Transcript Slide 1

CHAPTER 23 OPTIONS
Topics:
• 23.1
• 23.5
• 23.2 - 23.4
• 23.6
• 23.7
• 23.8
Background
Stock Option Quotations
Value of Call and Put Options at Expiration
Combinations of Options
Valuing Options
An Option Pricing Formula
1
23.1 Background
• A derivative security is simply a contract which has a value
that is dependent upon (or derived from) the value of some
other asset(s)
• Derivatives that we consider in this course:
– Futures and forward contracts (Chapter 26)
– Options
• there are many different kinds of options: stock options, index
options, futures options, foreign exchange options, interest rate
caps, callable bonds, convertible bonds, retractable/extendable
bonds, etc.
2
Why option is important in corporate finance
• Important financial markets besides stock and bond markets
• Many employees are compensated in stock options
– You need to what they’re worth
– You need to know how their value might depend upon the
actions chosen by those employees
• Many corporate finance projects have implicit real options in
them. A static valuation (i.e., that ignores this option value)
can give misleading results
• In fact, almost any security can be thought of in terms of
options (including stocks and corporate bonds)
3
Terminology
• Option: Gives the owner the right to buy or sell an asset on
or before a specified date for a predetermined price
Expiry date, T
The underlying asset
(Current price: Spot price, S)
Exercise price, K or X
– Call: the right to buy (C)
– Put: the right to sell (P)
4
Terminology cont’d
• Owner of an option
– Buy
– Long position
• Seller of an option
– Short
– Write
Has a right
Has an obligation (A
contingent obligation)
• The act of buying or selling the underlying asset via the option
contract is exercising the option
• European options can only be exercised at the expiry date, while
American options can be exercised at any time up to and
including the expiry date
(unless otherwise stated, the options we consider will be European
options)
• Value of the option is called premium
5
Terminology cont’d
• Option contracts are either exchange-traded or available on a
customized basis in the over-the-counter market
• Standardized exchange-traded option contracts (on the
CBOE):
– Usually are for 100 options (1 contract)
– Have strike prices $2.50 apart in the range of $5 to $25, $5
apart in the range of $25 to $200, and $10 apart for strike
prices above $200
– Expiration months are two near term months plus two
additional months from the Jan, Feb, or Mar quarterly cycle
– The expiration date is usually the Saturday following the third
Friday of the expiration month (which is the last trading day)
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23.5 Stock Option Quotations
RBC’s Nov. 08 options
•
•
•
•
•
Strike: strike price
Exp: Expiry month
Bid: the bid price (The price at which somebody bids to buy)
Ask: the ask price (The price at which somebody asks to sell)
Open int.: Open interest, or number of outstanding contracts (one
contract usually equals 100 options)
7
Option quotations cont’d
• Options are not usually protected against cash dividends but
are protected against stock-splits and stock dividends
– Suppose in Oct. you buy 1 call option of RY with expiry of
Jan. and a strike of $30.
• In Nov. RY pays $50 cash dividend.
• In Nov. RY does a 2:1 split. Your 1 call option will become 2
options with strike price halved
8
23.2-4 Value of Options
Value of a Call Option at Expiration Date (T)
Example: An option on a common stock:
ST = market price of the common stock on the expiration date, T.
Suppose the exercise price, X = $8
Payoff on the expiration date (The third Friday in June)
ST > 8, let ST = $9
ST = $8
ST < 8 let ST = $7
Call option value
• If ST = 9 at the expiry date, exercise option, purchase share at 8 and then
sell share for 9. Payoff =
C = max(ST – X, 0)
9
Value of a Put Option at Expiration Date (T)
• A put. Exercise price X = $11
Payoff on the expiration date (The third Friday in Sept.)
ST > 11, let ST = $12
ST = $11
ST < 11 let ST = 10
Put option value
• If ST = 10 at the expiry date, exercise option, purchase share at 10
and then sell share for 11. Payoff =
P = max(X - ST, 0)
10
Moneyness
• an in the money option is one that would lead to a positive
cash flow if exercised immediately
• an at the money option is one that would lead to a zero cash
flow if exercised immediately
• an out of the money option is one that would lead to a
negative cash flow if exercised immediately
• Let X denote the strike price of the option and St denote the
current price of the underlying asset:
11
Value components
• Intrinsic Value: the intrinsic value of an option is the
maximum of zero and the option’s immediate exercise value
• Time Value
– The difference between the option premium and the intrinsic
value of the option.
