Chapter
19
Options
Learning Objectives




Define options and discuss why they are
used.
Describe how options work and give some
basic strategies.
Explain the valuation of options.
Identify types of options other than puts
and calls.
Options

Call (Put): Buyer has the right, but not the
obligation, to purchase (sell) a fixed
quantity from (to) the seller at a fixed price
before a certain date



Exercise (strike) price: “fixed price”
Expiration (maturity) date: “certain date”
Option premium or price: paid by buyer to
the seller to get the “right”
Why Options Markets?



Financial derivative securities: derive all or
part of their value from another (underlying)
security
Options are created by investors, sold to
other investors
Why trade these indirect claims?

Expand investment opportunities, lower cost,
increase leverage
Option Terminology



Exercise (Strike) price: the per-share price
at which the common stock may be
purchased or sold
Expiration date: last date at which an option
can be exercised
Option premium: the price paid by the
option buyer to the writer of the option,
whether put or call
Options Trading

Options exchanges



Chicago Board Options Exchange (CBOE)
Montreal Exchange (ME)
Standardized exercise dates, exercise
prices, and quantities

Facilitate offsetting positions through a
clearing corporation
 Clearing
corporation is guarantor,
handles deliveries
Options Characteristics

In-the-money options have a positive
cash flow if exercised immediately



Out-of-the-money options should not be
exercised immediately



Call options: S > E
Put options: S < E
Call options: S < E
Put options: S > E
If S = E, an option is at the money
Options Characteristics

Intrinsic value is the value realized from
immediate exercise



Call options: maximum (S0-E, 0)
Put options: maximum (E-S0, 0)
Prior to option maturity, option premiums
exceed intrinsic value
Time Value = Option Price - Intrinsic Value
Payoff Diagram for a Call Option
Profit per
Option ($)
Buyer
4
0
25
27
29
Stock Price
at Expiration
-4
Seller
How does buying a stock compare
with buying a call option?
Payoff Diagram for a Put Option
Profit per
Option ($)
4
Buyer
0
23
-4
25
27
Stock Price
at Expiration
Seller
How does selling a stock compare
with buying a put option?
Covered Call Writing
Profit ($)
Purchased
share
Combined
4
0
23
-4
25
27
29
Stock Price
at Expiration
Written call
Protective Put Buying
Profit ($)
Purchased
share
Combined
4
0
23
-4
25
27
29
Stock Price
at Expiration
Purchased
put
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
Portfolio Insurance
Profit ($)
Purchased
share
Combined
2
0
23
25
27
29
Stock Price
at Expiration
-2
Purchased
put
Should Options be Exercised
Early?

Exercise prior to maturity implies the
option owner receives intrinsic value
only, not time value

For call options, buy stock at below market
price
 Would

more be earned by selling option?
For put options, receive cash from selling
stock at above market price
 Could
cash be reinvested for a higher return?
Option Price Boundaries

At maturity, option prices are equal to their
intrinsic values


Intrinsic value is minimum price prior to maturity
Maximum option prices prior to maturity


Call options: price of stock, S0
Put options: exercise price, E
Option Price Boundaries
C =S
Put E
Prices
Call
Prices
E
Stock Prices
E
Stock Prices
Black-Scholes Model


Five variables needed to value a
European call option on a non-dividend
paying stock
EPformula is:
The CP
Black-Scholes
pricing
 CMP  N(d1 )  rt  N(d2 )
e
2
ln(CMP EP)  (r  .5 )t
d1 
 t
d2  d1   t
Put-Call Parity



Black-Scholes valuation is for call options
Put-call parity shows relationship between
call and put options so that riskless
arbitrage is not possible
Price of put = E/(ert) - S +C
Put replicated by riskless lending, short
sale of stock, purchased call
Factors Affecting Prices
Variable
Stock Price
Exercise Price
Time to maturity
Stock volatility
Interest rates
Cash dividends
Call
+
+
+
+
-
Put
+
+
+
+
Hedge Ratios

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 call written = N(d1)
Shares purchased per put purchased = N(d1) - 1
Other Types of Options



Stock-Index Options: option contracts on a
stock market index
Interest Rate Options: option contracts on
fixed income securities
Currency Options: Option contracts whose
value is based on the value of an
underlying currency
Basics of Stock-Index Options




Options available on S&P/TSE 60 Index,
S&P 500 Index, NYSE Index, etc.
Bullish on capital markets implies buying
calls or writing puts
Bearish on capital markets implies buying
puts or writing calls
At maturity or upon exercise, cash
settlement of position
Strategies with Stock-Index
Options


Speculation opportunities similar to options
on individual stocks
Hedging opportunities permit the
management of market risk


Well-diversified portfolio of stocks hedged by
writing calls or buying puts on stock index
What return can investor expect?
Appendix 19-A
Combinations of Options

Straddle – A combination of a put and a call
on the same stock with the same exercise
date and exercise price




A purchaser believes that the underlying stock
price is highly volatile and may go either up or
down
A seller believes that the underlying stock price
will exhibit small volatility but could go up or down
Strip – A combination of two puts and a call
on the same security, same exercise date
and price
Strap – combines two calls with a put
Appendix 19-A Spreads of Options


The purchase and sale of an equivalent
option varying in only one respect
Two basic spreads:


Money spread involves the purchase of a call
option at one exercise price and the sale of
the same maturity option, but with a different
exercise price
Time spread involves the purchase and sale of
options are identical except for expiration
dates
Appendix 19-B
Rights and Warrants


Right – to purchase a stated number of
common shares at a specified price with
a specified time (often several months)
Warrant – to purchase a stated number
or common shares at a specified price
with a specified time (often several
years)
Appendix 19-C Put-Call Parity


No-Arbitrage Argument
Example:
Portfolio
A
B
Action
Buy 1 call
Invest PV(E) in Tbills
Total Payoff
Buy 1 share
Buy 1 put
Total payoff
Payoff at T
S(T) <E
S(T) >E
0
S(T) – E
E
E
E
S(T)
E – S(T)
E
S(T)
S(T)
0
S(T)