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Spotting and Valuing Options Principles of Corporate Finance Brealey and Myers Sixth Edition Slides by Matthew Will Chapter 20 ©The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill
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Spotting and Valuing Options
Principles of Corporate FinanceBrealey and Myers Sixth Edition
Slides by
Matthew Will Chapter 20
©The McGraw-Hill Companies, Inc., 2000Irwin/McGraw Hill
©The McGraw-Hill Companies, Inc., 2000Irwin/McGraw Hill
20- 2
Topics Covered
Calls, Puts and Shares Financial Alchemy with Options What Determines Option Value Option Valuation
©The McGraw-Hill Companies, Inc., 2000Irwin/McGraw Hill
20- 3
Option Terminology
Call Option
Right to buy an asset at a specified exercise price on or before the exercise date.
©The McGraw-Hill Companies, Inc., 2000Irwin/McGraw Hill
20- 4
Option Terminology
Put Option
Right to sell an asset at a specified exercise price on or before the exercise date.
Call Option
Right to buy an asset at a specified exercise price on or before the exercise date.
©The McGraw-Hill Companies, Inc., 2000Irwin/McGraw Hill
20- 5
Option Obligations
Buyer Seller
Call option Right to buy asset Obligation to sell asset
Put option Right to sell asset Obligation to buy asset
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Option Value
The value of an option at expiration is a function of the stock price and the exercise price.
©The McGraw-Hill Companies, Inc., 2000Irwin/McGraw Hill
20- 7
Option Value
The value of an option at expiration is a function of the stock price and the exercise price.
Example - Option values given a exercise price of $85
00051525ValuePut
25155000Value Call
110100908070$60eStock Pric
©The McGraw-Hill Companies, Inc., 2000Irwin/McGraw Hill
20- 8
Option Value
Call option value (graphic) given a $85 exercise price.
Share Price
Cal
l opt
ion
valu
e
85 105
$20
©The McGraw-Hill Companies, Inc., 2000Irwin/McGraw Hill
20- 9
Option Value
Put option value (graphic) given a $85 exercise price.
Share Price
Put
opt
ion
valu
e
80 85
$5
©The McGraw-Hill Companies, Inc., 2000Irwin/McGraw Hill
20- 10
Option Value
Call option payoff (to seller) given a $85 exercise price.
Share Price
Cal
l opt
ion
$ pa
yoff
85
©The McGraw-Hill Companies, Inc., 2000Irwin/McGraw Hill
20- 11
Option Value
Put option payoff (to seller) given a $85 exercise price.
Share Price
Put
opt
ion
$ pa
yoff
85
©The McGraw-Hill Companies, Inc., 2000Irwin/McGraw Hill
20- 12
Option Value
Protective Put - Long stock and long put
Share Price
Pos
itio
n V
alue
Long Stock
©The McGraw-Hill Companies, Inc., 2000Irwin/McGraw Hill
20- 13
Option Value
Protective Put - Long stock and long put
Share Price
Pos
itio
n V
alue
Long Put
©The McGraw-Hill Companies, Inc., 2000Irwin/McGraw Hill
20- 14
Option Value
Protective Put - Long stock and long put
Share Price
Pos
itio
n V
alue Protective Put
Long Put
Long Stock
©The McGraw-Hill Companies, Inc., 2000Irwin/McGraw Hill
20- 15
Option Value
Protective Put - Long stock and long put
Share Price
Pos
itio
n V
alue Protective Put
©The McGraw-Hill Companies, Inc., 2000Irwin/McGraw Hill
20- 16
Option ValueStraddle - Long call and long put
- Strategy for profiting from high volatility
Share Price
Pos
itio
n V
alue Long call
©The McGraw-Hill Companies, Inc., 2000Irwin/McGraw Hill
20- 17
Option ValueStraddle - Long call and long put
- Strategy for profiting from high volatility
Share Price
Pos
itio
n V
alue
Long put
©The McGraw-Hill Companies, Inc., 2000Irwin/McGraw Hill
20- 18
Option ValueStraddle - Long call and long put
- Strategy for profiting from high volatility
Share Price
Pos
itio
n V
alue
Straddle
©The McGraw-Hill Companies, Inc., 2000Irwin/McGraw Hill
20- 19
Option ValueStraddle - Long call and long put
- Strategy for profiting from high volatility
Share Price
Pos
itio
n V
alue
Straddle
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20- 20
Option Value
Upper Limit
Stock Price
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20- 21
Option Value
Upper Limit
Stock Price
Lower Limit
(Stock price - exercise price) or 0whichever is higher
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20- 22
Option Value
Components of the Option Price1 - 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)
©The McGraw-Hill Companies, Inc., 2000Irwin/McGraw Hill
20- 23
Option Value
Black-Scholes Option Pricing ModelBlack-Scholes Option Pricing Model
OC = Ps[N(d1)] - S[N(d2)]e-rt
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20- 24
OC = Ps[N(d1)] - S[N(d2)]e-rt
OC- Call Option Price
Ps - Stock Price
N(d1) - Cumulative normal density function of (d1)
S - 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
Black-Scholes Option Pricing ModelBlack-Scholes Option Pricing Model
©The McGraw-Hill Companies, Inc., 2000Irwin/McGraw Hill
20- 25
(d1)=
ln + ( r + ) tPs
S
v2
2
v t
32 34 36 38 40
N(d1)=
Black-Scholes Option Pricing ModelBlack-Scholes Option Pricing Model
©The McGraw-Hill Companies, Inc., 2000Irwin/McGraw Hill
20- 26
(d1)=
ln + ( r + ) tPs
S
v2
2
v t
Cumulative Normal Density FunctionCumulative Normal Density Function
(d2) = d1 - v t
©The McGraw-Hill Companies, Inc., 2000Irwin/McGraw Hill
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Call Option
Example
What is the price of a call option given the following?
P = 36 r = 10% v = .40
S = 40 t = 90 days / 365
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20- 28
Call Option
(d1) =
ln + ( r + ) tPs
S
v2
2
v t
(d1) = - .3070 N(d1) = 1 - .6206 = .3794
Example
What is the price of a call option given the following?
P = 36 r = 10% v = .40
S = 40 t = 90 days / 365
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20- 29
Call Option
(d2) = - .5056
N(d2) = 1 - .6935 = .3065
(d2) = d1 - v t
Example
What is the price of a call option given the following?
P = 36 r = 10% v = .40
S = 40 t = 90 days / 365
©The McGraw-Hill Companies, Inc., 2000Irwin/McGraw Hill
20- 30
Call Option
OC = Ps[N(d1)] - S[N(d2)]e-rt
OC = 36[.3794] - 40[.3065]e - (.10)(.2466)
OC = $ 1.70
Example
What is the price of a call option given the following?
P = 36 r = 10% v = .40
S = 40 t = 90 days / 365
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Put - Call Parity
Put Price = Oc + S - P - Carrying Cost + Div.
Carrying cost = r x S x t
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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?
Put - Call Parity
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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?
Put - Call Parity
Op = Oc + S - P - Carrying Cost + Div.
Op = 4 + 40 - 41 - (.10x 40 x .50) + .50
Op = 3 - 2 + .5
Op = $1.50
