Transcript The Basics of Options

Basics of Stock Options
Timothy R. Mayes, Ph.D.
FIN 3600: Chapter 15
Introduction
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Options are very old instruments, going back, perhaps, to the time of
Thales the Milesian (c. 624 BC to c. 547 BC).
Thales, according to Aristotle, purchased call options on the entire
autumn olive harvest (or the use of the olive presses) and made a
fortune.
Joseph de la Vega (in “Confusión de Confusiones,” 1688, 104 years
before the NYSE was founded under the buttonwood tree) also
wrote about how options were dominating trading on the Amsterdam
stock exchange.
Dubofsky reports that options existed in ancient Greece and Rome,
and that options were used during the tulipmania in Holland from
1624-1636.
In the U.S., options were traded as early as the 1800’s and were
available only as customized OTC products until the CBOE opened
on April 26, 1973.
What is an Option?
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A call option is a financial instrument that gives the buyer the right,
but not the obligation, to purchase the underlying asset at a prespecified price on or before a specified date
A put option is a financial instrument that gives the buyer the right,
but not the obligation, to sell the underlying asset at a pre-specified
price on or before a specified date
A call option is like a rain check. Suppose you spot an ad in the
newspaper for an item you really want. By the time you get to the
store, the item is sold out. However, the manager offers you a rain
check to buy the product at the sale price when it is back in stock.
You now hold a call option on the product with the strike price equal
to the sale price and an intrinsic value equal to the difference
between the regular and sale prices. Note that you do not have to
use the rain check. You do so only at your own option. In fact, if the
price of the product is lowered further before you return, you would
let the rain check expire and buy the item at the lower price.
Options are Contracts
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The option contract specifies:
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The underlying instrument
The quantity to be delivered
The price at which delivery occurs
The date that the contract expires
Three parties to each contract
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The Buyer
The Writer (seller)
The Clearinghouse
The Option Buyer
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The purchaser of an option contract is buying the right to
exercise the option against the seller. The timing of the
exercise privilege depends on the type of option:
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American-style options can be exercised any time before
expiration
European-style options may only be exercised during a short
window before expiration
Purchasing this right conveys no obligations, the buyer
can let the option expire if they so desire.
The price paid for this right is the option premium. Note
that the worst that can happen to an option buyer is that
she loses 100% of the premium.
The Option Writer
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The writer of an option contract is accepting the obligation to have
the option exercised against her, and receiving the premium in
return.
If the option is exercised, the writer must:
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If it is a call, sell the stock to the option buyer at the exercise price
(which will be lower than the market price of the stock).
If it is a put, buy the stock from the put buyer at the exercise price
(which will be higher than the market price of the stock).
Note that the option writer can potentially lose far more than the
option premium received. In some cases the potential loss is
(theoretically) unlimited.
Writing and option contract is not the same thing as selling an
option. Selling implies the liquidation of a long position, whereas
the writer is a party to the contract.
The Role of the Clearinghouse
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The clearinghouse (the Options Clearing Corporation)
exists to minimize counter-party risk.
The clearinghouse is a buyer to each seller, and a seller to
each buyer.
Because the clearinghouse is well diversified and
capitalized, the other parties to the contract do not have
to worry about default. Additionally, since it takes the
opposite side of every transaction, it has no net risk
(other than the small risk of default on a trade).
Also handles assignment of exercise notices.
Examples of Options
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Direct options are traded on:
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There are options embedded in:
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Stocks, bonds, futures, currencies, etc.
Convertible bonds
Mortgages
Insurance contracts
Most corporate capital budgeting projects
etc.
Even stocks are options!
Option Terminology
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Strike (Exercise) Price - this is the price at which the underlying security can be
bought or sold.
Premium - the price which is paid for the option. For equity options this is the price
per share. The total cost is the premium times the number of shares (usually 100).
Expiration Date – This is the date by which the option must be exercised. For stock
options, this is usually the Saturday following the third Friday of the month. In
practice, this means the third Friday.
