Chapter 15 – Options Markets
CHAPTER FIFTEEN
OPTIONS MARKETS
CHAPTER OVERVIEW
This chapter describes characteristics of options, terminology used in the options’ markets,
option payoffs and profits to both option owners and sellers (called writers), and positions that
are comprised of combinations of options and stock or multiple option contracts. Option-like
assets, such as callable bonds, warrants, and collateralized loans are also described.
LEARNING OBJECTIVES
After studying this chapter, the student should be able to calculate potential profits resulting from
various option trading strategies and to formulate portfolio management strategies to modify the
risk-return attributes of the portfolio. The student should be able to identify the embedded
options in various assets and to determine how these option characteristics affect the prices of
these assets.
CHAPTER OUTLINE
1. The Option Contract
PPT 15-2 through PPT 15-9
A listed call option is a contract giving the holder the right to buy 100 shares of stock at a preset
price called the exercise or strike price. A listed put option is a contract giving the holder the
right to sell 100 shares of stock at a preset price. Expirations of 1,2,3,6, 9 months and sometimes
1 year are normal contract periods. Contracts expire on the Saturday following the third Friday
of the expiration month. Friday is the last day you can exercise. Contracts may be sold prior to
maturity. This is an important point. You don’t have to exercise to realize the value of the
option. In fact in most cases an option should be sold rather than exercised because exercising
forfeits the option’s time value (See Chapter 16). 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
American vs. European options
Chapter 15 – Options Markets
With an American style option the option can be exercised at any date after purchase whereas
with a European style option the option can only be exercised immediately before expiration
(only on the last Friday before expiration). Most options that are traded in this country are
American options. Foreign currency and stock index options that trade on the Chicago Board
Options Exchange are exceptions. European style options are cheaper, that is the motivation for
them. Note that the style (American vs. European) has nothing to do with where the options are
traded.
Options Uses
The OCC
The option exchanges operate the Option Clearing Corporation (OCC). An option buyer or
seller technically buys or sells from or to the OCC. The OCC backs performance of both
counterparties. This allows liquid anonymous trading to occur. To limit the OCC’s risk the
option seller (or writer) must post margin. The margin varies with option price and whether the
option position is covered or exposed. An in the money option requires more margin than an out
of the money option. Margin varies with the exposure of the option seller. A covered call writer
write a call on which they own stock. The writer can post the stock to satisfy the margin
requirement, whereas a naked call writer must post cash. 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.
Options are available on a variety of financial assets including a host of interest rates products
and currencies. Index options are very popular instruments used in hedging. Options are also
available on other derivative instruments such as futures contracts. Most of the pricing and
payoff examples that are built in the text are stock options.
2. Values of Options at Expiration
PPT 15-10 through PPT 15-28
Chapter 15 – Options Markets
This section requires the use of some terminology:
Symbols & Valuation
Ct = Price paid for a call option at time t. t = 0 is today,
T = Immediately before the option’s expiration.
Pt = Price paid for a put option at time t.
St = Stock price at time t.
X = Exercise or Strike Price
A call is “in the money” if St > X. A put is “in the money” if St < X.
A call is “out of the money” if St < X. A put is “out of the money” if St > X.
An option is in the money if you could profitably exercise it right now. Basic option pricing
boundaries are developed below:
C and P are greater than zero because the holders have a choice to use them or not. A simple
arbitrage argument (shown above) can be used to demonstrate that the call price must be greater
than or equal to the difference between the stock price and the exercise price. This is the basis
for the price boundary of a call Ct ≥ Max (0, St – X).
Constructing a profit table is an excellent method to model and understand the payoffs of any
option strategy and having students work though some of these tables is an excellent teaching
exercise. For example the profit at expiration of buying a call if ST < X is –C0, therefore profit is
a straight line at the level equal to –C0. If ST > X then profit = –C0 + ST – X. Since the horizontal
axis on the profit graph (see below) is ST and the profit equation in this region has a +1
coefficient, the profit diagram is a positive slope 45° line. See the profit table below:
Chapter 15 – Options Markets
Chapter 15 – Options Markets
The put writer has unlimited loss potential if the stock price falls. The profit for a put writer is
limited to a premium of the option. The text has an excellent boxed item entitled, “The Black
Hole: How Some Investors Lost All Their Money in the Market Crash.” The example of the risk
involved in writing naked puts surrounding the October 1987 Market Crash points out the
substantial risk in writing naked options. The profit graphs are based on the value of the option at
expiration.