OPTION VALUE
(PREMIUM)
=
Intrinsic Value
+
Time
value
E.g.: (1) The Nov. RY $30 Call. Price 8.20. Spot 37.10.
(2) The Nov. RY $30 Put. Price 1.05.
12
Option payoffs cont’d
Payoff
Profit/loss from Buying a stock, e.g., at 15
$0
15
Share Price
$-15
13
Payoff/profit of Long Call
• Let X = $15. What’s your payoff/profit of buying a call at T?
• Payoff is just the final value of the option CT, profit takes the option
premium into account.
• When you long an option, you buy the option at a cost (the
option premium)
$20
15
35
Share Price
14
Payoff/profit to buy a Put option, given a $15 exercise
price.
$5
10 15
Share Price
15
The buyer and seller always have “mirror image” payoffs
Long call
15
Share Price
Profit•When you go short in an option, you sell the option
(and receive premium)
16
Exercise
• Plot the payoff/profit diagrams for (1) short stock (suppose
the sell price is 15) and (2) selling put (suppose X = 15).
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23.6 Combinations of Options and stocks
• Portfolios of stocks and options.
• Firms and individuals’ portfolios (asset holdings) may
consist of different options and stocks on the same
underlying asset. These positions may offset each other or
compound the payoff possibilities.
• You want to combine them and consider the risk of changes
in the price of the underlying asset to the aggregate portfolio.
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• Short call + Long put with same
strike and expiry (called synthetic
short sale)
• Long Call + Short put with same
strike and expiry (let X = 55)
Long call + Short put
$ payoff
Long call
Share Price
55
Short put
• Equivalent to:
• Equivalent to:
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Writing a Covered Call: Long stock + short call
• X = 55, and cost of stock (S0) = $55. Option premium = $5.
• Payoff and Profit:
ST
45
50
Buy 1 share
-5
Short 1 call
0
Total payoff
-5
Profit
0
55
60
5
5
• Long stock position covers or protects a trader from the
payoff on the short call that becomes necessary if there is a
sharp increase in stock price.
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Covered call cont’d
• Payoff and profit (When strike = purchase price)
• Break-even point
• Maximum profit
• What if strike ≠ purchase price?
21
Protective Put: Long stock + long put
• Use puts to limit downside
– Often used with index options to provide portfolio insurance
• Let X = 40, S0=40
ST
35
40
45
50
Buy 1 share
10
Buy 1 put
0
Total payoff
10
Profit
5
22
Protective put cont’d
Protective put
Long stock
0
Share Price
40
Long put
Profit: You start to make $ when
Otherwise, you lose at most P.
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Straddle: Buy 1 call and 1 put (same X, T)
• e.g. S0 = 40, C = 10, P = 10, X = 50
ST
35
40
45
Buy 1 call
0
Buy 1 put
50
55
60
65
0
10
15
10
5
0
0
Total payoff
10
5
10
15
Profit
-10
-15
-10
-5
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Profit Diagram of Long Straddle
Long Straddle: Buy a Call and a Put
Value at
expiry
Buy a call with an
exercise price of
$50 for $10
$40
$30
$0
-$10
-$20
$30 $40 $50 $60
Buy a put with an
$70 exercise price of
$50 for $10
A Long Straddle only makes money if the
stock price moves $20 away from $50.
Value of
stock at
expiry
You do not make $ if
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22.7 (Arbitrage) Bounds on Call Option
• Objective: derive restrictions on option values which (i) any
reasonable option pricing model must satisfy; and (ii) do not
depend on any assumptions about the statistical distribution
of the price of the underlying asset
• To simplify matters, we will assume that no dividends are
paid by the underlying asset during the life of the option
• Let’s look at a call only:
– Fact 1: A call option with a lower exercise price is worth more.
• A call option with an exercise price of zero is effectively the
same financial security as the stock itself.
• An upper bound for the call option price is the price of the stock.
