Post on 28-Dec-2015
2007
Page 1F. MICHAUX
CORPORATE FINANCE Financial and Real Options
2007
Page 2F. MICHAUX
GENERAL AGENDA
Financial and Real Options
2007
Page 3F. MICHAUX
TOPICS COVERED
• Calls, Puts and Shares• Financial Alchemy with Options• What Determines Option Value• Option Valuation• Real Options
– Follow Up Investments– Abandon– Wait– Vary Output or Production
• Binomial Model
2007
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OPTION TERMINOLGY
Call Option
Right to buy an asset at a specified exercise price on or before the exercise date.
Put Option
Right to sell an asset at a specified exercise price on or before the exercise date.
2007
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Buyer Seller
Call option Right to buy asset Obligation to sell asset
Put option Right to sell asset Obligation to buy asset
OPTION OBLIGATIONS
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The value of an option at expiration is a function of the stock price and the exercise
price.
OPTION VALUE
2007
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• 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
OPTION VALUE
2007
Page 8F. MICHAUX
Call option value (graphic) given a $85 exercise price.
Share Price
Cal
l opt
ion
valu
e
85 105
$20
OPTION VALUE
2007
Page 9F. MICHAUX
Put option value (graphic) given a $85 exercise price.
Share Price
Put
opt
ion
valu
e
80 85
$5
OPTION VALUE
2007
Page 10F. MICHAUX
Call option payoff (to seller) given a $85 exercise price.
Share Price
Cal
l opt
ion
$ pa
yoff
85
OPTION VALUE
2007
Page 11F. MICHAUX
Put option payoff (to seller) given a $85 exercise price.
Share Price
Put
opt
ion
$ pa
yoff
85
OPTION VALUE
2007
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Protective Put - Long stock and long put
Share Price
Pos
itio
n V
alue
Long Stock
OPTION VALUE
2007
Page 13F. MICHAUX
Protective Put - Long stock and long put
Share Price
Pos
itio
n V
alue
Long Put
OPTION VALUE
2007
Page 14F. MICHAUX
Protective Put - Long stock and long put
Share Price
Pos
itio
n V
alue Protective Put
Long Put
Long Stock
OPTION VALUE
2007
Page 15F. MICHAUX
Protective Put - Long stock and long put
Share Price
Pos
itio
n V
alue Protective Put
OPTION VALUE
2007
Page 16F. MICHAUX
Straddle - Long call and long put
- Strategy for profiting from high volatility
Share Price
Pos
itio
n V
alue Long call
OPTION VALUE
2007
Page 17F. MICHAUX
Straddle - Long call and long put
- Strategy for profiting from high volatility
Share Price
Pos
itio
n V
alue
Long put
OPTION VALUE
2007
Page 18F. MICHAUX
Straddle - Long call and long put
- Strategy for profiting from high volatility
Share Price
Pos
itio
n V
alue
Straddle
OPTION VALUE
2007
Page 19F. MICHAUX
Straddle - Long call and long put
- Strategy for profiting from high volatility
Share Price
Pos
itio
n V
alue
Straddle
OPTION VALUE
2007
Page 20F. MICHAUX
Strip – 1 Long call and 2 long put
- Strategy for profiting from high volatility
Share Price
Pos
itio
n V
alue Long call
OPTION VALUE
2007
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Strip – 1 Long call and 2 long put
- Strategy for profiting from high volatility
Share Price
Pos
itio
n V
alue
2 Long put
OPTION VALUE
2007
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Strip – 1 Long call and 2 long put
- Strategy for profiting from high volatility
Share Price
Pos
itio
n V
alue
Strip
OPTION VALUE
2007
Page 23F. MICHAUX
Strip – 1 Long call and 2 long put
- Strategy for profiting from high volatility
Share Price
Pos
itio
n V
alue
Strip
OPTION VALUE
2007
Page 24F. MICHAUX
Strap – 2 Long call and 1 long put
- Strategy for profiting from high volatility
Share Price
Pos
itio
n V
alue 2 Long call
OPTION VALUE
2007
Page 25F. MICHAUX
Strap – 2 Long call and 1 long put
- Strategy for profiting from high volatility
Share Price
Pos
itio
n V
alue
Long put
OPTION VALUE
2007
Page 26F. MICHAUX
Strap – 2 Long call and 1 long put
- Strategy for profiting from high volatility
Share Price
Pos
itio
n V
alue
Strap
OPTION VALUE
2007
Page 27F. MICHAUX
Strap – 2 Long call and 1 long put
- Strategy for profiting from high volatility
Share Price
Pos
itio
n V
alue
Strap
OPTION VALUE
2007
Page 28F. MICHAUX
Upper Limit
Stock Price
OPTION VALUE
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Page 29F. MICHAUX
Upper Limit
Stock Price
Lower Limit
(Stock price - exercise price) or 0whichever is higher
OPTION VALUE
2007
Page 30F. MICHAUX
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)
OPTION VALUE
2007
Page 31F. MICHAUX
Black-Scholes Option Pricing ModelBlack-Scholes Option Pricing Model
OC = Ps[N(d1)] - S[N(d2)]e-rt
OPTION VALUE
04/19/23 2007
Page 32F. MICHAUX
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
04/19/23 2007
Page 33F. MICHAUX
(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
04/19/23 2007
Page 34F. MICHAUX
(d1)=
ln + ( r + ) tPs
S
v2
2
v t
Cumulative Normal Density FunctionCumulative Normal Density Function
(d2) = d1 - v t
04/19/23 2007
Page 35F. MICHAUX
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
04/19/23 2007
Page 36F. MICHAUX
(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
CALL OPTION
04/19/23 2007
Page 37F. MICHAUX
(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
CALL OPTION
04/19/23 2007
Page 38F. MICHAUX
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
CALL OPTION
04/19/23 2007
Page 39F. MICHAUX
Intrinsic Value
OPTION TO WAIT
Option Price
Stock Price
04/19/23 2007
Page 40F. MICHAUX
Intrinsic Value + Time Premium = Option Value
Time Premium = Vale of being able to wait
Option Price
Stock Price
OPTION TO WAIT
04/19/23 2007
Page 41F. MICHAUX
More time = More value
Option Price
Stock Price
OPTION TO WAIT