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CHAPTER
22Options and Corporate
Finance: Basic Concepts
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Chapter Outline22.1 Options22.2 Call Options22.3 Put Options22.4 Selling Options22.5 Reading The Wall Street Journal22.6 Combinations of Options22.7 Valuing Options22.8 An Option‑Pricing Formula22.9 Stocks and Bonds as Options22.10 Capital-Structure Policy and Options22.11 Mergers and Options22.12 Investment in Real Projects and Options22.13 Summary and Conclusions
22.1 Options22.2 Call Options22.3 Put Options22.4 Selling Options22.5 Reading The Wall Street Journal22.6 Combinations of Options22.7 Valuing Options22.8 An Option‑Pricing Formula22.9 Stocks and Bonds as Options22.10 Capital-Structure Policy and Options22.11 Mergers and Options22.12 Investment in Real Projects and Options22.13 Summary and Conclusions
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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.
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.
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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 PutsCall 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.
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 PutsCall 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.
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22.1 Options Contracts: Preliminaries
Exercising the OptionThe act of buying or selling the underlying asset through the option contract.
Strike Price or Exercise PriceRefers to the fixed price in the option contract at which the holder can buy or sell the underlying asset.
ExpiryThe maturity date of the option is referred to as the expiration date, or the expiry.
European versus American optionsEuropean options can be exercised only at expiry.
American options can be exercised at any time up to expiry.
Exercising the OptionThe act of buying or selling the underlying asset through the option contract.
Strike Price or Exercise PriceRefers to the fixed price in the option contract at which the holder can buy or sell the underlying asset.
ExpiryThe maturity date of the option is referred to as the expiration date, or the expiry.
European versus American optionsEuropean options can be exercised only at expiry.
American options can be exercised at any time up to expiry.
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Options Contracts: Preliminaries
In-the-MoneyThe exercise price is less than the spot price of the underlying asset.
At-the-MoneyThe exercise price is equal to the spot price of the underlying asset.
Out-of-the-MoneyThe exercise price is more than the spot price of the underlying asset.
In-the-MoneyThe exercise price is less than the spot price of the underlying asset.
At-the-MoneyThe exercise price is equal to the spot price of the underlying asset.
Out-of-the-MoneyThe exercise price is more than the spot price of the underlying asset.
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Options Contracts: Preliminaries
Intrinsic ValueThe difference between the exercise price of the option and the spot price of the underlying asset.
Speculative ValueThe difference between the option premium and the intrinsic value of the option.
Intrinsic ValueThe difference between the exercise price of the option and the spot price of the underlying asset.
Speculative ValueThe difference between the option premium and the intrinsic value of the option.
Option Premium =
Intrinsic Value
Speculative Value
+
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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.
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.
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Basic Call Option Pricing Relationshipsat 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
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
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Call Option Payoffs
–20
12020 40 60 80 100
–40
20
40
60
Stock price ($)
Op
tion
pay
offs
($) Buy
a ca
ll
Exercise price = $50
50
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Call Option Payoffs
–20
12020 40 60 80 100
–40
20
40
60
Stock price ($)
Op
tion
pay
offs
($)
Sell a call
Exercise price = $50
50
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Call Option Profits
Exercise price = $50; option premium = $10
Sell a call
Buy a call
–20
12020 40 60 80 100
–40
20
40
60
Stock price ($)
Op
tion
pay
offs
($)
50–10
10
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22.3 Put Options
Put options gives the holder the right, but not the obligation, to sell a given quantity of an asset on or before some time in the future, at prices agreed upon today.
When exercising a put, you “put” the asset to someone.
Put options gives the holder the right, but not the obligation, to sell a given quantity of an asset on or before some time in the future, at prices agreed upon today.
When exercising a put, you “put” the asset to someone.
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Basic Put Option Pricing Relationshipsat Expiry
At expiry, an American put option is worth the same as a European option with the same characteristics.
If the put is in-the-money, it is worth E – ST.
If the put is out-of-the-money, it is worthless.
P = Max[E – ST, 0]
At expiry, an American put option is worth the same as a European option with the same characteristics.
If the put is in-the-money, it is worth E – ST.
If the put is out-of-the-money, it is worthless.
