Chapter 15
Options
Markets
McGraw-Hill/Irwin
Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved.
Option Terminology
1. What is a listed stock call option?
– A contract giving the holder the right to buy 100 shares of stock
at a preset price called the exercise or strike price.
– Expirations of 1,2,3,6,& 9 months and sometimes 1 year are
normal contract periods. Contracts expire on the third Saturday
of the expiration month.
– Contracts may be resold prior to maturity.
2.
What is a listed stock Put option?
- A contract giving the holder the right to sell 100 shares of stock at
a preset price
15-2
Option Characteristics
• If a call option holder wishes to purchase the stock, he or she will
exercise the option. The option holder must pay the exercise price to
the option writer.
• Exercise prices are adjusted for stock splits and stock dividends, but
not cash dividends.
• The cost of an option is called the premium and it is a small
percentage of the cost of the underlying asset. The option buyer
pays the cost; the option writer receives the cost at the time of sale of
the option.
• The underlying company is not involved in the option market.
• Options are a zero sum game.
15-3
American vs. European Options
American: the option can be exercised any time, but no
Later than the expiration date
European: the option can only be exercised at the
expiration date
15-4
Figure 15.1 Options on IBM
15-5
3. Uses of options:
a. To hedge changes in stock price.
b. Change your risk and return profile
• For example, buying a call is analogous to buying
stock on margin.
c. Short sale constraints can be avoided with
puts.
15-6
Option Clearing Corporation
(OCC)
• OCC is jointly owned by option exchanges
• OCC backs performance of both counterparties
– To limit OCC’s risk, option seller (or writer) must post margin.
Margin varies with option price and whether the option position is
covered or exposed.
• When an option is exercised an option seller is randomly
selected.
– If a call is exercised the selected call writer must deliver 100
shares of stock in exchange for receiving the strike price.
– If a put is exercised the selected put writer must purchase 100
shares of stock at the strike price.
15-7
4. Types of options
Listed Options vs OTC Options
o
o
o
o
o
Index Options
Options on Futures
Foreign Currency Options
Interest Rate Options
Exotic Options
15-8
15.2 Values of Options at
Expiration
15-9
5. Symbols & Valuation
Ct = Price paid for a call option at time t. t = 0 is today,
T = option's expiration date.
Pt = Price paid for a put option at time t.
St = Stock price at time t.
Xc, Xp= Exercise or Strike Price
> Xc.
A call is “in the money” if St ____
A call is “out of the money” if St ____ Xc.
A put is “in the money” if St ____ Xp.
A put is “out of the money” if St ____
> Xp.
>
>
15-10
6. The basics of option pricing
a) Price boundaries
o Ct ≥ 0,
Why?
o Ct ≥ St – X, Why?
o Pt  0
o Pt  X - St
$5 $60 $50
– If Ct < St – X How could you take advantage of this?
o Thus Ct  Max (0, St – X)
o Pt  Max (0, X – St)
o Just before expiration at time T:
If ST < X then CT = 0
if ST > X then CT = ST – X
15-11
IBM Option Quotes
15-12
7. Option strategies and profits at expiration
BUYING A CALL
Profit Table
ST < X
ST > X
– C0
– C0
– C0
+CT
0
ST – X
= Profit
– C0
– C 0 + ST – X
Breakeven
ST = X + C 0
15-13
Profit
Call profit at expiration
ST = X + C 0
-$735
$100
$92.65
$0
$107.35
-C0 + ST – X
-C0
Stock
PriceT
Ex = $100
 Bullish or bearish?
IBM Jul 100 call option
Stock Price = $96.14
Exercise = $100
Call premium = $735
Contract Size 100 shares
 High or low volatility strategy?
15-14
Writing a naked call
WRITING A NAKED CALL
Profit Table
ST < X
ST > X
+C0
+C0
+C0
– CT
0
–(ST – X)
= Profit
+C0
+C0 – ST + X
Breakeven
ST = X + C 0
15-15
Writing a naked call
Profit
+C0 – ST + X
+C0
$0
X
S T = X + C0
Stock
PriceT
 Bullish or bearish?
 High or low volatility strategy?
