Ross7eCh22

Options and Corporate Finance: Basic ConceptsCHAPTER
22
McGraw-Hill/Irwin Corporate Finance, 7/e
Chapter Outline
22.1 Options
22.6 Combinations of Options
22.9 Stocks and Bonds as Options
22.10 Capital-Structure Policy and Options
22.11 Mergers and Options
22.13 Summary and Conclusions
22.1 Options
Many corporate securities are similar to the stock options that are traded on organized exchanges.
Almost every issue of corporate stocks and bonds has option features.
In addition, capital structure and capital budgeting decisions can be viewed in terms of options.
22.1 Options Contracts: Preliminaries
An option gives the holder the right, but not the obligation, to buy or sell a given quantity of an asset on (or perhaps before) a given date, at prices agreed upon today.
Calls versus Puts
Call options gives the holder the right, but not the obligation, to buy a given quantity of some asset at some time in the future, at prices agreed upon today. When exercising a call option, you “call in” the asset.
Put options gives the holder the right, but not the obligation, to sell a given quantity of an asset at some time in the future, at prices agreed upon today. When exercising a put, you “put” the asset to someone.
22.1 Options Contracts: Preliminaries
Exercising the Option
The act of buying or selling the underlying asset through the option contract.
Strike Price or Exercise Price
Refers to the fixed price in the option contract at which the holder can buy or sell the underlying asset.
Expiry
The maturity date of the option is referred to as the expiration date, or the expiry.
European versus American options
European options can be exercised only at expiry.
American options can be exercised at any time up to expiry.
Options Contracts: Preliminaries
In-the-Money
The exercise price is less than the spot price of the underlying asset.
At-the-Money
The exercise price is equal to the spot price of the underlying asset.
Out-of-the-Money
The exercise price is more than the spot price of the underlying asset.
Options Contracts: Preliminaries
Intrinsic Value
The difference between the exercise price of the option and the spot price of the underlying asset.
Speculative Value
The difference between the option premium and the intrinsic value of the option.
Option Premium
22.2 Call Options
Call options gives the holder the right, but not the obligation, to buy a given quantity of some asset on or before some time in the future, at prices agreed upon today.
When exercising a call option, you “call in” the asset.
Basic Call Option Pricing Relationships
at Expiry
At expiry, an American call option is worth the same as a European option with the same characteristics.
If the call is in-the-money, it is worth ST – E.
If the call is out-of-the-money, it is worthless:
C = Max[ST – E, 0]
Where
ST is the value of the stock at expiry (time T)
E is the exercise price.
C is the value of the call option at expiry
Call Option Payoffs
Call Option Payoffs
Call Option Profits
Sell a call
Buy a call
22.3 Put Options
Put options gives the holder the right, but not the obligation, to sell a given quantity of an asset on or before some time in the future, at prices agreed upon today.
When exercising a put, you “put” the asset to someone.
Basic Put Option Pricing Relationships
at Expiry
At expiry, an American put option is worth the same as a European option with the same characteristics.
If the put is in-the-money, it is worth E – ST.
If the put is out-of-the-money, it is worthless.
P = Max[E – ST, 0]
Put Option Payoffs
Put Option Payoffs
Put Option Profits
–10
10
22.4 Selling Options
Sell a call
Buy a call
The seller (or writer) of an option has an obligation.
The purchaser of an option has an option.
–10
10
22.5 Reading The Wall
22.5 Reading The Wall Street Journal
This option has a strike price of $135;
a recent price for the stock is $138.25
July is the expiration month
Sheet1
This makes a call option with this exercise price in-the-money by $3.25 = $138¼ – $135.
Puts with this exercise price are out-of-the-money.
Sheet1
On this day, 2,365 call options with this
exercise price were traded.
The CALL option with a strike price
of $135 is trading for $4.75.
Since the option is on 100 shares of stock, buying
this option would cost $475 plus commissions.
Sheet1
On this day, 2,431 put options with this
exercise price were traded.
The PUT option with a strike price of $135 is trading for $.8125.
Since the option is on 100 shares of stock, buying this option would cost $81.25 plus commissions.
Sheet1
22.6 Combinations of Options
Puts and calls can serve as the building blocks for more complex option contracts.
If you understand this, you can become a financial engineer, tailoring the risk-return profile to meet your client’s needs.
© 2005 The McGraw-Hill Companies, Inc. All Rights Reserved.
Protective Put Strategy: Buy a Put and Buy the Underlying Stock: Payoffs at Expiry
Buy a put with an exercise price of $50
Buy the stock
Protective Put payoffs
Protective Put Strategy Profits
Buy a put with exercise price of $50 for $10
Buy the stock at $40
$40
$40
$0
-$40
$50
-$10
Covered Call Strategy
Sell a call with exercise price of $50 for $10
Buy the stock at $40
$40
-$30
$10
30
40
60
70
30
40
Buy a put with exercise price of $50 for $10
Buy a call with exercise price of $50 for $10
A Long Straddle only makes money if the stock price moves $20 away from $50.
