Options

1
Options

• Spring 2007
• Lecture Notes 4.6.1
• ReadingsMayo 28

2
Goals

• Definitions
• Options
• Call option
• Put option
• Option strategies

3
Derivatives Definition

• Derivative Any security whose payoff depends on
  any other security

4
Goals

• Definitions
• Options
• Call option
• Put option
• Option strategies

5
Options

• Two types
• Call Option to buy
• Put Option to sell
• Parts
• Option price
• Strike price
• Expiration

6
Call Option

• Option to purchase asset at the strike price
• Horizon(two types)
• American Anytime between now and the expiration
  date
• European On the expiration date only
• Strike price Price at which the security can be
  purchased

7
Example Buying a call option on Amazon

• Amazon share price 100
• Purchase American call option
• Option price 5
• Strike price 120
• Expiration 2 months from now
• Case A price goes to 150
• Exercise option
• Buy at 120, sell at 150
• Total 150-120-5 25
• Case B price goes to 50
• Dont exercise option
• Total -5 (lose entire investment)

8
Example Writing (selling) a call option on
Amazon

• Amazon share price 100
• Write American call option
• Option price 5
• Strike price 120
• Expiration 2 months from now
• Case A price goes to 150
• Purchaser exercises option
• Buy at 150, sell at 120
• Total -1501205 -25
• Case B price goes to 50
• Purchaser doesnt exercise option
• Total 5

9
Options and Insurance

• The writer is kind of selling insurance to the
  buyer
• As long as the price doesnt go up by too much
  (20) the writer gets to pocket the 5
• Like an insurance premium
• Danger If price rises by large amount, option
  writer can lose lots of money

10
How do you lose big money with options?

• Write (sell) a naked call on Amazon.com (p
  100), strike price 150
• Sell for 5
• You feel very happy (5)
• Then Amazon goes to 250
• The other side of your option trade exercises the
  option
• You must buy Amazon at 250, and sell it for 150

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Option Terms

• In-the-money
• Stock price call option strike price
• At-the-money
• Stock price call option strike price
• Out-of-the-money
• Stock price

12
Intrinsic ValueValue of option if used today

• Strike price 100

Intrinsic Value
5
Stock Price
0
105
104
100
13
Option Pricing

• Is it as easy as
• (Price strike price) when strike
• 0 if strike is stock price
• Why does this get more complicated?
• Have to consider today plus all days to the
  expiration date
• Even though the price is in the zero value range
  today (out-of-the-money, it might move into the
  positive value range tomorrow

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General Properties of an option price

• Option value will be higher
• When the expiration date is farther in the future
• When the stock price moves around more
• (This is known as higher volatility)

15
Option Pricing

• There are different formulas that try to take
  account of all this stuff
• Black/Scholes is the most famous of these
• Techniques used
• Arbitrage
• Stochastic calculus

16
Option Price (red) versusIntrinsic Value
(black)Value of option if used today

• Strike price 100

Intrinsic Value
5
Stock Price
0
105
104
100
17
Goals

• Definitions
• Options
• Call option
• Put option
• Option strategies
• Real options

18
Put Option

• Same as Call
• Price
• Strike price
• Expiration
• Difference Option to Sell

19
Example Put Value

• Strike price 100

Intrinsic Value
10
5
Stock Price
0
96
90
100
95
20
Goals

• Definitions
• Futures
• Options
• Call option
• Put option
• Option strategies

21
OptionsStocks

• Holding option alone is known as holding a naked
  option
• Holding option with the stock is known as a
  covered option

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Insuring gains by buying a put option

• Purchasing a put option on stock you already own
  sets a floor on what you can sell
• Buy stock at 75, price rises to 100
• Lock in gains, buy put at strike 100
• Gains will be at least 100-75
• Cost price of the put option

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Example 1 Buy Stock Put

• Strike price 100
• How much would your portfolio (option stock) be
  worth for different prices?

Total Value
105
Stock Price
100
100
105
24
Example 2 Option Straddle

• Purchase a put and call at the same strike price
• Strategy makes money when stock price moves a lot
  (volatility is high)

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Straddle Example

• Current stock price 100
• Purchase at-the-money call (strike 100) for 2
• Purchase at-the-money put (strike 100) for 3
• What is the total value of your option portfolio
  for different stock prices?

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Straddle Performance

• Lose money when no change in price
• Price goes up Call makes money
• Price goes down Put makes money
• Strategy makes money when price moves a lot
  (depends on option prices)

27
Straddle Contingency GraphPlot of net gain as
a function of stock price

• Strike price 100
• Option prices call 2, put 3

Net Gain
1
0
Stock Price
-5
106
105
95
94
100
28
Writing Call Options

• Writing a naked call
• Writing a naked put

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Writing a Naked Call Option(1 share, option
price 5, strike 100)
5
105
110
0
100
Stock Price
-5
30
Writing a Covered Call Option(1 share, option
price 5, strike 100, stock purchased at 100)
5
90
0
100
95
Stock Price
-5
31
Other Combinations

• Many other combinations are possible
• As with futures, you can use options to reduce
  risk or increase risk if you want

32
Exotic Options

• More complicated functions of prices
• Often involve time path of prices
• Ordinary options do not care about path
• Example Barrier option
• deactivates if price crosses a barrier any time
  during a given period

33
Other Applications

• Stock options
• Investment options

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Option Summary

• Can be used to either reduce, or increase risk
• Have insurance like characteristics
• Derivatives as fire