P = Max[E – ST, 0]
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Put Option Payoffs
–20
0 20 40 60 80 100
–40
20
0
40
60
Stock price ($)
Op
tion
pay
offs
($)
Buy a put
Exercise price = $50
50
50
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Put Option Payoffs
–20
0 20 40 60 80 100
–40
20
0
40
–50
Stock price ($)
Op
tion
pay
offs
($)
Sell a put
Exercise price = $50
50
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Put Option Profits
–20
20 40 60 80 100
–40
20
40
60
Stock price ($)
Op
tion
pay
offs
($)
Buy a put
Exercise price = $50; option premium = $10
–10
10Sell a put
50
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22.4 Selling Options
Exercise price = $50; option premium = $10 Sell a call
Buy a call
50 6040 100
–40
40
Stock price ($)
Op
tion
pay
offs
($)
Buy a put
Sell a put
The seller (or writer) of an option has an obligation.
The purchaser of an option has an option.
–10
10
Buy a call
Sell a
put
Buy a put
Sell a call
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22.5 Reading The WallStreet Journal
Option/Strike Exp. Vol. Last Vol. LastIBM 130 Oct 364 15¼ 107 5¼138¼ 130 Jan 112 19½ 420 9¼138¼ 135 Jul 2365 4¾ 2431 13/16
138¼ 135 Aug 1231 9¼ 94 5½138¼ 140 Jul 1826 1¾ 427 2¾138¼ 140 Aug 2193 6½ 58 7½
--Put----Call--
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22.5 Reading The Wall Street Journal
Option/Strike Exp. Vol. Last Vol. LastIBM 130 Oct 364 15¼ 107 5¼138¼ 130 Jan 112 19½ 420 9¼138¼ 135 Jul 2365 4¾ 2431 13/16
138¼ 135 Aug 1231 9¼ 94 5½138¼ 140 Jul 1826 1¾ 427 2¾138¼ 140 Aug 2193 6½ 58 7½
--Put----Call--
This option has a strike price of $135;
a recent price for the stock is $138.25
July is the expiration month
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22.5 Reading The Wall Street Journal
Option/Strike Exp. Vol. Last Vol. LastIBM 130 Oct 364 15¼ 107 5¼138¼ 130 Jan 112 19½ 420 9¼138¼ 135 Jul 2365 4¾ 2431 13/16
138¼ 135 Aug 1231 9¼ 94 5½138¼ 140 Jul 1826 1¾ 427 2¾138¼ 140 Aug 2193 6½ 58 7½
--Put----Call--
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.
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22.5 Reading The Wall Street Journal
Option/Strike Exp. Vol. Last Vol. LastIBM 130 Oct 364 15¼ 107 5¼138¼ 130 Jan 112 19½ 420 9¼138¼ 135 Jul 2365 4¾ 2431 13/16
138¼ 135 Aug 1231 9¼ 94 5½138¼ 140 Jul 1826 1¾ 427 2¾138¼ 140 Aug 2193 6½ 58 7½
--Put----Call--
On this day, 2,365 call options with thisexercise price were traded.
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22.5 Reading The Wall Street Journal
Option/Strike Exp. Vol. Last Vol. LastIBM 130 Oct 364 15¼ 107 5¼138¼ 130 Jan 112 19½ 420 9¼138¼ 135 Jul 2365 4¾ 2431 13/16
138¼ 135 Aug 1231 9¼ 94 5½138¼ 140 Jul 1826 1¾ 427 2¾138¼ 140 Aug 2193 6½ 58 7½
--Put----Call--
The CALL option with a strike priceof $135 is trading for $4.75.
Since the option is on 100 shares of stock, buying this option would cost $475 plus commissions.
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22.5 Reading The Wall Street Journal
Option/Strike Exp. Vol. Last Vol. LastIBM 130 Oct 364 15¼ 107 5¼138¼ 130 Jan 112 19½ 420 9¼138¼ 135 Jul 2365 4¾ 2431 13/16
138¼ 135 Aug 1231 9¼ 94 5½138¼ 140 Jul 1826 1¾ 427 2¾138¼ 140 Aug 2193 6½ 58 7½
--Put----Call--
On this day, 2,431 put options with thisexercise price were traded.
