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Options
(Chapter 19 Jones)
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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 mispriced

Investment cost reduction
- To hedge portfolio risks more efficiently and less costly than would
otherwise be possible
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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
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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.
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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
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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
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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.
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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!
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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!
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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)
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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%)
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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%
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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]
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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
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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

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Buying Call Options
3,000
Profit from Strategy
2,500
Exercise Price = $70
2,000
Option Price
= $6.13
1,500
1,000
500
0
(500)
(1,000)
40
Stock Price at
Expiration
50
60
70
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80
90
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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 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
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Selling Call Options
1,000
500
Profit from Uncovered Call
Strategy
Exercise Price = $70
Option Price
= $6.13
0
(500)
(1,000)
(1,500)
(2,000)
(2,500)
(3,000)
40
Stock Price at
Expiration
50
60
70
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90
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Covered call
S< E
Payoff of stock S
Payoff call
-0
Premium
C
Total payoff
C+S
20
S>E
S
-(S-E)
C
C+E
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Covered Call Writing
Profit ($)
Purchased
share
0
Combined
Stock Price
at Expiration
Written call
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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)

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Buying Put Options
3,000
Profit from Strategy
2,500
2,000
Exercise Price = $70
1,500
Option Price
= $2.25
1,000
500
0
Stock Price at
Expiration
(500)
(1,000)
40
50
60
70
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90
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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
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Protective put
S< E
Payoff of stock S
Payoff put
E-S
S>E
S
0
Premium
-P
-P
Total payoff
E-P
S-P
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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)
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Selling Put Options
1,000
Profit from Strategy
500
0
Exercise Price = $70
(500)
Option Price
(1,000)
= $2.25
(1,500)
(2,000)
(2,500)
(3,000)
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Stock Price at
Expiration
50
60
70
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90
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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.
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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
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Factors Affecting Prices
Variable
Stock Price
Exercise Price
Time to maturity
Stock volatility
Interest rates
Cash dividends
Call
+
+
+
+
30
Put
+
+
+
+
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Black-Scholes Option Pricing Model
Call
Value of

price upside potential

Opportunit y cost
of invested funds
X
C  S N (d1 )  rt N (d 2 )
e
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
d1 


ln S X   r  0.5 2 t
d 2  d1   t
 t
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Riskless Hedging
(NOT on the exam)
Options can be used to control the riskiness of
common stocks
- If stock owned, sell calls or buy puts
 Call or put option prices do not usually change
the same dollar amount as the stock being
hedged
- Shares purchased per calls written =N(d1)
- Shares purchased per puts purchased =N(d1) - 1

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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, 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 p523-524; Put
option valuation, riskless hedging, Stock index options p 528-534;
Recommended End-of-chapter questions:19-1 to 14
• Recommended End-of-chapter problems:19.1, 2, 3
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