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Cont’d
– Fact 2: The option value is at least the payoff if exercised
immediately
• The action of exercising gives you the underlying asset
• However, if you want the asset
– If you exercise now you pay exercise price now
– Or better, you can exercise on the expiry day and pay the exercise
price later.
» Equivalently, if you exercise immediately, you only need to pay
the present value of (Exercise price)
• Lower bound of call: St – PV(X)
– Fact 3: As the stock price gets large (relative to exercise price)
• the probability that the option expires worthless vanishes
• the value of the call approaches:
Value of stock – PV (Exercise Price) ≈ St - X
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Bounds for Call option
ST
Call
Market Value
Time value
Intrinsic value
0
PV(X)
ST
The value of a call option Ct must fall within
Max(St – PV(X),0) < Ct < St
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Implications of Call Bounds
•
•
•
•
If St = 0 then Ct = 0.
If X = 0 then Ct = St.
If T-t = ∞, then Ct = St.
For an American option, it is not optimal to exercise a call
option before its expiry date (if the underlying stock will not pay any
dividends over the life of the option).
– Note that this implies that the value of an American call option
will be equal to that of a corresponding European option (same
underlying asset, X, T).
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It’s never optimal to exercise the American call early
• Why?
– If you exercise a call at any time t, you receive the intrinsic value: (St – X)
– But the option is always worth at least the intrinsic value.
• Example: St = 60, T - t = 3 months, X = $55, r =10%
– if you exercise you receive $5 but you lose time value of the call.
• The option is worth at least
– At least a dominant strategy is to put $55 in bank and wait until the expiry
to exercise.
• You get interest income on the $55.
– If you want the underlying, hold the option and you can buy it any time
you want.
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Call bounds example
What is the lower bound for the price of a six-month call
option on a non-dividend-paying stock when the stock price
is $80, the strike price is $75, and the risk-free interest rate is
10 percent per annum?
31
Arbitrage Bounds on Put Option Values
• For put options, we will show that
X ≥ Pt ≥ max(0, X – St)
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Arbitrage Bounds on Put Option Values (cont’d)
33
Implications of Put Option Bounds
• If St = 0 then Pt = X.
• If X = 0 then Pt = 0.
• For a European put,
and if T-t = ∞, then Pt = 0.
• It may be optimal to exercise an American put option before
its expiry date, even if the underlying asset does not pay
dividends during the life of the option (consider what
happens if S → 0)
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An aside: Continuously compounding
 In option pricing, people generally use continuously compounding
instead of discrete compounding that is used in Chapter 8.
 Continuous compounding assumes that compounding period for
effective return is as short as possible (think of milliseconds). A dollar
with nominal return of r over a period of T will become the following
continuous-time proceeds:
r mT
FV ($ 1)  lim m (1  )
 e rT
m
where m is the compounding frequency.
PV ($1)  e rT
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European options: Put-Call Parity (no dividends)
Suppose you buy one share of stock, buy one put option on the stock, and
sell one call option on the stock (same X, T). Cashflow at expiry
ST < X
ST  X
1. Buy stock
2. Buy put
3. Write call
Cashflow at expiry
• No matter what happens, you end up with a payoff of X
• Today’s value of your synthetic investments must equal PV(cf @ expiry):
St  Pt  Ct  Xer (T t )
36
Put-call parity cont’d
•
Given any three of risk free bond, stock, put, and call, the
fourth can always be created synthetically. (In fact, this was
done before 1977 on the CBOE to construct puts)
• Holding stock and put today is equal to holding a call the
PV(X) amount of riskfree bond.
St  Pt  Ct  Xer (T t )
– Note that the LHS is the value of protective put.
• You can also use the profit graph of protective put to prove
put-call parity
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Put call parity with dividend paying stocks
• We can also derive parity relationships when there are
dividends paid by the underlying asset, when the options are
American, etc.
• In the case of European options on a stock paying known
dividends before the expiry date, the result is
where It is the present value (at t) of the dividends paid
before T
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Put-call parity example 1
The price of a European call which expires in six months and
has a strike price of $30 is $2. The underlying stock price is
$29, and there is no dividend payment. The term structure is
flat, with all risk-free interest rates being 10 percent. What is
the price of a European put option that expires in six months
and has a strike price of $30?
