Option Basics
Professor XXXXX
Course Name / Number
Economic Benefits Provided by
Options
Derivative securities are instruments that derive
their value from the value of other assets.
Derivatives include options, futures, and swaps.
Options and other derivative securities have several important
economic functions:
– Help bring about more efficient allocation of risk
– Save transactions costs…sometimes it is cheaper to trade a derivative than
its underlying asset.
– Permit investments strategies that would not otherwise be possible
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Options Vocabulary
Long position
• The buyer of an option has a long
position, and has the ability to exercise
the option.
Short position
• The seller (or writer) of an option has a
short position, and must fulfill the contract
if the buyer exercises.
• As compensation, the seller receives the
option premium.
Generally, neither trader has any connection to the
underlying firm.
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Options trade on an exchange (such as CBOE) or in the
over-the-counter market.
Options Vocabulary
Call option
• Gives the holder the right to purchase an
asset at a specified price on or before a
certain date
Put option
• Gives the holder the right to sell as asset
at a specified price on or before a certain
date
Strike price or exercise price: the price specified for
purchase or sale in an option contract
American or
European
option
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• American options allow holders to
exercise at any point prior to expiration.
• European options allow holders to
exercise only on the expiration date.
Moneyness of Options
S = current stock price
X = strike price
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Call
Put
S>X
In-the-money
Out-of-the-money
S=X
At-the-money
At-the-money
S<X
Out-of-the-money
In-the-money
Option Quotations
• Option quotations specify the per share price for an option contract,
which is a contract to buy or sell 100 shares of the underlying stock.
– CBOE options expire on the third Saturday of the expiration
month.
General
Expires Strike
Electric
6
Call
Put
46.31 March
45
4.00
2.38
46.31 June
45
5.88
3.88
46.31 March
50
1.50
5.25
46.31 June
50
3.50
6.50
In-the-money calls
Out-of-the-money puts
In-the-money puts
Out-of-the-money calls
Intrinsic and Time Value of Options
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Intrinsic
value
• For in the money options: the difference
between the current price of the underlying
asset and the strike price
• For out of the money options: the intrinsic
value is zero
Time value
• The difference between the option’s intrinsic
value and its market price (premium)
• Consider the March call with $45 strike price from previous
table:
– Intrinsic value = $46.31 - $45 = $1.31
– Time value considers the size of the option’s premium:
$4 - $1.31 = $2.69.
Payoff Diagrams
Show the value of an option, or the value at
expiration
Y-axis plots exercise value or “intrinsic value.”
X-axis plots price of underlying asset.
Long and short positions
Use payoff
diagrams for:
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Gross and net positions (the net
positions subtract the option premium)
Payoff: the price of the option at expiration date
Long Call Option Payoffs
Payoff at Expiration
x = $50, premium = $5
Gross payoff
slope = 1
-5
50
Net payoff
9
55
stock price
Short Call Option Payoffs
x = $50, premium = $5
Payoff at expiration
+5
10
50
Gross payoff
55
stock price
Net payoff
slope = -1
• Both long and short positions have zero net payoff at a price of $55.
– At a price of $45, the buyer loses $5, the seller gains $5.
– At a price of $65, the buyer gains $10, the seller loses $10.
Long Put Option Payoffs
x = 50, premium = $4
50
Payoff at expiration
46
11
Gross payoff
Price of stock
-4
46 50
Net payoff
Short Put Option Payoffs
Payoff at expiration
x = 50, premium = $4
12
Net payoff
4
46
50
Gross payoff
-50
Stock price
Portfolios of Options
Look at payoff diagrams for combinations of options rather
than just one.
Diagrams show the range of potential strategies made
possible by options.
Some positions, in combination with other positions, can be
a form of portfolio insurance.
An example: a portfolio that allows an investor to speculate
on the volatility (or lack thereof) of a stock rather than
betting on which direction it will move
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Long Straddle
Call x = 60, premium = $5, Put x = 60, premium = $4
Gross payoff
Net payoff
60
51
14
69
-9
• Buy a put and a call of the same stock at the same strike price and
the same expiration date.