$50
–20
–30
30
40
60
70
–40
$50
This Short Straddle only loses money if the stock price moves $20 away from $50.
Sell a put with exercise price of
$50 for $10
exercise price of $50 for $10
20
Put-Call Parity: p0 + S0 = c0 + E/(1+ r)T
25
25
Stock price ($)
Option payoffs ($)
Consider the payoffs from holding a portfolio consisting of a call with a strike price of $25 and a bond with a future value of $25.
Call
25
25
Stock price ($)
Option payoffs ($)
Consider the payoffs from holding a portfolio consisting of a share of stock and a put with a $25 strike.
Portfolio value today = p0 + S0
Portfolio payoff
Since these portfolios have identical payoffs, they must have the same value today: hence
Put-Call Parity: c0 + E/(1+r)T = p0 + S0
Portfolio value today
22.7 Valuing Options
The last section concerned itself with the value of an option at expiry.
This section considers the value of an option prior to the expiration date.
A much more interesting question.
Option Value Determinants
Expiration date + +
The value of a call option C0 must fall within
max (S0 – E, 0) < C0 < S0.
The precise position will depend on these factors.
Market Value, Time Value and Intrinsic Value
for an American Call
The value of a call option C0 must fall within max (S0 – E, 0) < C0 < S0.
25
22.8 An OptionPricing Formula
We will start with a binomial option pricing formula to build our intuition.
Then we will graduate to the normal approximation to the binomial for some real-world option valuation.
Binomial Option Pricing Model
Suppose a stock is worth $25 today and in one period will either be worth 15% more or 15% less. S0= $25 today and in one year S1is either $28.75 or $21.25. The risk-free rate is 5%. What is the value of an at-the-money call option?
$25
S0
A call option on this stock with exercise price of $25 will have the following payoffs.
We can replicate the payoffs of the call option. With a levered position in the stock.
$25
$21.25
$28.75
S1
S0
C1
$3.75
$0
Borrow the present value of $21.25 today and buy 1 share.
The net payoff for this levered equity portfolio in one period is either $7.50 or $0.
The levered equity portfolio has twice the option’s payoff so the portfolio is worth twice the call option value.
$25
$21.25
$28.75
S1
S0
debt
– $21.25
portfolio
$7.50
$0
The value today of the levered equity portfolio is today’s value of one share less the present value of a $21.25 debt:
$25
$21.25
$28.75
S1
S0
debt
– $21.25
portfolio
$7.50
$0
levered equity portfolio:
The Binomial Option Pricing Model
If the interest rate is 5%, the call is worth:
$25
$21.25
$28.75
S1
S0
debt
– $21.25
portfolio
$7.50
$0
the replicating portfolio intuition.
Many derivative securities can be valued by valuing portfolios of primitive securities when those portfolios have the same payoffs as the derivative securities.
The most important lesson (so far) from the binomial option pricing model is:
Delta and the Hedge Ratio
This practice of the construction of a riskless hedge is called delta hedging.
The delta of a call option is positive.
Recall from the example:
D =
Delta
Value of a call = Stock price × Delta – Amount borrowed
$2.38 = $25 × ½ – Amount borrowed
Amount borrowed = $10.12
The Risk-Neutral Approach to Valuation
We could value V(0) as the value of the replicating portfolio. An equivalent method is risk-neutral valuation
S(0), V(0)
S(U), V(U)
S(D), V(D)
S(0) is the value of the underlying asset today.
S(0), V(0)
S(U), V(U)
S(D), V(D)
S(U) and S(D) are the values of the asset in the next period following an up move and a down move, respectively.
q
1- q
V(U) and V(D) are the values of the asset in the next period following an up move and a down move, respectively.
q is the risk-neutral probability of an “up” move.
The key to finding q is to note that it is already impounded into an observable security price: the value of S(0):
A minor bit of algebra yields:
S(0), V(0)
S(U), V(U)
S(D), V(D)
Example of the Risk-Neutral Valuation of a Call:
Suppose a stock is worth $25 today and in one period will either be worth 15% more or 15% less. The risk-free rate is 5%. What is the value of an at-the-money call option?
The binomial tree would look like this:
)
The next step would be to compute the risk neutral probabilities
$21.25,C(D)
2/3
1/3
$25,C(0)
$28.75,C(D)
After that, find the value of the call in the up state and down state.
$21.25, $0
Finally, find the value of the call at time 0:
$25,$2.38
Risk-Neutral Valuation
and the Replicating Portfolio
This risk-neutral result is consistent with valuing the call using a replicating portfolio.
The replicating portfolio consists of buying one share of stock today and borrowing the present value of $21.25. The payoffs to the portfolio are twice those of the call, therefore the portfolio is worth twice as much as a call. Since we can value the portfolio, we can value the call.
