1. Chapter 18 Valuing Options Principles of Corporate Finance
Concise Edition
Valuing Options
Slides by
Matthew Will
McGraw Hill/Irwin
Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights reserved.

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

3. Option Valuation Methods
Genentech call options have an exercise price of $80.
Case 1
Stock price falls to $60
Option value = $0
Case 2
Stock price rises to $106.67
Option value = $26.67

4. Option Valuation Methods
Assume you borrow 4/7 of the value of the Genentech exercise price ($33.45).
Value of Call = 80 x (4/7) – = $12.26

5. Option Valuation Methods
Since the Genentech call option is equal to a leveraged position in 4/7 shares, the option delta can be computed as follows.

6. Option Valuation Methods
If we are risk neutral, the expected return on Genentech call options is 2.5%. Accordingly, we can determine the probability of a rise in the stock price as follows.

7. Option Valuation Method
The Genentech option can then be valued based on the following method.

8. Binomial Pricing
The prior example can be generalized as the binomial model and shown as follows.

9. 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

10. Binomial Pricing
40.37
32.10 36

11. Binomial Pricing
40.37
32.10 36

12. 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

13. 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

14. 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

15. 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

16. Binomial Model
The price of an option, using the Binomial method, is significantly impacted by the time intervals selected. The Genentech example illustrates this fact.

17. 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

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

19. 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

20. Black-Scholes Option Pricing Model7

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

22. Cumulative Normal Density Function9

23. Call Option Example - Genentech
What is the price of a call option given the following?
P = 80 r = 5% v = .4068
EX = 80 t = 180 days / 365 11

24. Call Option Example - Genentech
What is the price of a call option given the following?
P = 80 r = 5% v = .4068
EX = 80 t = 180 days / 365 12

25. Call Option Example - Genentech
What is the price of a call option given the following?
P = 80 r = 5% v = .4068
EX = 80 t = 180 days / 365 13

26. 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

27. 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

28. 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

29. Black Scholes Comparisons

30. Implied Volatility
The unobservable variable in the option price is volatility. This figure can be estimated, forecasted, or derived from the other variables used to calculate the option price, when the option price is known.
Implied Volatility (%)

31. 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

32. 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

33. 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.

34. 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.

35. 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

36. Dilution

37. Web Resources Web Links Click to access web sites
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