Transcript Mechanics of Options Markets

Mechanics of
Options Markets
The size of option market and
importance of options
• The size of option market size is far
smaller than futures markets. However, as
a nonlinear derivative product, its
theoretical significance is far greater than
other linear products.
• All real investments are nonlinear. Initially
one invest a lot, without any payoff. Later
one invest very little, but with huge payoff.
Options
• A call option is • A put is an
an option to buy
option to sell a
a certain asset
certain asset by
by a certain
a certain date
date for a
for a certain
certain price
price (the strike
(the strike
price)
price)
Types of Options
• A European option can be exercised only
at the end of its life
• An American option can be exercised at
any time before the contract expires
• There are many other types of options
– Parisian option: Many convertible bonds are
Parisian options
– Asian options: Average price as strike price
Specification of
Exchange-Traded Options
•
•
•
•
Expiration date
Strike price
European or American
Call or Put (option class)
Long Call on Microsoft
Profit from buying a European call option on Microsoft:
option price = $5, strike price = $60
30 Profit ($)
20
10
30
0
-5
40
50
Terminal
stock price ($)
60
70
80
90
Short Call on Microsoft
Profit from writing a European call option on Microsoft:
option price = $5, strike price = $60
Profit ($)
5
0
-10
-20
-30
70
30
40
50 60
80
90
Terminal
stock price ($)
Long Put on IBM
Profit from buying a European put option on IBM:
option price = $7, strike price = $90
30 Profit ($)
20
10
0
-7
Terminal
stock price ($)
60
70
80
90
100 110 120
Short Put on IBM
Profit from writing a European put option on IBM:
option price = $7, strike price = $90
Profit ($)
7
0
-10
-20
-30
60
70
Terminal
stock price ($)
80
90
100 110 120
Payoffs from Options
What is the Option Position in Each Case?
K = Strike price, ST = Price of asset at maturity
Payoff
Payoff
K
K
ST
Payoff
ST
Payoff
K
K
ST
ST
Observation
• The graph of the payoff structure of long
call is identical to energy of electrons in
photoelectric effect, a quantum effect.
• The mathematical method we will use to
find option prices is similar to methods in
quantum mechanics.
Terminology
Moneyness :
–At-the-money option
–In-the-money option
–Out-of-the-money option
Terminology
• Intrinsic value
– Value realized if exercised immediately
• Time value
– Value over level of intrinsic value
• Example
– Spot price: 53; strike price: 50; Call option
price: 5
– Intrinsic value: 53 – 50 = 3
– Time value: 5 – 3 = 2
Market Makers
• Most exchanges use market makers to
facilitate options trading
• A market maker quotes both bid and ask
prices when requested
• The market maker does not know whether
the individual requesting the quotes wants
to buy or sell
Warrants
• Warrants are options that are issued (or
written) by a corporation or a financial
institution
• The number of warrants outstanding is
determined by the size of the original
issue and changes only when they are
exercised or when they expire
Warrants
(continued)
• Warrants are traded in the same way as
stocks
• The issuer settles up with the holder when a
warrant is exercised
• When call warrants are issued by a
corporation on its own stock, exercise will
lead to new stocks being issued
Executive Stock Options
• Option issued by a company to executives
• The purpose
• When the option is exercised the company
issues more stock
• Usually at-the-money when issued
• They cannot be sold
• They often last for as long as 10 or 15
years
Executive Stock Options
continued
• What executives do when they are issued
options?
• Business Week, September 23, 2002 | Finance - Stock repurchases can enrich execs at
investors' expense
• Execs may forfeit investing in projects with long
term value so they have extra cash for
repurchasing stocks, or the cash reserve
becomes lower than it should be.
• Discussion: Is there a perfect substitute?
Employee options
• Startup or young companies often issue
employee options.
• If companies do well, early employees can
become very wealthy. It is an very effective way
to stimulate employees.
• Bill Gates attributed the rapid growth of Microsoft
in great part to its employee option program.
• Do employee options have similar effect for
large and mature companies?