39
Put-call parity example 2
• Several years ago, the Australian firm Bond Corporation
sold some land that it owned near Rome for $110 million
and as a result boosted its reported earnings for that year by
$74 million. The next year it was revealed that the buyer was
given a put option to sell the land back to Bond for $110
million and also that Bond had paid $20 million for a call
option to repurchase the land for the same price of $110
million.
1. What happens if the land is worth more than $110 million
when the options expire? What if it is worth less than $110
million?
2. Assuming that the options expire in one year, what is the
interest rate?
3. Was it misleading to record a profit from selling the land?
40
41
How do we value options?
• Why the discounted cash flow approach will not work?
– Expected cash flows?
– Opportunity cost of capital?
• We are going to use a replicating portfolio method
– Owning the option is equivalent to owning some number of
shares and borrowing money
– Therefore the price of the option should be the same as the
value of this replicating portfolio.
42
The Binomial Model (Two-State Option Pricing)
• In order to use the replicating portfolio method, we need to
make some assumptions about how the underlying stock
behaves
– The simplest possible setting is one in which there are only
two possible outcomes of stock price at the expiry date of 1
period (“binomial”)
• Also assume
– the underlying stock won’t pay a dividend over the life of the
option
– interest rates are constant over the life of the option
43
Example I
• Let’s assume a stock’s current price is $25. It may go up (u)
or down (d) by 15% next year, with equal probabilities.
–
–
–
–
The discount rate for the stock is 10%.
The stock has a beta of 1.
T-bills are yielding 5%.
A call option on the stock is traded on the NYSE. The strike
price of this option is 25, and the maturity is one year.
– What is the option worth?
44
The method: Replicate the payoffs of the option using
only the stock and loan
• Step 1: Find the payoffs of the option in both “good” and
“bad” states.
• Step 2: Choose the right number of shares to make the
difference in outcomes equal to the option.
• Step 3: Replicate the payoffs by adding the right size loan to
your shares
45
Example cont’d: Matching cash flows
Investment strategy
State 1 (future price =
State 2 (future price=
1. buy a call
2.
(i) Buy 0.5(delta) shares of
stock
(ii) Borrow 10.119 @ 5% a
year
Total from replicating
strategy—strategy 2
Value of the option:
46
A generalization of option replicating portfolios:
deciding delta and loan
• Form a portfolio with ∆ shares of stock and B borrowed or
invested in the risk-free bond. The current value of the
portfolio
V0 = S0 ∆ +B
• The basic idea is to pick ∆ and B to replicate the payoffs of
the call option at its expiry
• The number of shares bought, ∆, is called the hedge ratio or
option delta
• If B < 0, then it is borrowing; if B > 0, then it is lending
(investing in T-bills).
47
Solve for ∆ and B: Graph representation
t=0
t =1
S1,u , V1,u
S0, V0
S1,d , V1,d
To match the cashflows:
(1) V1,u  S1,u  B (1  r f )
(2) V1,d  S1, d  B (1  r f )
Note: rf is interest rate for the length of one period.
48
Cont’d
Solve for ∆, B:

(1) – (2),
and
B
V1,u  V1,d
S1,u  S1,d
V1,u  S1,u
1  rf
• In words:
∆ = (Spread of possible option prices)/ (Spread of possible
stock prices)
In the previous example
49
Possibly more intuitive
• You might think of option deltas as solving
(Option delta) * (Spread in Share price) = Spread in option price
– That is, the delta “scales” the amount of variation in the stock
price so that the spread of outcomes in your replicating
portfolio is the same as in the option.
• (The implicit loan in options) Note that we just showed the
call option is like a levered version of stock.
– It’s like buying the stock “bundled” with personal debt.
– Levered equity: higher risk or higher beta.
50
Optional: Example continued: Call Options are riskier than the
stock.
• Find the option’s beta.
C = S0 ∆ +B
Portfolio beta. (Answer: 5.25)
51
Valuing the put option
• Method 1: Same as before.
