Options and Futures

1

• Options and Futures
• (Chapter 18 and 19 Hirschey and Nofsinger)

2
Potential Benefits of Derivatives

• Derivative instruments Value is determined by,
  or derived from, the value of another instrument
  vehicle, called the underlying asset or security
• Risk shifting
• Especially shifting the risk of asset price
  changes or interest rate changes to another party
  willing to bear that risk
• Price formation
• Speculation opportunities when some investors may
  feel assets are mis-priced
• Investment cost reduction
• To hedge portfolio risks more efficiently and
  less costly than would otherwise be possible

3
Forward Contracts

• An agreement between two parties to exchange an
  asset at a specified price on a specified date
• Buyer is long, seller is short symmetric gains
  and losses as price changes, zero sum game
• Contracts are OTC, have negotiable terms, and are
  not liquid
• Subject to credit risk or default risk
• Value realized only at expiration
• Popular in currency exchange markets

4
Futures Contracts

• Like forward contracts
• Buyer is long and is obligated to buy
• Seller is short and is obligated to sell
• Unlike forward contracts
• Traded on an exchange
• Standardized size, maturity
• More liquidity - can reverse a position and
  offset the future obligation, other party is the
  exchange
• Less credit risk - initial margin required
• Additional margin needs are determined through a
  daily marking to market based on price changes

5
Futures Contracts

• Futures Quotations
• One contract is for a fixed amount of the
  underlying asset
• 5,000 bushels of corn (of a certain grade)
• 250 x Index for SP 500 Index Futures (of a
  certain maturity)
• Prices are given in terms of the underlying asset
• Cents per bushel (grains)
• Value of the index
• Value of one contract is price x contract amount

6
Futures Contracts

• Example Suppose you bought (go long) the most
  recent (June) SP 500 contract at the settle
  price of 1180.80.
• What was the original contract value?
• Value 250 x 1180.80 295,200
• What is your profit if you close your position
  (sell a contract) for 1250.00?
• Value 250 x 1250.00 312,500
• Profit 312,500 - 295,200 17,300

7
Options

• Option to buy is a call option
• Call options gives the holder the right, but not
  the obligation, to buy a given quantity of some
  asset at some time in the future, at prices
  agreed upon today.
• Option to sell is a put option
• Put options gives the holder the right, but not
  the obligation, to sell a given quantity of some
  asset at some time in the future, at prices
  agreed upon today
• Option premium price paid for the option
• Exercise price or strike price the price at
  which the asset can be bought or sold under the
  contract
• Open interest number of outstanding options
• Expiration date
• European can be exercised only at expiration
• American exercised any time before expiration

8
Options Contracts Preliminaries

• A call option is
• In-the-money
• The exercise price is less than the spot price of
  the underlying asset.
• At-the-money
• The exercise price is equal to the spot price of
  the underlying asset.
• Out-of-the-money
• The exercise price is more than the spot price of
  the underlying asset.

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Options Contracts Preliminaries

• A put option is
• In-the-money
• The exercise price is greater than the spot price
  of the underlying asset.
• At-the-money
• The exercise price is equal to the spot price of
  the underlying asset.
• Out-of-the-money
• The exercise price is less than the spot price of
  the underlying asset.

10
Options

• Example Suppose you own a call option with an
  exercise (strike) price of 30.
• If the stock price is 40 (in-the-money)
• Your option has an intrinsic value of 10
• You have the right to buy at 30, and you can
  exercise and then sell for 40.
• If the stock price is 20 (out-of-the-money)
• Your option has no intrinsic value
• You would not exercise your right to buy
  something for 30 that you can buy for 20!

11
Options

• Example Suppose you own a put option with an
  exercise (strike) price of 30.
• If the stock price is 20 (in-the-money)
• Your option has an intrinsic value of 10
• You have the right to sell at 30, so you can buy
  the stock at 20 and then exercise and sell for
  30
• If the stock price is 40 (out-of-the-money)
• Your option has no intrinsic value
• You would not exercise your right to sell
  something for 30 that you can sell for 40!