Moneyness – This describes whether the option currently has an intrinsic value above
0 or not:
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In-the-Money –
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Out-of-the-Money –
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for a call this is when the stock price exceeds the strike price,
for a put this is when the stock price is below the strike price.
for a call this is when the stock price is below the strike price,
for a put this is when the stock price exceeds the strike price.
American-style - options which can be exercised before expiration.
European-style - options which cannot be exercised before expiration.
The Intrinsic Value of Options
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The intrinsic value of an option is the profit (not net profit!) that
would be received if the option were exercised immediately:
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For call options:
For put options:
IV = max(0, S - X)
IV = max(0, X - S)
At expiration, the value of an option is its intrinsic value.
Before expiration, the market value of an option is the sum of the
intrinsic value and the time value.
Since options can always be sold (not necessarily exercised) before
expiration, it is almost never optimal to exercise them early. If you
did so, you would lose the time value. You’d be better off to sell the
option, collect the premium, and then take your position in the
underlying security.
Profit
Profits from Buying a Call
4000
3500
3000
2500
2000
1500
1000
500
0
-500
-1000
S = 50
X = 50
r = 5%
t = 90 days
s = 30%
Call Price = 3.27
0
20
40
60
Stock Price at Expiration
80
100
Profit
Selling a Call
1000
500
0
-500
-1000
-1500
-2000
-2500
-3000
-3500
-4000
S = 50
X = 50
r = 5%
t = 90 days
s = 30%
Call Price = 3.27
0
20
40
60
Stock Price at Expiration
80
100
Profits from Buying a Put
4000
S = 50
X = 50
r = 5%
t = 90 days
s = 30%
Put Price = 2.65
Profit
3500
3000
2500
2000
1500
1000
500
0
-500
0
20
40
60
Stock Price at Expiration
80
100
Selling a Put
500
Profit
0
-500
-1000
-1500
S = 50
X = 50
r = 5%
t = 90 days
s = 30%
Put Price = 2.65
-2000
-2500
-3000
-3500
-4000
0
20
40
60
Stock Price at Expiration
80
100
Combination Strategies
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We can construct strategies consisting of
multiple options to achieve results that aren’t
otherwise possible, and to create cash flows that
mimic other securities
Some examples:
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Buy Write
Straddle
Synthetic Securities
The Buy-Write Strategy
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This strategy is more
conservative than
simply owning the
stock
It can be used to
generate extra
income from stock
investments
In this strategy we
buy the stock and
write a call
5000
S = 50 X = 50
r = 5% t = 90 days
s = 30%
Call Price = 3.27
4000
3000
2000
1000
Profit
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0
-1000
-2000
-3000
-4000
-5000
0
20
40
60
80
Stock Price at Expiration
Stock Profit
Call Profit
Strategy Profit
100
The Straddle
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If we buy a straddle, we
profit if the stock moves
a lot in either direction
If we sell a straddle, we
profit if the stock
doesn’t move much in
either direction
This straddle consists of
buying (or selling) both
a put and call at the
money
4000
S = 50 X = 50
r = 5% t = 90 days
s = 30%
Call Price = 3.27
Put Price = 2.65
3500
3000
2500
Profit
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2000
1500
1000
500
0
-500
-1000
0
20
40
60
80
Stock Price at Expiration
Put Profit
Call Profit
Strategy Profit
100
Synthetic Securities
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With appropriate combinations of the stock and options,
we can create a set of cash flows that are identical to
puts, calls, or the stock
We can create synthetic:
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Long Stock — Buy Call, Sell Put
Long Call — Buy Put, Buy Stock
Long Put — Buy Call, Sell Stock
Short Stock — Sell Call, Buy Put
Short Call — Sell Put, Sell Stock
Short Put — Sell Call, Buy Stock
The reasons that this works requires knowledge of PutCall Parity
Put-Call Parity
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Put-Call parity defines the relationship between put
prices and call prices that must exist to avoid possible
arbitrage profits:
P  C  S  Xe
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 rt
In other words, a put must sell for the same price as a
long call, short stock and lending the present value of the
strike price (why?).
