1. Options
(Chapter 19)

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
Options are created by investors, sold to other investors
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

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. How Options Work
Call buyer (seller) expects the price of the underlying security to increase (decrease or stay steady)
Put buyer (seller) expects the price of the underlying security to decrease (increase or stay steady)
At option maturity
Option may expire worthless, be exercised, or be sold

6. Options Trading
Option exchanges are continuous primary and secondary markets
Chicago Board Options Exchange largest
Standardized exercise dates, exercise prices, and quantities
Facilitates offsetting positions through Options Clearing Corporation
OCC is guarantor, handles deliveries

7. 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.

8. 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.

9. 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!

10. 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!

11. Options Stock Option Quotations Premiums are often small
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)

12. 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 = ( )/63.20 = (20.89%)

13. 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 = ( )/9 = 77.78%
What if you had invested in the stock?
Return = ( )/63.20 = 34.49%

14. Options Payoff diagrams
Show payoffs at expiration for different stock prices (S) for a particular option contract with a strike price of E
For calls:
if the S<E, the payoff is zero
If S>E, the payoff is S-E
Payoff = Max [0, S-E]
For puts:
if the S>E, the payoff is zero
If S<E, the payoff is E-S
Payoff = Max [0, E-S]

15. Option Trading Strategies
There are a number of different option strategies:
Buying call options
Selling call options
Covered call
Buying put options
Selling put options
Protective put

16. 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, S-E] – 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

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

18. 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 E-S)
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

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

20. Covered call
S< E S>E Payoff of stock S S Payoff call -0 -(S-E) Premium C C Total payoff C+S C+E

21. Covered Call Writing Profit ($) Purchased share Combined Stock Price
Stock Price
at Expiration
Profit ($)
Purchased share
Written call
Combined

22. 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, E-S] – Put Premium
Protective put: Buying a put while owning the stock (if the price declines, option gains offset portfolio losses)

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

24. Portfolio Insurance
Hedging strategy that provides a minimum return on the portfolio while keeping upside potential
Buy protective put that provides the minimum return
Put exercise price greater or less than the current portfolio value?
Problems in matching risk with contracts

25. Protective put S< E S>E Payoff of stock S S Payoff put E-S 0
Premium -P -P
Total payoff E-P S-P

26. 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 stock’s value cannot fall below zero)

27. Selling Put Options Profit from Strategy 1,000 500
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

28. 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.

29. 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 option’s strike price and current market price
Time value: speculative value.
Call price = Intrinsic value + time value
Exercise prior to maturity implies the option owner receives intrinsic value only, not time value

30. Factors Affecting Prices

31. 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

32. 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, covered call and protective put (numerical application)
Know the factors affecting option pricing; no numerical problems with Black-Scholes
NOT on the exam: Boundaries on option prices p ; Put option valuation, riskless hedging, Stock index options p ; Recommended End-of-chapter questions:19-1 to 14
Recommended End-of-chapter problems:19.1, 2, 3