12
Options

• Stock Option Quotations
• One contract is for 100 shares of stock
• Quotations give
• Underlying stock and its current price
• Strike price
• Month of expiration
• Premiums per share for puts and calls
• Volume of contracts
• Premiums are often small
• A small investment can be leveraged into high
  profits (or losses)

13
Options

• Example Suppose that you buy a January 60 call
  option on Hansen at a price (premium) of 9.
• Cost of your contract 9 x 100 900
• If the current stock price is 63.20, the
  intrinsic value is 3.20 per share.
• What is your dollar profit (loss) if, at
  expiration, Hansen is selling for 50?
• Out-of-the-money, so Profit (900)
• What is your percentage profit with options?
• Return (0-9)/9 -100
• What if you had invested in the stock?
• Return (50-63.20)/63.20 (20.89)

14
Options

• What is your dollar profit (loss) if, at
  expiration, Hansen is selling for 85?
• Profit 100(85-60) 900 1,600
• Is your percentage profit with options?
• Return (85-60-9)/9 77.78
• What if you had invested in the stock?
• Return (85-63.20)/63.20 34.49

15
Options

• Payoff diagrams
• Show payoffs at expiration for different stock
  prices (V) for a particular option contract with
  a strike price of X
• For calls
• if the VltX, the payoff is zero
• If VgtX, the payoff is V-X
• Payoff Max 0, V-X
• For puts
• if the VgtX, the payoff is zero
• If VltX, the payoff is X-V
• Payoff Max 0, X-V

16
Option Trading Strategies

• There are a number of different option
  strategies
• Buying call options
• Selling call options
• Buying put options
• Selling put options
• Option spreads

17
Buying Call Options

• Position taken in the expectation that the price
  will increase (long position)
• Profit for purchasing a Call Option
• Per Share Profit Max 0, V-X Call Premium
• The following diagram shows different total
  dollar profits for buying a call option with a
  strike price of 70 and a premium of 6.13

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Buying Call Options
Profit from Strategy
3,000
Exercise Price 70 Option Price 6.13
2,500
2,000
1,500
1,000
500
0
(500)
Stock Price at Expiration
(1,000)
40
50
60
70
80
90
100
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Selling Call Options

• Bet that the price will not increase greatly
  collect premium income with no payoff
• Can be a far riskier strategy than buying the
  same options
• The payoff for the buyer is the amount owed by
  the writer (no upper bound on V-X)
• Uncovered calls writer does not own the stock
  (riskier position)
• Covered calls writer owns the stock

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Selling Call Options
Profit from Uncovered Call Strategy
1,000
Exercise Price 70 Option Price 6.13
500
0
(500)
(1,000)
(1,500)
(2,000)
(2,500)
Stock Price at Expiration
(3,000)
40
50
60
70
80
90
100
21
Buying Put Options

• Position taken in the expectation that the price
  will decrease (short position)
• Profit for purchasing a Put Option
• Per Share Profit Max 0, X-V Put Premium
• Protective put Buying a put while owning the
  stock (if the price declines, option gains offset
  portfolio losses)

22
Buying Put Options
Profit from Strategy
3,000
2,500
2,000
Exercise Price 70 Option Price 2.25
1,500
1,000
500
0
Stock Price at Expiration
(500)
(1,000)
40
50
60
70
80
90
100
23
Selling Put Options

• Bet that the price will not decline greatly
  collect premium income with no payoff
• The payoff for the buyer is the amount owed by
  the writer (payoff loss limited to the strike
  price since the stocks value cannot fall below
  zero)

24
Selling Put Options
Profit from Strategy
1,000
500
0
Exercise Price 70 Option Price 2.25
(500)
(1,000)
(1,500)
(2,000)
(2,500)
Stock Price at Expiration
(3,000)
40
50
60
70
80
90
100
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Combinations

• Spread both buyer and writer of the same type of
  option on the same underlying asset
• Price spread purchase or sale of options on the
  same underlying asset but different exercise
  price
• Time spread purchase or sale of options on the
  same underlying asset but different expiration
  dates
• Bull call spread purchase of a low strike price
  call and sale of a high strike price call.
• Bull put spread sale of high strike price put
  and purchase or a low strike price put

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Payoff
Long call
Payoff
Straddle
Bull call spread
Long call
Short put
Short call
Payoff
Straddle purchasing a call and Writing a put on
the same asset, exercise price, and expiration
date
Long put
Bull put spread
Short put
27
Option pricing

• Factors contributing value of an option
• price of the underlying stock
• time until expiration
• volatility of underlying stock price
• cash dividend
• prevailing interest rate.
• Intrinsic value difference between an
  in-the-money options strike price and current
  market price
• Time value speculative value.
• Call price Intrinsic value time value

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Black-Scholes Option Pricing Model
Where C current price of a call option
S current market price of the underlying
stock X exercise price
r risk free rate t time until
expiration N(d1) and N (d2)
cumulative density functions for d1 and d2