By manipulating this equation, we can see how to create
synthetic securities (in the above form it shows how to
create a synthetic put option).
Put-Call Parity Example
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Assume that we find the following conditions:
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S = 100
r = 10%
C = 16.73
Action
Buy Call
Sell Stock
Buy Bond
Total
X = 100
t = 1 year
P=?
Cash Inflow
-16.73
100.00
-90.48
-7.21
Cash Flows At Expiration if
Stock Price Is:
110
100
90
10.00
0.00
0.00
-110.00 -100.00
-90.00
100.00
100.00
100.00
0.00
0.00
10.00
Synthetic Long Stock Position
We can create a
synthetic long
position in the
stock by buying a
call, selling a put,
and lending the
strike price at the
risk-free rate until
expiration
S  C  P  Xe
5000
S = 50 X = 50
r = 5% t = 90 days
s = 30%
Call Price = 3.27
Put Price = 2.65
4000
3000
2000
1000
Profit
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 rt
0
-1000
-2000
-3000
-4000
-5000
0
20
40
60
80
100
Stock Price at Expiration
Put Profit
Call Profit
Lend at Risk-free
Strategy Profit
Synthetic Long Call Position
We can create a
synthetic long
position in a call
by buying a put,
buying the
stock, and
borrowing the
strike price at
the risk-free rate
until expiration
5000
4000
3000
2000
1000
Profit
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C  P  S  Xe
 rt
0
-1000
-2000
S = 50 X = 50
r = 5% t = 90 days
s = 30%
Call Price = 3.27
Put Price = 2.65
-3000
-4000
-5000
0
20
40
60
80
100
Stock Price at Expiration
Put Profit
Stock Profit
Borrow at Risk-free
Strategy Profit
Synthetic Long Put Position
P  C  S  Xe
We can create a
synthetic long
position in a put
by buying a call,
selling the stock,
and lending the
strike price at the
risk-free rate
until expiration
5000
4000
3000
2000
1000
Profit
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 rt
0
-1000
-2000
S = 50 X = 50
r = 5% t = 90 days
s = 30%
Call Price = 3.27
Put Price = 2.65
-3000
-4000
-5000
0
20
40
60
80
100
Stock Price at Expiration
Stock Profit
Call Profit
Lend at Risk-free
Strategy Profit
Synthetic Short Stock Position
S  P  C  Xe  rt
We can create
a synthetic
short position
in the stock
by selling a
call, buying a
put, and
borrowing the
strike price at
the risk-free
rate until
expiration
5000
S = 50 X = 50
r = 5% t = 90 days
s = 30%
Call Price = 3.27
Put Price = 2.65
4000
3000
2000
1000
Profit
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0
-1000
-2000
-3000
-4000
-5000
0
20
40
60
80
100
Stock Price at Expiration
Put Profit
Call Profit
Borrow at Risk-free
Strategy Profit
Synthetic Short Call Position
 C   P  S  Xe
We can create a
synthetic short
position in a call
by selling a put,
selling the stock,
and lending the
strike price at the
risk-free rate
until expiration
5000
S = 50 X = 50
r = 5% t = 90 days
s = 30%
Call Price = 3.27
Put Price = 2.65
4000
3000
2000
1000
Profit
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 rt
0
-1000
-2000
-3000
-4000
-5000
0
20
40
60
80
100
Stock Price at Expiration
Put Profit
Stock Profit
Lend at Risk-free
Strategy Profit
Synthetic Short Put Position
 P  S  C  Xe
We can create a
synthetic short
position in a put
by selling a call,
buying the
stock, and
borrowing the
strike price at
the risk-free
rate until
expiration
5000
S = 50 X = 50
r = 5% t = 90 days
s = 30%
Call Price = 3.27
Put Price = 2.65
4000
3000
2000
1000
Profit
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 rt
0
-1000
-2000
-3000
-4000
-5000
0
20
40
60
80
100
Stock Price at Expiration
Stock Profit
Call Profit
Borrow at Risk-free
Strategy Profit
Option Valuation
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The value of an option is the present value of its
intrinsic value at expiration. Unfortunately, there
is no way to know this intrinsic value in advance.
