Options

1
Options

• Prepared by
• Paul A. Spindt

2
A Call Option

• Gives its owner the right (not obligation)
• to buy an asset (the underlying)
• at a specified price (the exercise price)
• on (and perhaps before) a given date (the
  expiration date)

3
A Put Option

• Gives its owner the right (not obligation)
• to sell an asset (the underlying)
• at a specified price (the exercise price)
• on (and perhaps before) a given date (the
  expiration date)

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Options Lingo

• option premium
• intrinsic value time value
• European American
• long short
• covered naked

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Example

• Heres a quote from Wednesdays Wall Street
  Journal

-Call- -Put- SunMic 583/4
60 Jan 540 35/8 1105 37/8
Wednesdays closing stock price
Premium
Expiration date
Option strike price
Volume
6
Option Payoff Calls
Payoff
Stock Price (at Expiration)
0
Strike Price
7
Option Payoff Puts
Payoff
Stock Price (at Expiration)
0
Strike Price
8
Option Value

• Intrinsic value
• The intrinsic value of a call is max(0,S-X)
• The intrinsic value of a put is max(X-S,0)
• Time value
• Time value is the option premium minus intrinsic
  value

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The Value of a Call
Value
X
This call option has an intrinsic value of 3.75
and time value of 3.50
-Call- -Put- SunMic 583/4
55 Jan 166 71/4 109 2
10
The Value of a Call
Value
X
This call option has an intrinsic value of 0 and
time value of 3.625
-Call- -Put- SunMic 583/4
60 Jan 540 35/8 1105 37/8
11
The Value of a Put
Value
X
This put option has an intrinsic value of 1.25
and time value of 2.625.
When S is less than X, the intrinsic value of the
put is (X-S)
-Call- -Put- SunMic 583/4
60 Jan 540 35/8 1105 37/8
12
The Value of a Put
Value
X
This put option has an intrinsic value of 0 and
a time value of 2.00
When S is greater than X, the intrinsic value of
the put is 0
-Call- -Put- SunMic 583/4
55 Jan 166 71/4 109 2
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Put-Call Parity

• In an efficient market two investments with the
  same payoff ought to have the same price.

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Put-Call Parity

• This principle implies that
• the current stock price plus the price of a put

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Put-Call Parity

• should equal
• the price of a call plus the PV of the exercise
  price

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The Payoff on a Stock
Payoff
Terminal value of investment in stock
A stock is currently selling at 45. A call and
a put each with a strike price of 50 and an
expiration date 6 months from now are available.
Stock Price at Expiration
50
50
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The Payoff on a Put
Payoff
Terminal value of investment in stock (minus 50)
Terminal value of investment in put
Stock Price at Expiration
0
50
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The Payoff on a Stock and a Put
Payoff
Terminal value of investment in both stock and put
Stock Price at Expiration
50
50
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The Payoff on a Call
Payoff
Terminal value of investment in call
Stock Price at Expiration
0
50
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The Payoff on a Bond
Payoff
Terminal value of investment in call (plus 50)
Stock Price at Expiration
50
50
Terminal value of investment in bond
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The Payoff on a Call and a Bond
Payoff
Terminal value of investment in call and bond
Stock Price at Expiration
50
50
Terminal value of investment in bond
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For Example

• Heres a put and a call on SunMic. Each has a
  strike price of 60. The current stock price is
  58.75, so the call is out of the money and the
  put is in the money. Both expire in one month.

-Call- -Put- SunMic 583/4
60 Jan 540 35/8 1105 37/8
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For Example

• Put-call parity implies that

-Call- -Put- SunMic 583/4
60 Jan 540 35/8 1105 37/8
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Determinants of Option Value

• The price of the underlying asset
• The value of a call rises (the value of a put
  falls) as the price of the underlying asset
  rises, all other things equal.
• The amount an options premium changes when the
  price of the underlying asset changes is called
  the options delta.

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Determinants of Option Value

• The strike price
• The value of a call falls (the value of a put
  rises) as the strike price rises, all other
  things equal.

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Determinants of Option Value

• Time to expiration
• The value of both puts and calls rises as the
  time to expiration increases, all other things
  equal.
• The amount an options premium changes when its
  time to maturity changes is called the options
  theta.

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Determinants of Option Value

• Volatility
• The volatility of the underlying asset is a
  measure of how uncertain we are about future
  changes in an assets value.
• The more volatility increases, other things
  equal, the greater the chance that an option will
  do very well.
• The value of both puts and calls rises as the
  volatility of the underlying asset increases.

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Determinants of Option Value

• The risk-free rate of interest
• The value of a call rises (the value of a put
  falls) when the risk-free interest rate rises.

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The Black-Scholes Formula

• The Black-Scholes pricing formula for a plain
  vanilla call option when the stock price is S,
  the strike price is X, the risk-free rate is r
  per annum and the time to expiration is t years
  is

N() is the cumulative standard normal
distribution evaluated at , and
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The Black-Scholes Formula

• d1 and d2 are functions of the stock price, the
  strike price, the interest rate, time and
  volatility

compare
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Normal Distribution
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Example
TelMex Jul 45 143 CB 23/8 -5/16 47 2,703
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Assignment

• Option Price Calculator
• Itos Dilemma (A)
• Itos Dilemma (B)