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22.5 Reading The Wall Street Journal
Option/Strike Exp. Vol. Last Vol. LastIBM 130 Oct 364 15¼ 107 5¼138¼ 130 Jan 112 19½ 420 9¼138¼ 135 Jul 2365 4¾ 2431 13/16
138¼ 135 Aug 1231 9¼ 94 5½138¼ 140 Jul 1826 1¾ 427 2¾138¼ 140 Aug 2193 6½ 58 7½
--Put----Call--
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.
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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.
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.
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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
$50
$0
$50
Value at expiry
Value of stock at expiry
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Protective Put Strategy Profits
Buy a put with exercise price of $50 for $10
Buy the stock at $40
$40
Protective Put strategy has
downside protection and upside potential
$40
$0
-$40
$50
Value at expiry
Value of stock at expiry
-$10
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Covered Call Strategy
Sell a call with exercise price of $50 for $10
Buy the stock at $40
$40
Covered Call strategy
$0
-$40
$50
Value at expiry
Value of stock at expiry
-$30
$10
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Long Straddle: Buy a Call and a Put
30 40 60 70
30
40
Stock price ($)
Op
tion
pay
offs
($)
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.
$50
–20
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Long Straddle: Buy a Call and a Put
–30
30 40 60 70
–40
Stock price ($)
Op
tion
pay
offs
($)
$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
Sell a call with an exercise price of $50 for $10
20
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bond
Put-Call Parity: p0 + S0 = c0 + E/(1+ r)T
25
25
Stock price ($)
Op
tion
pay
offs
($)
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 $25.
Call
Portfolio payoffPortfolio value today = c0 +(1+ r)T
E
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Put-Call Parity: p0 + S0 = c0 + E/(1+ r)T
25
25
Stock price ($)
Op
tion
pay
offs
($)
Consider the payoffs from holding a portfolio consisting of a share of stock and a put with a $25 strike.
Portfolio value today = p0 + S0
Portfolio payoff
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Put-Call Parity: p0 + S0 = c0 + E/(1+ r)T
Since these portfolios have identical payoffs, they must have the same value today: hence
Put-Call Parity: c0 + E/(1+r)T = p0 + S0
25
25
Stock price ($)
Opt
ion
payo
ffs
($)
25
25
Stock price ($)
Opt
ion
payo
ffs
($) Portfolio value today
= p0 + S0
Portfolio value today
(1+ r)T
E= c0 +
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22.7 Valuing Options
The last section concerned itself with the value of an option at expiry.
The last section concerned itself with the value of an option at expiry.
This section considers the value of an option prior to the expiration date.
A much more interesting question.
This section considers the value of an option prior to the expiration date.
A much more interesting question.
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Option Value Determinants
Call Put1. Stock price + –2. Exercise price – +3. Interest rate + –4. Volatility in the stock price + +5. Expiration date + +
The value of a call option C0 must fall within
max (S0 – E, 0) < C0 < S0.
The precise position will depend on these factors.
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Market Value, Time Value and Intrinsic Valuefor an American Call
The value of a call option C0 must fall within max (S0 – E, 0) < C0 < S0.
25
Op
tion
pay
offs
($) Call
ST
loss
E
Profit
ST
Time value
Intrinsic value
Market Value
In-the-moneyOut-of-the-money
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22.8 An Option‑Pricing Formula
We will start with a binomial option pricing formula to build our intuition.
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.
Then we will graduate to the normal approximation to the binomial for some real-world option valuation.
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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?
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
$21.25 = $25×(1 –.15)
$28.75 = $25×(1.15)S1S0
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Binomial Option Pricing Model1. A call option on this stock with exercise price of $25 will have
the following payoffs.
2. We can replicate the payoffs of the call option. With a levered position in the stock.
1. A call option on this stock with exercise price of $25 will have the following payoffs.
2. We can replicate the payoffs of the call option. With a levered position in the stock.
$25
$21.25
$28.75S1S0 C1
$3.75
$0
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Binomial Option Pricing Model
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.