The most famous (and first successful) option
pricing model, the Black-Scholes OPM, was
derived by eliminating all possibilities of
arbitrage.
Note that the Black-Scholes models work only
for European-style options.
Option Valuation Variables
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There are five variables in the Black-Scholes
OPM (in order of importance):
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Price of underlying security
Strike price
Annual volatility (standard deviation)
Time to expiration
Risk-free interest rate
Variables’ Affect on Option Prices
Variable
–
–
–
–
–
Stock Price
Strike Price
Volatility
Interest Rate
Time
Call Options
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Direct
Inverse
Direct
Direct
Direct
Put Options
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Inverse
Direct
Direct
Inverse
Direct
Option Valuation Variables: Underlying Price
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The current price of the underlying security is
the most important variable.
For a call option, the higher the price of the
underlying security, the higher the value of the
call.
For a put option, the lower the price of the
underlying security, the higher the value of the
put.
Option Valuation Variables: Strike Price
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The strike (exercise) price is fixed for the life of
the option, but every underlying security has
several strikes for each expiration month
For a call, the higher the strike price, the lower
the value of the call.
For a put, the higher the strike price, the higher
the value of the put.
Option Valuation Variables: Volatility
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Volatility is measured as the annualized standard
deviation of the returns on the underlying
security.
All options increase in value as volatility
increases.
This is due to the fact that options with higher
volatility have a greater chance of expiring inthe-money.
Option Valuation Variables: Time to Expiration
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The time to expiration is measured as the
fraction of a year.
As with volatility, longer times to expiration
increase the value of all options.
This is because there is a greater chance that the
option will expire in-the-money with a longer
time to expiration.
Option Valuation Variables: Risk-free Rate
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The risk-free rate of interest is the least important of the
variables.
It is used to discount the strike price, but because the
time to expiration is usually less than 9 months (with the
exception of LEAPs), and interest rates are usually fairly
low, the discount is small and has only a tiny effect on
the value of the option.
The risk-free rate, when it increases, effectively
decreases the strike price. Therefore, when interest rates
rise, call options increase in value and put options
decrease in value.
Note
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The following few slides on the Black-Scholes
model will not be tested. I consider the use of
these models to be beyond the scope of this
course.
I am including this information only for those
interested.
The Black-Scholes Call Valuation Model
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At the top (right) is the
Black-Scholes valuation
model for calls. Below
are the definitions of d1
and d2.
Note that S is the stock
price, X is the strike
price, s is the standard
deviation, t is the time to
expiration, and r is the
risk-free rate.
C  S N d 1   Xe rt N d 2 
 S
ln   rt  0.5s 2 t
 X
d1 
s t

d 2  d1  s
t

B-S Call Valuation Example
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Assume a call with the following variables:
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S = 100
X = 100
r = 0.05
s = 0.10
t = 90 days = 0.25 years
C  100 * N0.275  100 * e
d1 
 100 
ln
  0.05 * 0.25  0.5 * 0.01 * 0.25
 100 
01
. * 0.25
d 2  0.275  01
. * 0.25  0.225
 0.05*0.25
 0.275
N0.225  2.66
The Black-Scholes Put Valuation Model
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At right is the BlackScholes put valuation
model.
The variables are all the
same as with the call
valuation model.
Note: N(-d1) = 1 - N(d1)
P  Xe  rt N  d 2   S N  d 1 
d1 
 S
ln   rt  0.5s 2 t
 X

s t
d 2  d1  s t

B-S Put Valuation Example
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Assume a put with the following variables:
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S = 100
X = 100
r = 0.05
s = 0.10
t = 90 days = 0.25 years
P  100 * e
d1 
 0.05*0.25
N 0.225  100 * N 0.275  142
.
 100 
ln
  0.05 * 0.25  0.5 * 0.01 * 0.25
 100 
01
. * 0.25
d 2  0.275  01
. * 0.25  0.225
 0.275