15-16
Buying a put option
BUYING A PUT
Profit Table
ST < X
ST > X
– P0
– P0
– P0
+PT
X – ST
0
= Profit
X – ST – P0
– P0
Breakeven
ST = X – P0
15-17
IBM Option Quotes
15-18
Profit
$8,834
$0
-$1,166
Buying a put option
IBM Dec 100 put option
Stock price = $96.14
Exercise = $100
Put premium = $1,166
Contract Size 100 shares
Short
position in
IBM
X – ST – P0
$100
$88.34
$111.66
– P0
B.E.: ST = X – P0
Ex = $100
 Bullish or bearish?
Stock
Pricet
Put
Alternative Stock Strategy?
 High or low volatility strategy?
15-19
Writing a put option
Writing A Put
Profit Table
ST < X
ST > X
+P0
+P0
+P0
– PT
–(X – ST )
0
= Profit
ST – X + P 0
+P0
Breakeven
ST = X – P0
15-20
Profit
Writing a put option
$1,166
ST – X + P0
$0
$88.34
$100
Long
Position
in
Xx IBM
= $100
- $8,834
 Bullish or bearish?
$111.66
+P0
Stock
Pricet
IBM Jul 100 put option
Stock price = $96.14
Exercise = $100
Put premium = $1,166
Contract Size 100
shares
Alternative Stock Strategy?
 High or low volatility strategy?
15-21
Buy stocks and at the money puts:
Profit
Protective Put
Long
position in
IBM
Hedged
Position
$0
Stock
Pricet
X
Put
Hedged profit equals sum of profits of put and stock
at each stock price.
15-22
Writing Covered Calls
Profit
Long
position in
IBM
Covered Call
Written call
$0
S0
ST = S0 - C0
Stock
Pricet
• Bullish or bearish?
• High or low volatility strategy?
15-23
Bullish Price Spread
Bull perpendicular or price spread with
calls; write (sell) the high exercise price
call and buy the low exercise price call. All
other option terms identical. L=low
exercise price, H=high exercise price
15-24
Bullish Price Spread
BULLISH PRICE SPREAD
Profit Table
ST < X L
XL < S T < X H
ST > X H
– C0L
– C0L
– C0L
– C0L
+C0H
+C0H
+C0H
+C0H
+CTL
0
ST – X L
ST – XL
– CTH
0
0
–(ST – XH )
= Profit
C0H – C0L
ST – XL – C0L +C0H
XH – XL – C0L + C0H
Breakeven
–
ST = XL + C0L – C0H
+
Profit
XH
XL
Stock
Pricet
• Bullish or bearish?
• High or low volatility strategy?
15-25
Long or Bull Straddle
Long or bull straddle: buy a put and a call
with the same T and X.
(For bear or short straddle, sell both put and
call and just flip the graph upside down.)
15-26
Long or Bull Straddle
BULL STRADDLE
Profit Table
ST < X
ST > X
– C0
– C0
– C0
– P0
– P0
– P0
+CT
0
ST – X
+PT
X – ST
0
= Profit
X – ST – C0 – P0
ST – X – C0 – P0
Breakeven
ST = X – C0 – P0
ST = X + C 0 + P 0
Profit
$0
X – C0 – P0
X
X + C0 + P0
Stock
Price t
• Bullish or bearish? _____________
Neutral
Max Loss: C0 + P0
• High or low volatility strategy?
15-27
Strips and Straps
•
Long or bull strap; buy two calls and one
put, more bullish than straddle.
•
Long or bull strip; buy two puts and one
call, more bearish than straddle.
Think about bear versions of each.
15-28
Short Strangle:
Sell out of the money
put and call
Short Strangle
Profit Table
ST < X L
XL < S T < X H
ST > X H
+ P0L
+ P0L
+ P0L
+ P0L
+C0H
+C0H
+C0H
+C0H
– PTL
– (XL – ST )
0
0
– CTH
0
0
–(ST – XH )
= Profit
ST – XL+ P0L + C0H
P0L + C0H
XH – ST + P0L + C0H
Breakeven
ST = XL– P0L– C0H
+
ST = XH + P0L + C0H
Profit
ST= XL–P0L–C0H
XL
XH
ST = XH + P0L + C0H
Stock
Pricet
15-29
8. Warnings about options
positions
o Options may have to move 10-15% or more in a short
time period before an investor recovers the price &
commission.
o Options are by definition short term instruments; an
investor can ride out bad times in spot markets but not in
options.
