Futures

1
Futures Forwards

• Eddie Herdemian
• Michael A. Flaherty

MAT 5900 Quant Finance April
22, 2009
2
A Definition

• Standardized contract to buy or sell a specified
  commodity at a certain date in the future for an
  agreed price
• Options on futures also exist
• Future contract
• Holder has obligation to exercise
• Future option
• Holder has option to exercise

3
The Underlying

• Underlying assets can be
• Energies
• Oil, natural gas
• Currencies
• Swiss franc, Mexican peso
• Indices
• SP 500, Nikkei 225
• Metals
• Gold, silver, aluminum
• And more

4
Future Exchanges

• Futures are traded on hundreds of exchanges
  worldwide including
• Chicago Mercantile Exchange
• London Metal Exchange
• New York Mercantile Exchange
• Tokyo Commodity Exchange

5
Chicago Mercantile Exchange
6
Standardization

• Futures are standardized
• Parties are matched by a clearinghouse
• Specify underlying asset and amount
• Type of settlement
• Currency used
• Grade of deliverable
• Delivery date or expiry

7
Futures Pricing

• Prices are determined by either
• Arbitrage
• Supply and demand
• Pricing terms
• Contango - future prices are higher than current
  spot price
• Backwardation future prices are lower than
  current spot price

8
Margin

• Futures are margined
• Traders must post an initial margin, 5-15
• Margined thereafter to spot price daily
• Prevents large balances between parties
• Kept in margin accounts
• Reduces credit risk

9
End of Contract

• Settlement
• Physical delivery
• Cash settlement
• Expiry
• Arbitrage opportunity in last moments
• Underlying spot price vs. futures price

10
Convergence Arbitrage

• Example Future are higher than spot price-
• Arbitrage Time!
• - Short futures
• - Buy the underlying asset
• - Close out positions

11
Who Trades?

• Types of traders
• Hedgers
• Have an interest in owning the underlying, want
  to limit their exposure to risk
• Speculators
• Have no interest in underlying, willing to take
  on risk for opportunity to profit

12
Types of Hedges

• Long hedge
• Used to protect the purchase price of a commodity
  one is planning to buy
• Short hedge
• Used to protect the selling price of a commodity
  one is planning to sell

13
Southwest Airlines

• Current price per barrel 48.79
• Southwest Airlines overspent by 71M on fuel in
  the first quarter of 2009 due to their oil
  contracts

14
(No Transcript)
15
Forward Contracts

• Similar to future contracts
• Agreement to buy or sell an asset in the future
  for a certain price
• Differs from futures in that it is traded in the
  over- the- counter market and less standardization

16
Over-the-counter Market (OTC)

• Computer linked network of dealers who do not
  physically meet
• Typically, the trades are much larger
• Advantage terms arent specified by an exchange
• Disadvantage credit risk

17
Size of the OTC Market

• By 2006 the OTC market has grown to 370 trillion
  and the exchange market to 84 trillion

18
Basic Example

• I want to buy a house in a year
• Mike has a house valued at 100,000 and wants to
  sell in a year
• We enter a forward contract in which Mike agrees
  to sell the house to me for 104,000

19
Basic Example (cont)

• Suppose after 1 year the house is valued at
  110,000
• I profit 6,000
• Mike has a potential loss of 6,000, but an
  actual profit of 4,000

20
(No Transcript)
21
Hedging Using Forward Contracts

• Suppose it is July 14, 2006 and ImportCo (company
  based in the US) knows it will have to pay 10
  million pounds on October 14, 2006 for goods from
  a British supplier.
• ImportCo can hedge its risk of foreign exchange
  risk by buying pounds from the financial
  institution in 3 month forward market at 1.8405
  (offer from table).
• This fixes the price to be paid to the British
  exporter at 18,405,000.

22
Hedging Using Forward Contracts

• Now consider ExportCo (US based) that exports to
  the UK. On July 14, 2006 it knows it will
  receive 30 million pounds in 3 months
• ExportCo can hedge foreign exchange risk by
  selling 30 million pounds in the 3 month forward
  market at an exchange rate of 1.8400 (bid from
  table)
• This would lock the US dollars realized to
  55,200,000

23
Forward Price for an Investment Asset

• Easiest to value because it provides the holder
  with no income

• Forward price 39
• Action now
• Short 1 unit of asset to realize 40
• Invest 40 at 5 for 3 months
• Enter into a forward contract to buy asset in 3
  months for 39
• Action in 3 months
• Buy asset for 39
• Close short position
• Receive 40.50 from investment
• Profit realized - 1.50

• Forward price 43
• Action now
• Borrow 40 at 5 for 3 months
• Buy one unit of asset
• Enter into forward contract to sell asset in 3
  months for 43
• Action in 3 months
• Sell asset for 43
• Use 40.50 to repay loan with interest
• Profit realized 2.50

24
Generalization

• S0 -gt Asset Price T -gt Time to Maturity
• r -gt Riskless IR F0 -gt Forward Price

If F0 gt S0ert then the arbitrageurs can buy the
asset and short the forward contract
If F0 lt S0ert then the arbitrageurs can short the
asset and enter into a long forward contract
25
Forward Price from a know Income

• Example
• Stock price is 50
• IR continuously compounded at 8 per annum
• Dividends 0.75 per share expected after 3, 6,
  9 months
• I 0.75e-0.08x0.25 x 0.75e-0.08x0.5 x
  0.75e-0.08x0.75 2.126
• T 10 months
• F0 (50 2.162) e0.08x(10/12) 51.14
• Generalization
• F0 (S0 I)ert

26
Valuing Forward Contracts

• Suppose that
• K is delivery price in a forward contract
• F0 is forward price that would apply to the
  contract today
• The value of a long forward contract, , is
  (F0 K )erT
• Similarly, the value of a short forward contract
  is (K F0 )erT

27
Example

• S0 25, T 0.5, r 0.10, K 24
• F0 25e(0.5 x 0.10) 26.28
• f (26.28 24)e(-0.1 x 0.5) 2.17

28
Are Forward Future Prices Equal?

• In theory they are, when risk- free interest rate
  is constant and the same for all maturities
• When IRs vary unpredictably the prices begin to
  differ
• Get a sense, think of the situation where the
  price of S is positively correlated to interest
  rates
• Future prices tend to be higher
• Taxes
• Transaction costs
• Treatment of margins
• Future contracts are more liquid and easier to
  trade

29
Questions??
MAT 5900 Quant Finance April
22, 2009
30
References

• Hull, John C. Fundamentals of Futures and Options
  Markets. 6th ed. Upper Saddle River, NJ Pearson
  Prentice Hall, 2008.
• http//www.theponytail.net/DOL/DOLnode20.htm
• http//www.bloomberg.com/energy/
• http//www.usatoday.com/travel/columnist/grossman/
  2005-07-15-grossman_x.htm