bear it.

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Social Costs of Derivatives

• Many socially beneficial things can be abused
  e.g., fire.
  
• Society evolves mechanisms for keeping abuse
  under control e.g., technologies like furnaces,
  institutions like fire departments, and
  regulations like fire codes

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Infamous Examples of Abuse

• The Treasurer of Orange County CA used derivative
  to speculate with county funds rather than
  hedge.
  
• A trader in the Singapore office of Barings Bank
  lost billions and bankrupted it.
  
• A trader in the Paris office of Societe Generale
  lost about 7 B in unauthorized speculations.

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Responses to Abuses of Derivatives

• Appropriate response better institutions of
  governance such as
  
• Removing discretion of public officials to
  speculate with funds under their management
  
• Imposing tighter internal controls by managements
  of financial institutions on their traders
  
• Greater understanding of the risks
• More equity backing over-the-counter options
• Exchange rather than over-the-counter trading
• Inappropriate response hinder the use of
  derivatives by the market as a whole