Fin4328 (Moore)
Basic Option Pricing and Characteristics
Summer 2006
BASIC PROPERTIES OF OPTIONS
Learning Goals:
 Learn Basic Option Terminology
 Develop Understanding of Basic Comparative Statics for Option Pricing
Model
 Develop Skills for Option Payoff Tables (No Arbitrage Pricing)
 Understand and Develop Put-Call Parity
Four Basic Option Positions and Basic Pricing
Call Option
Buy
 You decide whether
option is exercised
 Exercise occurs if
ST > X
 If Option Exercised,
you
- Pay $X
- Acquire the
Asset
Profit = S T - X
Put Option
Write
 Counter-Party decides
whether option
exercised
 Exercise occurs if
ST > X
 If Option Exercised,
you
- Receive $X
- Deliver the Asset
Loss = -(S T - X)
 You decide whether
option is exercised
 Exercise occurs if
ST < X
 If Option Exercised,
you
- Receive $X
- Deliver the
Asset
 Counter-Party decides
whether option
exercised
 Exercise occurs if
ST < X
 If Option Exercised,
you
- Pay $X
- Acquire the
Asset
Profit = X - S T
Loss = -(X - S T)
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Fin4328 (Moore)
Basic Option Pricing and Characteristics
Summer 2006
1. Terminology
A. Definition
 A call (put) option is a contract that gives the holder the right but not the obligation to
buy (sell) a fixed quantity of an underlying asset at a fixed price and at any time on or
before a given date

 The call writer agrees and has an obligation to sell the underlying asset at a fixed price
to the call buyer.

 The put writer agrees and has an obligation to buy the underlying asset at a fixed price
from the put buyer.
B. Types of Options

 American options: options that can be exercised at any time up to and including the
expiration date.

 European options: options that can only be exercised at the expiration date itself
C. Specification of an Option(Notation)
Underlying asset (S): The security based upon which the option contract is written. Its
underlying asset price is denoted as S.
Quantity:
The number of shares of the underlying asset involved in one contract of the
option. Usually one board lot of the underlying stock.
Exercise (or strike) price (X):
be bought (sold).
The predetermined price at which the underlying asset can
Expiration (or maturity) date (T): The date on which the option expires, or the last date on
which it can be exercised.
Option premium (C for call and P for put): The price that the buyer needs to pay in order
to acquire the right. It is determined by the supply and demand of the option. (what we try
to value)
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Fin4328 (Moore)
Basic Option Pricing and Characteristics
Summer 2006
2. Exercise Decision At Expiration Date
A. Moneyness
When
S  X
The call is
In-the-Money
The put is
Out-of-the-Money
S
At-the-Money
At-the-Money
Out-of-the-Money
In-the-Money
= X
S  X
B. Decision Rules at Time T
For Call Option
For Put Option
• Exercise
if ST  X
if ST  X
• Not Exercise
if ST
 X
if ST
 X
C. Option Value at Time T (Expiration)
Define:
CT
  the value of a call (per share) on its expiration date
PT
 
the value of a put (per share) on its expiration date
Decision Rules (B) imply:
CT
  Max [ 0, ST X ]
PT
 
Max [ 0, X ST ]
3 Call Option Value
Assume the underlying stock does not pay dividends.

Value of the call (before expiration date) consists of two components:
1. Intrinsic Value (IV) = Max[0, S X] (the parity value)
2. Time Premium (TP) = Insurance value + Interest saving from deferred payment
of the strike price.

 Since the time premium is always positive, and value of the call is always higher
than the intrinsic value.
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Fin4328 (Moore)
Basic Option Pricing and Characteristics
Summer 2006
A. Boundary for call option value:
 Upper bound:
C S
Call option gives the holder the right to buy the stock at the (nonnegative) strike price.
Therefore, the option can never be worth more the stock.
 Lower Bound: C Max [0, S – X e -rT ] where r is the annual interest rate, and T
is the time to maturity (in year)
The call option gives you the right to buy the stock at the strike price on the expiration
date. The right to buy has insurance value.
Example 1.
What if C < Max [0, S – X e -rT ] ?
 Assume the following:
The stock price is $25. A call option on the stock with exercise price $20 and 3
months to maturity is selling at $5. The riskless rate of interest is 10% per year.
could arbitrage by buying a call, short selling a stock, and lending $20  e – 0.10  0.25 ,
and close out position on the expiration date.
____________Cash flows____________________
Time 0
Time T
ST < 20
ST > 20
ST - 20
Buy a call
-5
0
Short sell a stock
25
-ST
Lend X e – rT
-20 e – 0.10  0.25
-ST
20
20
_________________________________________
20(1 - e – 0.10  0.25)
20 - ST
> 0
> 0
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0
0
Fin4328 (Moore)
B.
Basic Option Pricing and Characteristics
Summer 2006
Comparative Statics (Price Sensitivity)
 Basic Option Pricing Notation
C = Value of Call Option
P = Value of Put Option
T = Time to Maturity
X = Strike (Exercise) Price
S = Stock Price (now)
 = Volatility = instantaneous
Std. Dev. of stock return
(annualized)
R = riskless interest rate
(continuous time)
 Option Pricing Model (Black-Scholes - 1973)
Ct  St  N (d1 )  X  e rT  N (d2 )
Pt   St  N ( d1 )  X  e rT  N ( d2 )
or
where
ln( St / X )  r   2 / 2T
d1 
 T
and
ln( St / X )  r   2 / 2T
d1 
 T
 Now Look at Relative Changes in CT given a change in 1 parameter
(e.g. C |   )
Change in:
r

T 
S 
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X 
Fin4328 (Moore)
Basic Option Pricing and Characteristics
Summer 2006
C. Early Exercise Decision for American Call Options
 Calls on a non dividend paying stock
 If you exercise the (in-the-money) call prior to expiration date, receive intrinsic
value = S - X.
If you don't early exercise, you can sell the call option in the market at C > Max [0,
S - X e – rT ] > S - X.



 It is never optimal to exercise an American call option on a non-dividend-paying
stock early. If you exercise early, lose the time premium (insurance value + time
value of the strike price)
 If you believe the stock is overpriced, sell the call option and should not early
exercise.
 Since the American call is never exercised early, the price should be the same as a
European Call.
Calls on a Dividend-Paying Stock
 Stock option is not protected against cash dividend distributions.

 After the ex-dividend date, the stock price will go down (ex-dividend stock price),
and therefore call price will also go down (ex-dividend call price).

 Should early exercise the call option (right before the ex-dividend date) if the
intrinsic value prior to the ex-dividend date is greater than the ex-dividend call
price.
4. Put Option Value

Suppose the underlying stock does not pay dividends.

Value of the put (before expiration date) consists of two components:
1. Intrinsic Value (IV) = Max[0, S X] (the parity value)
2. Time Premium (TP):= Insurance value - Interest forgone from deferred receipt of
the strike price.

 The time premium could be positive or negative, and therefore the put option price
could be above or below the intrinsic value.
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