– Profits come with large price changes in either direction, so a
straddle represents a volatility position.
– Positive net payoff results if the price rises above $69 or falls
below $51.
Short Straddle
Call x = 60, premium = $5, Put x = 60, premium = $4
+9
51
69
60
Net payoff
Gross payoff
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• Sell a put and a call of the same stock at the same strike price and
the same expiration date.
– Provides opposite payoffs of the long straddle.
– Profits result if the stock price stays between $51 and $69.
Other Option Portfolio Payoffs
Now look at portfolios containing options, stocks,
and bonds.
Looking at these payoffs will help lead us to an important
option pricing relationship: put-call parity.
Construct portfolios that include options, stocks and bonds.
Stock and put options
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Bond and call options
Payoff at expiration
Gross Payoff of Stock + Put
$X = strike price of put
x
x
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Stock price
• This position allows an investor to profit if stock price rises above $X.
• If stock price falls below $X the portfolio provides protection in that
the put option allows the investor to sell at a price no lower than $X.
Payoff at expiration
Gross Payoff of Bond + Call
$X = strike price of call
and face value of bond
x
x
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stock price
• The bond assures a minimum payoff of $X
Thisallows
payoff
the one
identical!
• The call
fordiagram
a higherand
payoff
if thebefore
stock are
price
rises
Put-Call Parity
Future payoffs of “stock+put” are identical to payoffs of
“bond+call” provided.
–
–
–
–
–
Put and call have same exercise price and expiration date.
The underlying stock pays no dividends during the life of the options.
Put and call are European options.
Bond is risk-free, zero-coupon, FV = strike (X).
Bond matures when options expire.
If two assets, A and B, have the same future payoffs with
certainty, then they should sell for the same price now.
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Price of put + price of stock = Price of call + price of bond
P+S=C+B
P + S = C + PV(X)
Using Put-Call Parity
Put-call parity relationship can be used in:
– Finding arbitrage opportunities
– Corporate finance applications
Using put-call parity,
we can construct
synthetic positions
•
•
•
•
Long put: P = C + PV(X) – S
Long stock: S = C + PV(X) – P
Short stock: -S = - C - PV(X) + P
Long call: C = S + P – PV(X)
In these equations “+” means “buy” and “-” means “sell” or
“short sell.”
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For example, the first line shows that buying a put is equivalent to
simultaneously buying a call and a bond and shorting the stock.
Put-Call Parity and Arbitrage
Assumptions
• Stock price = $46; call price (X = $45) $5.
• Options expire in 3 months.
• Risk-free rate for 3-month T-bill is 5%.
P+
=C
++
B ($45/(1.05).25)
P +S$46
= $5
P = $3.45
What if the 3-month put option with X = $45 actually sells for $4 rather
than $3.45?
The put is overpriced, so you want to sell it.
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To offset the risk you must buy a synthetic put:
P = B + C – S.
Put-Call Parity Arbitrage
Sell a put for $4, buy a bond for $44.45, buy a call for $5,
and short the stock for $46.
If stock
price is
Short put
Long bond
Long call
Short
Stock
Net value
is
35
-10
45
0
-35
0
40
-5
45
0
-40
0
45
0
45
0
-45
0
50
0
45
5
-50
0
55
0
45
10
-55
0
Risk-free profit of $0.55 because we sold one real put and bought one
“synthetic put” with identical risk.
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Put-Call Parity Corporate Finance
Applications
P-C parity offers alternative ways to get something done
financially if the most obvious approach is blocked.
• An example…
• Netscape went public at $26/share, but price immediately rose into
the mid $50s.
– In pre-IPO phase, Times-Mirror bought 2 million shares of
Netscape at $2 per share.
– In exchange for the good price, TM agreed not to sell their
Netscape shares for two years.
What problem does TM face once Netscape has gone public?