– Find the option’s delta
• Option Delta = (Spread of possible option prices)/(Spread
of possible stock prices)
– Then find the bank loan that equates the payoff of option and
the payoff of (stock position + loan)
• Method 2:
– Since we already have the call option value, just use put-call
parity to infer the put option value.
52
Exercise: Suppose Example I is a put option instead of a call.
Use the binomial model to find its delta, replicate the
payoffs, and find the value of the put.

V1,u  V1,d
S1,u  S1,d
B
V1,u  S1,u
1  rf

Put graph here.

P = S0 ∆ +B =
Interpret ∆ and B for put:
53
Implication of irrelevance of the underlying’s
expected return in the real world
• The option value does not directly depend on:
– Probabilities and expected returns of the underlying
– Individual preferences about risk aversion
• If there are just options traded, expected return from the option payoffs
should be the same, which is the riskfree rate.
– Indirectly, these factors do affect the option value, but only by determining
the current stock price S0
• A very useful trick that can be used to simplify calculations is to exploit
the fact that investors’ risk aversion doesn’t matter and just assume that
they are risk-neutral
• In this case, all assets should earn the risk free rate of return
1) Expected returns of stock = riskfree rate
2) Expected option payoffs = option value (1 + riskfree rate)
54
Binomial option pricing: risk neutral pricing
S1,u , V1,u
q
Let S1,u = u S0 and
S0, V0
S1,d = d S0
1- q
S1,d , V1,d
• The key is to find risk-neutral probabilities for stock price
movements. Let q be the “risk-neutral” probability of an “up”
move.
• To find q, by meaning (1) of previous slide, we have
S0 
q  S1,u  (1  q )  S1,d
(1  rf )
q  u  S 0  (1  q )  d  S 0

(1  rf )
55
Risk neutral pricing
• A minor bit of algebra yields:
(1  rf )  S0  S1, d (1  rf )  d
q

S1,u  S1, d
ud
• By meaning (2) of previous slide, value of option can now
be derived as:
V0 
q  V1,u  (1  q)  V1, d
(1  rf )
• A big advantage of risk-neutral pricing is we can circumvent
the dynamic hedging nuisance in multi-period pricing.
56
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% for one-period. What is the value of an at-the-money call
option with a maturity of one-period?
$28.75  $25  (1.15)
The binomial tree
q
$25,C0
$28.75,C1,u
$21.25  $25  (1  .15)
1- q
$21.25,C1,d
57
Example cont’d
• Step 1: Compute risk neutral probabilities
• Step 2: Find the value of the call in the up state and down
state
• Step 3: Find the value of the call at time 0.
58
Exercise
Suppose the option is a put in Example I. Use risk-neutrality to
value the put. (You should be able to do this without the help
of graphs.)
59
Binomial to Black Scholes
Expanding the binomial model to allow more possible
price changes
1 step
2 steps
4 steps
(2 outcomes)
(3 outcomes)
(5 outcomes)
etc. etc.
60
The Black-Scholes Model
• As the number of intervals N , underlying stock price follows
a random walk with a positive growth rate.
• In this case, solving the option value using the portfolio
replicating method yields the famous Black-Scholes equations.
•Solving the Black-Scholes equations for the basic version of
European call options with no dividends yields the Black-Scholes
formula:
Ct  St N (d1 )  Xer (T t ) N (d2 )
Where
S
1
ln( t )  ( r   2 )( T  t )
X
2
d1 
 T t
d 2  d1   ( T  t )
61
5 inputs:
1.
2.
3.
4.
5.
Inputs to Black-Scholes
X: Strike
S: Spot (current stock price)
σ = annual standard deviation of underlying stock’s return
r = continuously compounded annual risk free interest rate
T-t: Time to maturity expressed as fraction of year
N(.) is the cumulative standard normal distribution function, i.e.,
N(d1) is the probability that a variable distributed normally with
mean zero and standard deviation of one will be less than or
equal to d1
Note that we don’t need expected return of the underlying asset
to figure out the stock option value.
62
Black-Scholes and Binomial Methods
Com paring:
Ct  St N (d1 )  Xe r (T t ) N (d 2 )
with
Ct  S t   B
1. N(d1) is delta, the number of shares held in the replicating portfolio
2. The amount borrowed is Xe r( T  t ) N ( d 2 )
63
Some properties of Standard Normal Distribution
N(d1 = 3) = 0.9987: There is 99.87% probability that a drawing
from a standard normal distribution will be below 3.
