1. Prepared by Paul A. Spindt
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)

4. Options Lingo option premium intrinsic value; time value
European; American
long; short
covered; naked

5. Wednesday’s closing stock price
Example
Here’s a quote from Wednesday’s Wall Street Journal:
-Call Put-
SunMic
583/ Jan / /8
Wednesday’s closing stock price
Premium
Expiration date
Option strike price
Volume

6. Option Payoff: Calls
Payoff
Stock Price (at Expiration)
Strike Price

7. Option Payoff: Puts
Payoff
Stock Price (at Expiration)
Strike Price

8. Option Value Intrinsic value Time 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

9. When S is greater than X, the intrinsic value of the call is $(S-X)
The Value of a Call
Value }
When S is greater than X, the intrinsic value of the call is $(S-X)
(S-X) S X
This call option has an intrinsic value of $3.75 and time value of $3.50
-Call Put-
SunMic
583/ Jan /

10. When S is less than X, the intrinsic value of the call is $0
The Value of a Call
Value
When S is less than X, the intrinsic value of the call is $0 X
This call option has an intrinsic value of $0 and time value of $3.625
-Call Put-
SunMic
583/ Jan / /8

11. When S is less than X, the intrinsic value of the put is $(X-S)
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/ Jan / /8

12. When S is greater than X, the intrinsic value of the put is $0
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/ Jan /

13. Put-Call Parity
In an efficient market two investments with the same payoff ought to have the same price.

14. Put-Call Parity This principle implies that
the current stock price plus the price of a put

15. Put-Call Parity should equal
the price of a call plus the PV of the exercise price

16. Stock Price at Expiration
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

17. Stock Price at Expiration
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

18. The Payoff on a Stock and a Put
Terminal value of investment in both stock and put
Stock Price at Expiration
$50
$50

19. Stock Price at Expiration
The Payoff on a Call
Payoff
Terminal value of investment in call
Stock Price at Expiration $0
$50

20. Stock Price at Expiration
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

21. The Payoff on a Call and a Bond
Terminal value of investment in call and bond
Stock Price at Expiration
$50
$50
Terminal value of investment in bond

22. For Example:
Here’s 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/ Jan / /8

23. For Example: Put-call parity implies that -Call- -Put- SunMic
583/ Jan / /8

24. 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 option’s premium changes when the price of the underlying asset changes is called the option’s delta.

25. 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.

26. 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 option’s premium changes when its time to maturity changes is called the option’s theta.

27. Determinants of Option Value
Volatility
The volatility of the underlying asset is a measure of how uncertain we are about future changes in an asset’s 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.

28. 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.

29. 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

30. The Black-Scholes Formula
d1 and d2 are functions of the stock price, the strike price, the interest rate, time and volatility:
compare

31. Normal Distribution

32. Example
TelMex Jul CB 23/8 -5/ ,703

33. Assignment
Option Price Calculator
Ito’s Dilemma (A)
Ito’s Dilemma (B)