Options

1

• Options
• (Chapter 18 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
Option characteristics

• 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
• Long-term Equity AnticiPation Securities (LEAPS)
  expiration dates up to three years.
• Long-term calls and puts.

4
Option characteristics

• Expiration date
• European can be exercised only at expiration
• American exercised any time before expiration

Option holder long the option position Option
writer short the option position Hedged
position option transaction to offset the risk
inherent in some other investment (to limit risk)
Speculative position option transaction to
profit from the inherent riskiness of some
underlying asset. Option contracts are a zero
sum game before commissions and other transaction
costs.
5
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.

6
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.

7
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!

8
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!

9
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)

10
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)

11
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

12
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

13
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

14
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

15
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
16
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
• Moderately bullish investors sell calls against
  holding stock to generate income

17
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
18
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)

19
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
20
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)

21
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
22
Exam type question
An investor bought two Google June 425 (exercise
price is 425) put contracts for a premium of
20 per share. At the maturity (expiration), the
Google stock price is 370. (i) Draw the payoff
diagram of the investment position. (ii)
Calculate the total profit/loss of the position
at the expiration.
23
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

24
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
25
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

26
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
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• Learning outcomes
• discuss the benefits of using financial
  derivatives
• know the basic characteristics of options
• know the options payoffs
• know how to calculate the profits/losses of a
  long/short call and put options (numerical
  application)
• Know the factors affecting option pricing (slide
  24) no numerical problems with Black-Scholes
• Recommended End-of-chapter questions 18.1,
  18.4,18.6
• Recommended End-of-chapter problems 18.7, 18.8,
  18.9, 18.10