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

Page 4F. MICHAUX

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

Page 5F. MICHAUX

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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Page 6F. MICHAUX

The value of an option at expiration is a function of the stock price and the exercise

price.

OPTION VALUE

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Page 7F. MICHAUX

• 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

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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

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Page 9F. MICHAUX

Put option value (graphic) given a $85 exercise price.

Share Price

Put

opt

ion

valu

e

80 85

$5

OPTION VALUE

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Page 10F. MICHAUX

Call option payoff (to seller) given a $85 exercise price.

Share Price

Cal

l opt

ion

$ pa

yoff

85

OPTION VALUE

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Page 11F. MICHAUX

Put option payoff (to seller) given a $85 exercise price.

Share Price

Put

opt

ion

$ pa

yoff

85

OPTION VALUE

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Page 12F. MICHAUX

Protective Put - Long stock and long put

Share Price

Pos

itio

n V

alue

Long Stock

OPTION VALUE

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Page 13F. MICHAUX

Protective Put - Long stock and long put

Share Price

Pos

itio

n V

alue

Long Put

OPTION VALUE

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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

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Page 15F. MICHAUX

Protective Put - Long stock and long put

Share Price

Pos

itio

n V

alue Protective Put

OPTION VALUE

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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

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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

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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

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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

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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

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Page 21F. MICHAUX

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

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Page 22F. 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

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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

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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

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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

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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

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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

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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

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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