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
$28.75S1S0 debt
– $21.25portfolio$7.50
$0
( – ) ==
=
C1
$3.75
$0– $21.25
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Binomial Option Pricing Model The value today of the levered equity portfolio is
today’s value of one share less the present value of a $21.25 debt:
The value today of the levered equity portfolio is today’s value of one share less the present value of a $21.25 debt:
)1(
25.21$25$
fr
$25
$21.25
$28.75S1S0 debt
– $21.25portfolio$7.50
$0
( – ) ==
=
C1
$3.75
$0– $21.25
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Binomial Option Pricing Model
We can value the call option todayas half of the value of thelevered equity portfolio:
We can value the call option todayas half of the value of thelevered equity portfolio:
)1(
25.21$25$
2
10
frC
$25
$21.25
$28.75S1S0 debt
– $21.25portfolio$7.50
$0
( – ) ==
=
C1
$3.75
$0– $21.25
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If the interest rate is 5%, the call is worth:If the interest rate is 5%, the call is worth:
The Binomial Option Pricing Model
38.2$24.2025$2
1
)05.1(
25.21$25$
2
10
C
$25
$21.25
$28.75S1S0 debt
– $21.25portfolio$7.50
$0
( – ) ==
=
C1
$3.75
$0– $21.25
$2.38
C0
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the replicating portfolio intuition.the replicating portfolio intuition.the replicating portfolio intuition.the replicating portfolio intuition.
Binomial Option Pricing Model
Many derivative securities can be valued by valuing portfolios of primitive securities when those portfolios have the same payoffs as the derivative securities.
The most important lesson (so far) from the binomial option pricing model is:
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Delta and the Hedge Ratio
This practice of the construction of a riskless hedge is called delta hedging.
The delta of a call option is positive.Recall from the example:
This practice of the construction of a riskless hedge is called delta hedging.
The delta of a call option is positive.Recall from the example:
The delta of a put option is negative.
2
1
5.7$
75.3$
25.21$75.28$
075.3$
Swing of callSwing of stock
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Delta
Determining the Amount of Borrowing:
Value of a call = Stock price × Delta – Amount borrowed
$2.38 = $25 × ½ – Amount borrowed
Amount borrowed = $10.12
Determining the Amount of Borrowing:
Value of a call = Stock price × Delta – Amount borrowed
$2.38 = $25 × ½ – Amount borrowed
Amount borrowed = $10.12
38.2$24.20$25$2
1
)05.1(
25.21$25$
2
10
C
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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
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)
q
1- q
)1(
)()1()()0(
fr
DVqUVqV
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The Risk-Neutral Approach to Valuation
S(0) is the value of the underlying asset today.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.
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Reserved.
The Risk-Neutral Approach to Valuation
The key to finding q is to note that it is already impounded into an observable security price: the value of S(0):The key to finding q is to note that it is already impounded into an observable security price: the value of S(0):
S(0), V(0)
S(U), V(U)
S(D), V(D)
q
1- q
A minor bit of algebra yields:)()(
)()0()1(
DSUS
DSSrq f
)1()()1()(
)0(fr
DSqUSqS
)1(
)()1()()0(
fr
DVqUVqV
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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:
$21.25,C(D)
q
1- q
$25,C(0)
$28.75,C(D)
)15.1(25$75.28$
)15.1(25$25.21$
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Example of the Risk-Neutral Valuation of a Call:
$21.25,C(D)
2/3
1/3
The next step would be to compute the risk neutral probabilities
$25,C(0)
$28.75,C(D)
)()(
)()0()1(
DSUS
DSSrq
f
3250.7$
5$
25.21$75.28$
25.21$25$)05.1(
q
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Example of the Risk-Neutral Valuation of a Call:
$21.25, $0
2/3
1/3
After that, find the value of the call in the up state and down state.
$25,C(0)
$28.75, $3.75
]0,75.28$25max[$)( DC
25$75.28$)( UC
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Example of the Risk-Neutral Valuation of a Call:
Finally, find the value of the call at time 0:
$21.25, $0
2/3
1/3
$25,C(0)
$28.75,$3.75
$25,$2.38
)1(
)()1()()0(
fr
DCqUCqC
)05.1(
0$)31(75.3$32)0(
C
38.2$)05.1(
50.2$)0( C
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This risk-neutral result is consistent with valuing the call using a replicating portfolio.
This risk-neutral result is consistent with valuing the call using a replicating portfolio.