Convertible Bonds
• Convertible bonds are regular bonds
that can be exchanged for equity at
certain times in the future according to
a predetermined exchange ratio
Convertible Bonds
(continued)
• Very often a convertible is callable
• The call provision is a way in which the
issuer can force conversion at a time
earlier than the holder might otherwise
choose
• Amazon
• Given that the value of an asset is affected
by many factors and represented by
relatively few financial instruments such as
stocks and bonds, the financial market is
far from complete. It is reasonable to
expect that some derivative securities are
created to better represent the values of
the underlying assets. The convertible
bond is an example.
• For young and small firms not rated by a rating agency, it
is difficult to issue straight bonds with low yield. At the
same time, they may not want to issue additional shares
at the current price level for this will dilute their
ownership. Usually, small firms are volatile, which is
often considered an unfavorable feature of a firm.
However, the design of the convertible bond turns this
feature into a positive one. The call options are highly
valued since volatility is high for small firms. Because of
the call option on the equity, convertible bonds pay lower
coupon than the straight bonds. Since the convertible
bonds properly “represent” the features of young and
small firms, they have become increasingly popular
among these firms, especially among high tech startups.
Price and volume of China Travel:
Why trading volume is so high on
some days?
160
6.5
6
5.5
Dollar
Number of shares
120
80
5
40
4.5
0
7/15/97
4
8/6/97
8/28/97
9/19/97
Volume
Price
Some background information
• Parisian option. The option can be exercised
only after the stock prices are over the strike
price for a period of time. This feature is
designed to prevent manipulation of share
prices.
• To force the conversion of the China Travel
convertible bond into common shares, the daily
closing price of China Travel stock had to stay
over 5.49 HK dollars, the call price, which was
150% of the conversion price, for more than
twenty of thirty consecutive trading days.
• On August 6, 1997, the share price of China Travel went
over the call price of HKD 5.49 for the first time. At that
time, share prices of China Travel were higher than its
CB prices, which is theoretically impossible. Figure
shows the unusually high trading volume around that
time, indicating strong market manipulation. However,
the financial markets around Asia turned very bearish
soon and China Travel managed to support its share
price over the call price for nineteen days before it
succumbed to the sharp fall of the general market.
• For all its effort, China Travel could not convert the bond
into equity.[1] The failure of conversion of China Travel
gave a clear sign of the trend reversal. [2]
• [1] According to the equity value of China Travel
at the end of 1998, it would have made over
sixty six million US dollar profit if the conversion
had been successful, comparing with the total
profit of seventeen million US dollar for the first
half of the 1998.
• [2] A trader confirmed that he spotted this signal
and used it in trading. Several traders in different
firms told me that borrowing shares of China
Travel at that time was very difficult, although
they didn’t understand why.
Homework 1
• A trader buys a call option with a strike
price of $45 and a put option with a strike
price of $40. Both options have the same
maturity. The call costs $3 and the put
costs $4. Draw a diagram showing the
variation of the trader’s profit with the
asset price.
Homework 2
• Two investors are bullish about gold. Each has one
hundred thousand dollars to invest. Current price of gold
is 1318 dollar per ounce. The first investor is a traditional
one. She used all her money to buy gold. The second
investor buys call options with the strike price at 1350
dollar per ounce. Suppose the option, which will mature
in six months, costs 66 dollars for per ounce of gold. If
gold price ends up at 1300 and1500 respectively after
six months. What is the final wealth of each investor?
What conclusion can you draw from the results? (For
simplicity, we assume one can buy a fractional number
of option contracts.)
Homework 3
• Explain why an American option is always
worth at least as much as a European
Option on the same asset with the same
strike price and exercise date.
• Explain why an American option is always
worth at least as much as its intrinsic
value.
Homework 4
• The asset values of companies A, B are both at 1000
million dollars. Each companies is purely financed with
equity, with100 million shares outstanding. The stock
prices of companies A, B are both at 10 dollars per
share. Both companies provide their CEOs with shares
or options as part of their packages. Company A
provides its CEO 1 million shares. Company B provides
its CEO call options on 10 million shares with strike price
at 10 dollars and a maturity of 5 years. After five years,
both companies’ asset value become 2000 million
dollars. Please calculate the share price of company A
and B, assuming share prices are accurate
representation of asset value.