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Times-Mirror and Netscape
TM would like to sell their NSCP shares but they
can’t…or can they?
1. Issued bond with face value equal to one Netscape share.
2. TM held the option to pay back investors one Netscape
share when the bonds matured (a put option).
3. Investors held the option to demand one Netscape share
from TM in exchange for par value (a call option).
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d. Net transaction: -B – P + C….but this just equals –S, a synthetic sale
of stock !
Factors Affecting Option Prices
(holding other factors equal)
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Price of
underlying
asset
• Asset price and call price are positively
related.
• Asset price and put price are negatively
related.
Time to
expiration
• More time usually makes options more
valuable.
Strike price
• Higher X means higher put price; lower X
means higher call price.
Interest
rate
• Calls: higher “r” means higher call value
• Puts: higher “r” reduces put value
Volatility and Option Prices
Suppose a stock now worth $40 might increase or decrease
in value by $10.
Call option with X = $40 will pay $10 or $0
Now suppose a stock worth $40 might increase or decrease
in value by $20.
Call option with X = $40 will pay $20 or $0
The 2nd call option is more valuable…upside is better, downside the
same as the 1st option.
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Binomial Option Pricing
An extremely flexible tool for valuing all types of options, real
and financial
– Presumes stock price moves either up or down in discrete steps
over a given time interval
– Derives an option price using the principle of “no arbitrage”
a. Find a hedged portfolio
Portfolio of stock and call options that gives a constant payoff in the
future regardless of whether the stock goes up or down
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Mixture of stock and options in this portfolio is called hedge
ratio.
Calculating Binomial Option
Prices
b. If the hedged portfolio offers risk-free payoff, determine
the portfolio’s current value by discounting future payoff at
the risk-free rate.
c. Once we know the value of the portfolio, can separate this
value into its component pieces.
• The value of the stock and the value of the option
Three step
procedure
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• Step 1: Create a risk-free portfolio.
• Step 2: Calculate the present value of the
portfolio.
• Step 3: Determine the price of the option.
An Example
Stock price
now
Price in one year
$60
$50
$40
Assume: rf = 5%
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Determine price of 1-year call option with x = $50.
Step 1
Calculate option’s payoffs for each possible future stock
price.
– - If stock goes to $60, option pays off $10.
– If stock goes to $40, option pays off $0.
Determine the composition of the hedged portfolio…start by
assuming it contains one share of stock and “h” call options.
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• Portfolio value = 1 share + h options
• If stock goes up, portfolio will pay:
• $60 + $10 x h.
• If stock goes down, portfolio will pay:
• $40 + $0 x h.
Step 1
To determine the composition of the hedged portfolio, find
the number of options that equates the payoffs:
• $60 + $10h = $40 + $0h
h = -2
Hedged portfolio is long one share of stock and short two call options.
Determine the exact dollar payoff of the hedged portfolio:
• $60 + $10h = $40 + $0h
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Payoff = $40
Thus, one stock plus two short call options replicates the payoffs of
a one-year, risk-free bond with a face value of $40.
Steps 2 and 3
Determine present value of hedged portfolio:
• Payoff = $40
• rf = 5%
PV = $40/1.05 = $38.10
Separate the current value of the portfolio into its component
parts:
• $50 of this value is the current price of the stock.
• The difference between $38.10 and $50 is the revenue received
for the two call options sold.
• $50 – 2 x call price = $38.10
Call price = $5.95
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A More Reasonable Approach
60
57.50
55
50
52.50
55
52.50
50
47.50
50
47.50
45
45
42.50
40
3 months 3 months 3 months 3 months
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4 periods,
3 months each
Option Basics
Options: contracts that grant the buyer the right to
buy or sell stock at a fixed price.
Options provide real economic benefit to society.
Put-call parity establishes a link between market
prices of calls, puts, shares, and bonds.
Factors that affect option prices: underlying price,
time to maturity, strike price, interest rate and
volatility.