1. Chapter 21 Valuing Options Principles of Corporate Finance
Eighth Edition
Chapter 21
Valuing Options
Slides by
Matthew Will
McGraw-Hill/Irwin
Copyright © 2006 by The McGraw-Hill Companies, Inc. All rights reserved

2. Topics Covered Simple Option Valuation Model Binomial Model
Black-Scholes Model
Black Scholes in Action
Option Values at a Glance

3. Binomial Pricing

4. Binomial Pricing Example Price = 36 s = .40 t = 90/365 D t = 30/365
Strike = 40 r = 10%
a =
u =
d = .8917
Pu = .5075
Pd = .4925

5. Binomial Pricing
40.37
32.10 36

6. Binomial Pricing
40.37
32.10 36

7. Binomial Pricing 50.78 = price 45.28 40.37 36 40.37 32.10 32.10 28.62
25.52
45.28 36
28.62
40.37
32.10 36

8. Binomial Pricing 50.78 = price 45.28 10.78 = intrinsic value 40.37 .37
32.10
25.52
45.28 36
28.62
40.37
32.10 36

9. Binomial Pricing The greater of 50.78 = price 45.28
10.78 = intrinsic value
40.37
.37
32.10
25.52
45.28
5.60 36
28.62
The greater of
40.37
32.10 36

10. Binomial Pricing 1.51 50.78 = price 45.28 10.78 = intrinsic value 5.60
40.37
.37
32.10
25.52
45.28
5.60 36
.19
28.62
40.37
2.91
32.10
.10 36
1.51

11. Option Value Components of the Option Price 1 - Underlying stock price
2 - Striking or Exercise price
3 - Volatility of the stock returns (standard deviation of annual returns)
4 - Time to option expiration
5 - Time value of money (discount rate) 22

12. Black-Scholes Option Pricing Model
Option Value
Black-Scholes Option Pricing Model 23

13. Black-Scholes Option Pricing Model
OC- Call Option Price
P - Stock Price
N(d1) - Cumulative normal density function of (d1)
PV(EX) - Present Value of Strike or Exercise price
N(d2) - Cumulative normal density function of (d2)
r - discount rate (90 day comm paper rate or risk free rate)
t - time to maturity of option (as % of year)
v - volatility - annualized standard deviation of daily returns 7

14. Black-Scholes Option Pricing Model7

15. Black-Scholes Option Pricing Model
N(d1)= 8

16. Cumulative Normal Density Function9

17. Call Option
Example
What is the price of a call option given the following?
P = 36 r = 10% v = .40
EX = 40 t = 90 days / 365 11

18. Call Option
Example
What is the price of a call option given the following?
P = 36 r = 10% v = .40
EX = 40 t = 90 days / 365 12

19. Call Option
Example
What is the price of a call option given the following?
P = 36 r = 10% v = .40
EX = 40 t = 90 days / 365 13

20. Black Scholes Comparisons

21. Put Price = Oc + EX - P - Carrying Cost + Div.
Put - Call Parity
Put Price = Oc + EX - P - Carrying Cost + Div.
Carrying cost = r x EX x t 14

22. Put - Call Parity Example
ABC is selling at $41 a share. A six month May 40 Call is selling for $4.00. If a May $ .50 dividend is expected and r=10%, what is the put price?
OP = OC + EX - P - Carrying Cost + Div.
OP = (.10x 40 x .50) + .50
OP =
Op = $1.50 15

23. Expanding the binomial model to allow more possible price changes
Binomial vs. Black Scholes
Expanding the binomial model to allow more possible price changes
1 step steps steps
(2 outcomes) (3 outcomes) (5 outcomes)
etc. etc.

24. Binomial vs. Black Scholes
Example
What is the price of a call option given the following?
P = 36 r = 10% v = .40
EX = 40 t = 90 days / 365
Binomial price = $1.51
Black Scholes price = $1.70
The limited number of binomial outcomes produces the difference. As the number of binomial outcomes is expanded, the price will approach, but not necessarily equal, the Black Scholes price.

25. How estimated call price changes as number of binomial steps increases
Binomial vs. Black Scholes
How estimated call price changes as number of binomial steps increases
No. of steps Estimated value
Black-Scholes

26. Dilution

27. Web Resources Web Links Click to access web sites
Internet connection required