Derivatives & Options

Historical Topics (Internal to the Corp)

1 - Capital Budgeting (Investment)

2 - Capital Structure (Financing)

Today

• We are leaving Internal Corporate Finance

• We are going to Wall St & “Capital Markets”

• Options - financial and corporate

• Options are a type of derivative

OptionsTerminology

Derivatives - Any financial instrument that is derived from another. (e.g.. options, warrants, futures, swaps, etc.)

Option - Gives the holder the right to buy or sell a security at a specified price during a specified period of time.

Call Option - The right to buy a security at a specified price within a specified time.

Put Option - The right to sell a security at a specified price within a specified time.

Option Premium - The price paid for the option, above the price of the underlying security.

Intrinsic Value - Diff between the strike price and the stock price

Time Premium - Value of option above the intrinsic value

Options

Terminology

Exercise Price - (Striking Price) The price at which you buy or sell the security.

Expiration Date - The last date on which the option can be exercised.

American Option - Can be exercised at any time prior to and including the expiration date.

European Option - Can be exercised only on the expiration date.

All options “usually” act like European options because you make more money if you sell the option before expiration (vs. exercising it).

3 vs. 70-68=2

Option Obligations

Buyer Seller

Call option Right to buy asset Obligation to sell asset

Put option Right to sell asset Obligation to buy asset

Option Value

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

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

Options

CBOE Success

1 - Creation of a central options market place.

2 - Creation of Clearing Corp - the guarantor of all trades.

3 - Standardized expiration dates - 3rd Friday

4 - Created a secondary market

Options

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)

Black-Scholes Option Pricing ModelBlack-Scholes Option Pricing Model

OC = Ps[N(d1)] - S[N(d2)]e-rt

Black-Scholes Option Pricing ModelBlack-Scholes Option Pricing Model

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

(d1)=

ln + ( r + ) tPs

S

v2

2

v t

32 34 36 38 40

Cumulative Normal Density FunctionCumulative Normal Density Function

N(d1)=

Cumulative Normal Density FunctionCumulative Normal Density Function

(d1)=

ln + ( r + ) tPs

S

v2

2

v t

Cumulative Normal Density FunctionCumulative Normal Density Function

(d2) = d1 - v t

Call OptionExample

What is the price of a call option given the following?.

P = 36 r = 10% v = .40

S = 40 t = 90 days / 365

Call OptionExample

What is the price of a call option given the following?.

P = 36 r = 10% v = .40

S = 40 t = 90 days / 365

(d1) =

ln + ( r + ) tPs

S

v2

2

v t

(d1) = - .3070 N(d1) = 1 - .6206 = .3794

Call Option.3070 = .3

= .00

= .007

Call OptionExample

What is the price of a call option given the following?.

P = 36 r = 10% v = .40

S = 40 t = 90 days / 365

(d2) = - .5056

N(d2) = 1 - .6935 = .3065

(d2) = d1 - v t

Call OptionExample

What is the price of a call option given the following?.

P = 36 r = 10% v = .40

S = 40 t = 90 days / 365

OC = Ps[N(d1)] - S[N(d2)]e-rt

OC = 36[.3794] - 40[.3065]e - (.10)(.2466)

OC = $ 1.70

Put - Call Parity

Put Price = Oc + S - P - Carrying Cost + Div.

Carrying cost = r x S x t

Example

IBM 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

Example

IBM 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

Warrants & Convertibles

Review Ch 22 (not going over in class)

Warrant - a call option with a longer time to expiration. Value a warrant as an option, plus factor in dividends and dilution.

Convertible - Bond with the option to exchange it for stock. Value as a regular bond + a call option.

Won’t require detailed valuation - general concept on valuation + new option calc and old bond calc.

Option Strategies

Option Strategies are viewed via charts.

How do you chart an option?

Stock Price

Profit

Loss

Option Strategies

• Long Stock Bought stock @ Ps = 100

P/L Ps

100 11090

+10

-10

Option Strategies

Long Call Bought Call @ Oc = 3 S=27 Ps=30

P/L Ps30 3627

+6

-3

Option Strategies

Short Call Sold Call @ Oc = 3 S=27 Ps=30

P/L Ps30 3627

-6

+3

Option Strategies

Long Put = Buy Put @ Op = 2 S=15 Ps=13

P/L Ps13 1510

-2

+3

Option Strategies

Short Put = Sell Put @ Op = 2 S=15 Ps=13

P/L Ps13 1510

-3

+2

Option Strategies• Synthetic Stock = Short Put & Long Call @

• Oc = 1.50 Op=1.50 S=27 Ps=27

P/L Ps27 3024

-1.50

+1.50

Option Strategies

P/L Ps27 3024

-1.50

+1.50

• Synthetic Stock = Short Put & Long Call @

• Oc = 1.50 Op=1.50 S=27 Ps=27

Option Strategies

P/L Ps27 3024

-1.50

+1.50

• Synthetic Stock = Short Put & Long Call @

• Oc = 1.50 Op=1.50 S=27 Ps=27

Option Strategies

Why?

1 - Reduce risk - butterfly spread

2 - Gamble - reverse straddle

3 - Arbitrage - as in synthetics

Arbitrage - If the price of a synthetic stock is different than the price of the actual stock, an opportunity for profit exists.

Corporate Options

Ch 21

3 types of “Real Options”

1 - The opportunity to make follow-up investments.

2 - The opportunity to abandon a project

3 - The opportunity to “wait” and invest later.

Value “Real Option” = NPV with option

- NPV w/o option

Example - Abandon

Mrs. Mulla gives you a non-retractable offer to buy your company for $150 mil at anytime within the next year. Given the following decision tree of possible outcomes, what is the value of the offer (i.e. the put option) and what is the most Mrs. Mulla could charge for the option?

Use a discount rate of 10%

Corporate Options

Example - AbandonMrs. Mulla gives you a non-retractable offer to buy your company for

$150 mil at anytime within the next year. Given the following decision tree of possible outcomes, what is the value of the offer (i.e. the put option) and what is the most Mrs. Mulla could charge for the option?

Corporate Options

Year 0 Year 1 Year 2

120 (.6)

100 (.6)

90 (.4)

NPV = 145

70 (.6)

50 (.4)

40 (.4)

Example - AbandonMrs. Mulla gives you a non-retractable offer to buy your company for

$150 mil at anytime within the next year. Given the following decision tree of possible outcomes, what is the value of the offer (i.e. the put option) and what is the most Mrs. Mulla could charge for the option?

Corporate Options

Year 0 Year 1 Year 2

120 (.6)

100 (.6)

90 (.4)

NPV = 162

150 (.4)

Option Value =

162 - 145 =

$17 mil

Reality

• Decision trees for valuing “real options” in a corporate setting can not be practically done by hand.

• We must introduce binomial theory & B-S models

Corporate Options

Expanding the binomial model to allow more possible price changes

1 step 2 steps 4 steps

(2 outcomes) (3 outcomes) (5 outcomes)

etc. etc.

Binomial vs. Black Scholes

How estimated call price changes as number of binomial steps increases

No. of steps Estimated value

1 48.1

2 41.0

3 42.1

5 41.8

10 41.4

50 40.3

100 40.6

Black-Scholes 40.5

Binomial vs. Black Scholes