Chapter 18
Options Basics
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© 2007 Thomson South-Western
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 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.
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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.
Options trade on an exchange (such as CBOE) or in the
over-the-counter market.
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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.
Option Price
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
General
Expires Strike
Electric
7
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
Intrinsic
value
Time value
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• 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
• The difference between the option’s
intrinsic value and its market price
(premium)
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
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Short Call Option Payoffs
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Long Put Option Payoffs
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Short Put Option Payoffs
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Naked Option Positions
Naked call option position - occurs
when an investor buys or sells an
option on a stock without already
owning the underlying stock
Naked put option positions – occurs
when a trader buys or sells a put option
without owning the underlying stock
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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.
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Straddle Positions
Long straddle - a portfolio consisting of
long positions in calls and puts on the
same stock with the same strike price
and expiration date
Short straddle - a portfolio consisting of
short positions in calls and puts on the
same stock with the same strike price
and expiration date
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Long Straddle
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Short Straddle
+9
51
69
60
Net payoff
Gross payoff
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Call x = 60, premium = $5, Put x = 60, premium = $4
Payoff Diagrams for Stocks and
Bonds
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Covered Call Strategy
Writing covered calls –common trading
strategy that mixes stock and call
options
 An investor who owns a share of stock
sells a call option on that stock.
 The investor receives the option premium
immediately.
 The trade-off is that if the stock price rises
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 the holder of the call option will exercise the
right to purchase it at the strike price
the investor will lose the opportunity to benefit
from the appreciation in the stock.
Payoff Diagram for Covered Call
Strategy
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Payoff of a Put Option and a Share
of Stock – a Protective Put
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Payoff of a Call Option and a ZeroCoupon Bond
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Put-Call Parity
Following conditions must be met:
1. The call and put options must be on the same
underlying stock.
2. The call and put options must have the same
exercise price.
3. The call and put options must share the same
expiration date.
4. The underlying stock must not pay a dividend
during the life of the options.
5. The call and put options must be European
options.
6. The bond must be a risk-free, zero-coupon bond
with a face value equal to the strike price of the
options and with a maturity date identical to the
options’ expiration date.
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Synthetic Put Option
Traders can create a synthetic put
option by purchasing a bond and a call
option while simultaneously shortselling the stock.
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Put-Call
Parity
Arbitrage
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Using Put-Call Parity to Create
Synthetic Positions
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Factors Affecting Option Values
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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
Factors Affecting Option Values
Holding other factors constant, call and put
option prices increase as the time to
expiration increases.
Call prices decrease and put prices increase
when the difference between the underlying
stock price and the exercise price (S − X)
decreases.
Call and put option prices increase as the
volatility of the underlying stock increases.
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Calculating Option Prices
The binomial options model recognizes
that investors can combine options
(either calls or puts) with shares of the
underlying asset to construct a portfolio
with a risk-free payoff.
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Binomial Option Pricing
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Binomial Option Pricing
Data needed:
The current price of the underlying stock
The amount of time remaining before the
option expires
The strike price of the option
The risk-free rate
The possible values of the underlying stock
in the future
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Multistage Binomial Trees
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Multistage Binomial Trees
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Risk-Neutral Method
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If a combination of stock and options is riskfree, it must sell for the same price as a riskfree bond.
If an asset promises a risk-free payoff, riskaverse and risk-neutral investors agree on
how it should be valued.
Whether investors are risk averse or risk
neutral, the binomial model’s calculations are
the same.
We can assume investors are risk neutral,
which gives us a new way to value options.