Risk-Neutral Valuationand the Replicating Portfolio
38.2$24.2025$2
1
)05.1(
25.21$25$
2
10
C
38.2$05.1
50.2$
)05.1(
0$)31(75.3$320
C
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The Black-Scholes Model
The Black-Scholes Model isThe Black-Scholes Model is
Where
C0 = the value of a European option at time t = 0r = the risk-free interest rate.
N(d) = Probability that a standardized, normally distributed, random variable will be less than or equal to d.
The Black-Scholes Model allows us to value options in the real world just as we have done in the 2-state world.
)N()N( 210 dEedSC rT
T
Tσ
rESd
)2
()/ln(2
1
Tdd 12
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The Black-Scholes Model
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.
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 $10—our answer must be at least that amount.
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The Black-Scholes Model
Let’s try our hand at using the model. If you have a calculator handy, follow along.
Let’s try our hand at using the model. If you have a calculator handy, follow along.
Then,
First calculate d1 and d2
T
TσrESd
)5.()/ln( 2
1
5282.05.30.0
5).)30.0(5.05(.)150/160ln( 2
1 d
31602.05.30.052815.012 Tdd
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The Black-Scholes Model
N(d1) = N(0.52815) = 0.7013
N(d2) = N(0.31602) = 0.62401
)N()N( 210 dEedSC rT
5282.01 d
31602.02 d
92.20$
62401.01507013.0160$
0
5.05.0
C
eC
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22.9 Stocks and Bonds as OptionsLevered 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 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.
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22.9 Stocks and Bonds as OptionsLevered 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.
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.
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22.9 Stocks and Bonds as Options
It all comes down to put-call parity.It all comes down to put-call parity.
Value of a call on the
firm
Value of a put on the
firm
Value of a risk-free
bond
Value of the firm= + –
Stockholder’s position in terms of call options
Stockholder’s position in terms of put options
c0 = S0 + p0 – (1+ r)T
E
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22.10 Capital-Structure Policyand 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.
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.
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Balance Sheet for a Companyin Distress
Assets BV MV Liabilities BV MV
Cash $200 $200 LT bonds $300
Fixed Asset $400 $0 Equity $300
Total $600 $200 Total $600 $200
What happens if the firm is liquidated today?
Assets BV MV Liabilities BV MV
Cash $200 $200 LT bonds $300
Fixed Asset $400 $0 Equity $300
Total $600 $200 Total $600 $200
What happens if the firm is liquidated today?
The bondholders get $200; the shareholders get nothing.
$200$0
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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%
Expected CF from the Gamble = $1000 × 0.10 + $0 = $100
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%
Expected CF from the Gamble = $1000 × 0.10 + $0 = $100
NPV = –$200 + $100
(1.10)
NPV = –$133
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Selfish Stockholders Accept Negative NPV Project with Large Risks
Expected CF from the GambleTo 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
Expected CF from the GambleTo 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
$20 =$30
(1.50) PV of Bonds With the Gamble:
$47 =$70
(1.50) PV of Stocks With the Gamble:
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.
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22.11 Mergers and Options
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.
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.
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22.11 Mergers and Options
Cash payment to
newly issued shares
$0
Value of General Mills in 1 year
$42.55$38
$4.55
The contingent value rights paidthe difference between $42.55 andGeneral Mills’ stock price in oneyear up to a maximum of $4.55.
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22.11 Mergers and Options
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
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
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22.11 Mergers and Options
$38
$0
Value of General Mills in 1 year
$42.55
$42.55
–$38
Own a putStrike $42.55
Sell a putStrike $38
– $38.00$4.55
$42.55
Cash payment to newly issued shares
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22.11 Mergers and Options
Value of a share
$38
$4.55
$0
$42.55
Value of General
Mills in 1 year
Value of General Mills in 1 year
Value of a share plus cash payment
$42.55
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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.
Classic NPV calculations typically ignore the flexibility that real-world firms typically have.
The next chapter will take up this point.
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22.13 Summary and Conclusions
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 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
c0– (1+ r)T
E= S0 + p0
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22.13 Summary and Conclusions
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.1. Common stock in a levered firm can be viewed as a call option on the
assets of the firm.2. Real projects often have hidden option that enhance value.
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.1. Common stock in a levered firm can be viewed as a call option on the
assets of the firm.2. Real projects often have hidden option that enhance value.