– The limited loss feature makes options appear safer than they
are.
– You have to compare equal $ investments in stocks and options
to really see the higher risk of the option position.
o Options are traded in a highly competitive market.
15-30
8. Warnings about options positions
Profit
What’s wrong with selling options?
o Covered calls (writing calls against stock you own)
Stock
Pricet
$0
– The investor never gets the occasional
large stock price run up and suffers most of the
loss of a big price drop.
Eliminates any positive skewness of stock returns
– Wind up with portfolio of poorer performers
o Naked calls (writing calls when you do not own the
stock)
– Maximum gain is limited to call premium but
unlimited loss, poor strategy in volatile markets
Profit
$0
Stock
Pricet
15-31
Optionlike Securities
1. Callable bonds
– Issuing firm has the right to call in the bond
and pay call price.
– When will the firm want to exercise its call
option?
15-32
Figure 15.11 Values of Callable Bonds
Compared with Straight Bonds
15-33
2. Convertible Securities
• Security holder has the option to convert the
bond to a fixed number of shares of common
stock.
• Bond’s Conversion Value = Conversion Ratio x
Common Stock Price
• If a bond is convertible to 20 shares of stock, stock is
priced at $60 per share. The bond’s conversion value
= $1,200
15-34
Figure 15.12 Value of a Convertible
Bond as a Function of Stock Price
The option is issued deep out
the money, the ‘option cost’ is
a lower coupon.
15-35
Convertibles (cont.)
Theoretical value of a convertible bond =
Value straight debt + Value of conversion option
In reality there are three complicating factors:
1. The conversion price may increase over time effectively
increasing the option’s exercise price.
2. Stocks may pay dividends, this makes it harder to value the
option to convert
3. Virtually all convertible bonds are callable by the firm. The firm
may call to force conversion, this makes the maturity of the
bond and the option indeterminate.
15-36
3. Warrants
– Firm sometimes issue warrants with its bonds.
The warrants are call options to purchase new
stock at a fixed price.
– Detachable “sweetener” to help sell the bond
– Exercise of warrants (and convertibles) can
result in dilution of earnings per share
15-37
4. Collateralized loans
–
–
Suppose a borrower is obligated to pay back L dollars at
loan maturity (Time T) and has posted collateral worth St
dollars.
The borrower has an option to repay the loan at maturity if
L > ST, otherwise the borrower can default and give up the
value of L.
5. A similar logic applies to corporate equity if a firm
has debt.
–
Equity holders effectively have a call option on firm value
as they can choose to pay off the debt if firm value > value
of the debt or default otherwise.
15-38
Collateralized Loan Payoffs
15-39
Exotic Options
Asian Options
Barrier Options
Payoff depends on the average (rather than the
final) price of the underlying asset during a
portion of the life of the option.
Example “down-and-out” expires worthless if
the stock price drops below a specified barrier.
Lookback Options
Payoff depends on minimum or max price
during life of option.
15-40
Exotic Options
Currency Translated Options or Quantos
Allows a variable amount of foreign currency
based on the performance of an investment to
be translated to dollars at a fixed exchange rate.
Binary or Digital Options
Pays a fixed amount if the option is in the money at
expiration.
15-41
Problem 1
a.
Purchase a straddle, i.e., buy both a put and a call on
the stock.
The total cost of the straddle would be: $10 + $7 = $17
$17
b.
15-42
Problem 3
Joe’s Protective Put Strategy
Profit Table
ST < $1,200
ST > $1,200
ST – $1,200
ST – $1,200
ST – $1,200
– P0
– $60
– $60
+PT
$1,200 – ST
0
= Profit
– $60
ST – $1,260
ST = $1,260
Breakeven
Sally’s Protective Put Strategy
Profit Table
ST < $1,170
ST > $1,170
ST – $1,200
ST – $1,200
ST – $1,200
– P0
– $45
– $45
+PT
$1,170 – ST
0
= Profit
– $75
ST – $1,245
Breakeven
ST = $1,245
Sally’s
Joe’s
$1245
$1260
-$60
-$75
15-44