The Black-Scholes Model
Where
C0 = the value of a European option at time t = 0
r = the risk-free interest rate.
N(d) = Probability that a standardized, normally distributed, random variable will be less than or equal to d.
)
Find the value of a six-month call option on the Microsoft with an exercise price of $150
The current value of a share of Microsoft is $160
The interest rate available in the U.S. is r = 5%.
The option maturity is 6 months (half of a year).
The volatility of the underlying asset is 30% per annum.
Before we start, note that the intrinsic value of the option is $10—our answer must be at least that amount.
Let’s try our hand at using the model. If you have a calculator handy, follow along.
Then,
T
T
σ
r
E
S
d
s
N(d1) = N(0.52815) = 0.7013
N(d2) = N(0.31602) = 0.62401
Another Black-Scholes Example
Assume S = $50, X = $45, T = 6 months, r = 10%,
and = 28%, calculate the value of a call and a put.
(
)
Levered Equity is a Call Option.
The underlying asset comprise the assets of the firm.
The strike price is the payoff of the bond.
If at the maturity of their debt, the assets of the firm are greater in value than the debt, the shareholders have an in-the-money call, they will pay the bondholders and “call in” the assets of the firm.
If at the maturity of the debt the shareholders have an out-of-the-money call, they will not pay the bondholders (i.e. the shareholders will declare bankruptcy) and let the call expire.
Levered Equity is a Put Option.
The underlying asset comprise the assets of the firm.
The strike price is the payoff of the bond.
If at the maturity of their debt, the assets of the firm are less in value than the debt, shareholders have an in-the-money put.
They will put the firm to the bondholders.
If at the maturity of the debt the shareholders have an out-of-the-money put, they will not exercise the option (i.e. NOT declare bankruptcy) and let the put expire.
It all comes down to put-call parity.
Stockholder’s position in terms of call options
Stockholder’s position in terms of put options
Value of a call on the firm
Value of a put on the firm
Value of a risk-free bond
Value of the firm
22.10 Capital-Structure Policy
and Options
Recall some of the agency costs of debt: they can all be seen in terms of options.
For example, recall the incentive shareholders in a levered firm have to take large risks.
Balance Sheet for a Company
in Distress
What happens if the firm is liquidated today?
The bondholders get $200; the shareholders get nothing.
$200
$0
Selfish Strategy 1: Take Large Risks
The Gamble Probability Payoff
Win Big 10% $1,000
Lose Big 90% $0
Cost of investment is $200 (all the firm’s cash)
Required return is 50%
NPV = –$133
NPV = –$200 +
Selfish Stockholders Accept Negative NPV Project with Large Risks
Expected CF from the Gamble
To Bondholders = $300 × 0.10 + $0 = $30
To Stockholders = ($1000 – $300) × 0.10 + $0 = $70
PV of Bonds Without the Gamble = $200
PV of Stocks Without the Gamble = $0
The stocks are worth more with the high risk project because the call option that the shareholders of the levered firm hold is worth more when the volatility of the firm is increased.
$20 =
$30
(1.50)
$47 =
$70
(1.50)
This is an area rich with optionality, both in the structuring of the deals and in their execution.
In the first half of 2000, General Mills was attempting to acquire the Pillsbury division of Diageo PLC.
The structure of the deal was Diageo’s stockholders received 141 million shares of General Mills stock (then valued at $42.55) plus contingent value rights of $4.55 per share.
$0
$4.55
General Mills’ stock price in one
year up to a maximum of $4.55.
$42.55
$38
The contingent value plan can be viewed in terms of puts:
Each newly issued share of General Mills given to Diageo’s shareholders came with a put option with an exercise price of $42.55.
But the shareholders of Diageo sold a put with an exercise price of $38
Cash payment to newly issued shares
$42.55
$42.55
–$38
Value of a share
$42.55
22.12 Investment in Real Projects & Options
Classic NPV calculations typically ignore the flexibility that real-world firms typically have.
The next chapter will take up this point.
The most familiar options are puts and calls.
Put options give the holder the right to sell stock at a set price for a given amount of time.
Call options give the holder the right to buy stock at a set price for a given amount of time.
Put-Call parity
The value of a stock option depends on six factors:
1. Current price of underlying stock.
2. Dividend yield of the underlying stock.
3. Strike price specified in the option contract.
4. Risk-free interest rate over the life of the contract.
5. Time remaining until the option contract expires.
6. Price volatility of the underlying stock.
Much of corporate financial theory can be presented in terms of options.
Common stock in a levered firm can be viewed as a call option on the assets of the firm.
Real projects often have hidden option that enhance value.
Option/StrikeExp.Vol.LastVol.Last
138¼135Jul23654¾2431
13/16
--Put----Call--
Option/StrikeExp.Vol.LastVol.Last
138¼135Jul23654¾2431
13/16
--Put----Call--

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Ross7eCh22