Corporate Financial Theory

CORPORATE FINANCIALTHEORYLecture 10

DerivativesInsuranceRisk ManagementLloydsShip BuildingJet FuelCost PredictabilityRevenue Certainty

Stocks (example) Bonds Indices Commodities (examples for metal and ag.) Currencies Weather Carbon emissions Radio bandwidth

Underlying Assets

Arbitrage Speculation Hedging

Derivative Uses

Derivatives are financial instruments whose price and value derive from the value of the underlying assets or other variables (ISDA)

Derivatives are a “zero sum game” Example: Insurance

Derivatives Definition

Derivatives & OptionsHistorical Topics (Internal to the Corp)1 - Capital Budgeting (Investment)2 - Capital Structure (Financing)

TodayWe are leaving Internal Corporate Finance

We are going to Wall St & “Capital Markets”

Options - financial and corporateOptions are a type of derivative

Options

assetbuy toObligationasset sell Right tooptionPut asset sell toObligationassetbuy Right tooption Call

ShortLong

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

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

Option ValueThe 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

OptionsCBOE Success1 - Creation of a central options market place.2 - Creation of Clearing Corp - the guarantor of all trades.3 - Standardized expiration dates - 3rd Friday4 - Created a secondary market

Option ValueComponents of the Option Price1 - Underlying stock price2 - Striking or Exercise price3 - Volatility of the stock returns (standard

deviation of annual returns)4 - Time to option expiration5 - Time value of money (discount rate)

)()()( 21 EXPVdNPdNOC

Black-Scholes Option Pricing Model

Option Value

OC- Call Option PriceP - Stock PriceN(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





rteEXEXPV )(

factordiscount gcompoundin continuous1

rtrt

ee

N(d1)=


tvtrd

vEXP )()ln( 2

1

2

Cumulative Normal Density Function

tvtrd

vEXP )()ln( 2

1

2

tvdd 12

Call Option

3070.1 d

tvtrd

vEXP )()ln( 2

1

2

3794.6206.1)( 1 dN

ExampleWhat is the price of a call option given the following? P = 36 r = 10% v = .40EX = 40 t = 90 days / 365

.3070 = .3= .00= .007

Call Option

3065.6935.1)(5056.

2

2

12

dNd

tvdd


Call Option

70.1$)40(3065.363794.

)()()()2466)(.10(.

21

C

C

rtC

OeO

eEXdNPdNO


Put - Call Parity

Put Price = Call + EX - P - Carrying Cost + Div.

or

Put = Call + EX(e-rt)– Ps - Carrying Cost + Div.

Carrying cost = r x EX x t

Put - Call ParityExample

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 = 4 + 40 - 41 - (.10x 40 x .50) + .50

OP = 3 - 2 + .5

Op = $1.50

Warrants & Convertibles Review Topics (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

• Long Stock Bought stock @ Ps = 100

P/L Ps100 11090

+10

-10

Option Strategies

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


@ • Oc = 1.50 Op=1.50 S=27 Ps=27

P/L Ps27 3024-1.50

+1.50


@ • Oc = 1.50 Op=1.50 S=27 Ps=27

P/L Ps27 3024-1.50

+1.50

Option StrategiesWhy? 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.

Recall discussion on Real Options

Dilution

NqNNqV

EXexerciseafter price Share

shares goutstandin of #shares new of #1

1factorDilution

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

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Corporate Financial Theory