Some other strategies are illustrated in the PPT. A protective put involves the purchase of stock
and the purchase of puts on an equivalent number of shares. The strategy reduces upside
potential if the stock price rises by the cost of the put but it limits the loss if the stock declines in
price.
A covered call involves ownership of stock and writing a call option. It is referred to as covered
since the stock is owned if the option buyer exercised their option. The position has limited
upside potential and offers some protection to the owner of the stock if the stock price declines.
A straddle is constructed by purchasing a call and a put with the same exercise date and maturity
date. A straddle will result in profits if the stock price increases or decreases enough to
overcome the premiums for the options.
Chapter 15 – Options Markets
Bullish spreads allow an option investor to gain a limited amount of profit if the stock price rises
while also protecting the investor if the stock price declines.
A collar is an options strategy that brackets the value of a portfolio between two bounds and may
be appropriate for an investor who has a target wealth goal but is unwilling to risk losses beyond
a certain level.
Warnings about Option Strategies
Options may have to move 10-15% or more in a short time period before an investor recovers the
price & commission. Most options expire worthless. 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 dollar
investments in stocks and options to truly see the higher risk of the option position. Options are
traded in a highly competitive market and are priced according to expected volatility of the
underlying asset. To profit in options you must be able to forecast price or volatility better than
the competition and your gains must exceed your transactions costs. This is a tall order in a
competitive market. Many brokers and planners recommend writing covered calls to gain some
steady income, and most of the time the stock will not be called away from you. However, the
investor never gets the occasional large stock price run up and suffers most of the loss of a big
price drop. This strategy eliminates any positive skew of stock returns and is likely to leave the
investor with a portfolio of poorer performers. Writing naked calls (writing calls when you do
not own the stock) limits the writer’s gain to the call premium but exposes the writer to unlimited
loss, and this is a poor strategy in volatile markets.
Chapter 15 – Options Markets
3. Optionlike Securities
PPT 15-29 through PPT 15-35
Many securities are complex products that include imbedded options. The payoffs and profits
associated with securities that contain imbedded options will present payoffs that are similar to
options or groups of options. Examples that demonstrate the impact of embedded options include
callable bonds, convertible bonds, collateralized loans and levered equity and these are covered
in the PPT. The discussion of convertible bonds is particularly important because students
routinely think that convertible bonds are a good deal that combine the safety of a bond with the
upside potential of equity. There is no free lunch (other than diversification) in finance. When
issued the convertible option is out of the money and investors must accept a lower yield rate to
get it. Often stock prices will have to increase 20% to 25% before conversion becomes
profitable. Virtually all convertibles are callable as well. The issuing firm may call the bond
when it is profitable to convert in order to ‘force’ conversion. This may shorten the expected
maturity of the bond.
4. Exotic Options
PPT 15-36
Discussion of these options is useful in making students aware of the all the various types of
options that are available to construct different desired payoffs. Asian- Payoffs depend on the
average (rather than the final) price of the underlying asset during a portion of the life of the
option. Barrier Options’ value depends on whether the underlying asset price has passed through
some barrier during the life of the option. For example “down-and-out” options expire worthless
if the stock price drops below a specified barrier. A lookback option payoff depends on the
minimum or maximum price during life of option. Currency Translated Options allow a variable
amount of foreign currency based on the performance of an investment to be translated to dollars
at a fixed exchange rate. Digital options pay a fixed amount if the option is in the money
regardless of how far in the money the option goes. Digital options are being used to make bets
on economic data such as the number of jobless claims or inflation.
Excel Applications
Chapter 15 – Options Markets
There are two spreadsheet applications available on the web site. The first one allows the
students to examine the changes in profitability and rates of return for an example that is similar
to the example in the text. The spreadsheet can be modified to allow for different combinations
of options, lending and levels of stock ownership. The second spreadsheet allows students to
examine the changes in payoffs and rates of returns for various spread and straddle strategies.