N(0) = 0.5, N(+∞)=1
N(-d1) = 1 - N(d1)
N(d1 = 0) = 0.5
64
Table 23.3 Cumulative Probabilities of Standard Normal Dist’n
d
0.00
0.00
0.01
0.02
0.03
0.0000
0.0040
0.0080
0.0120
…
0.09
0.0359
0.10
0.20
0.0793
0.0910
0.4987
0.4988
…
…
3.00
0.4990
N(0.23) =
N(-0.23) =
In excel, the function is normsdist( ).
65
Linear Interpolation
N (-0.0886) = ?
From Table 23.3:
N ( - 0.08) = 0.5 – 0.0319 = 0.4681
N ( - 0.09) = 0.5 – 0.0359 = 0.4641
• Linear interpolation:
• Exercise
N(0.0886) =
66
Black-Scholes Value of Put
The corresponding Black-Scholes formula for puts is:
Pt  Xer( T t ) N( d 2 )  St N ( d1 )
• Exercise: Prove that the B-S call and put formulae satisfy the
put-call parity.
67
Example
Call option. Inputs: T-t = 0.25 (time to expiry 3 months), St = $53, X =
$55, r =.05,  = 0.30. What’s the value of the call? (2.5895)
Ct  St N (d1 )  Xer (T t ) N (d2 )
S
1
ln( t )  ( r   2 )( T  t )
X
2
d1 
 T t
N(d2) =
N(d1) =
d 2  d1   ( T  t )
Xe r( T t )
C=
68
Example cont’d
• What is the value of the corresponding put option? (3.9063)
Pt  Xer (T t ) N (d2 )  St N (d1 )
69
Factors determining option values
Ct  St N ( d1 )  Xe r( T t ) N ( d 2 )
Pt  Xer( T t ) N( d 2 )  St N ( d1 )
Volatility is probably the most important consideration in
options, since option value is very sensitive to volatility.
70
The Black-Scholes Model with Dividends (European options)
• Options are protected against stock splits but not cash dividends.
• Two possible adjustment to B-S value for dividends:
1. Discrete dividend payments:
– For options on a single stock, one approach is to assume that
dividends are known up to the option expiry date. The
underlying stock is then viewed as consisting of two
components:
• A risk free series of dividends known up until T
• The risky stock value
– Effectively the spot price is lower from the perspective of
option holder.
 Replace in the B-S formula S with the new after-dividend S, i.e.,
with S – PV(Dividend).
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Example
• S = 50, X = 45, σ = 20%, rf = 6%, t = 3 mths, div. = $0.50
(payable in 2 mths)
S = 50
0
Div = $2
2
X = 45
3
• Adjust the stock price
S’ = 50 – 0.50 e(-0.06* 2/12) = 49.505
• Recalculate the BS call value using S’ instead of S
throughout. (C = 5.494)
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2. Continuous Dividend Yield
• In some cases it is reasonable to assume that dividends are paid
continuously as a known percentage of the value of the underlying
asset.
•Examples include stock indexes, foreign currencies and futures
contracts
• If an asset pays a continuous dividend yield q, we would do the
similar adjustment.
• Adjust back dividend to St :
 Replace St with S e q (T t )
t
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Example
• S = 50, X = 45, σ = 20%, rf = 6%, t = 3 mths, q = 4%
• Adjust the stock price
S’ = 50 e(-0.04* 3/12) = 49.502
Recalculate the BS call value using S’ instead of S
throughout. ( C = 5.491)
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Review Questions
1. Two stocks have identical firm-specific risks but different
betas. All else being equal, a put option on the high-beta
stock is worth more than one on the low-beta stock.
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2. Value of portfolio of options and option on portfolios:
Suppose you have two stocks (stocks 1 and 2) in a portfolio. The return
correlation of the two stocks is 0.5. Currently, stocks 1 and 2 are both
trading at $20, and both stocks have same volatility. The weight of
stock 1 in the portfolio is 0.5, and the weight of stock 2 is also 0.5.
There are three call options, written on stock 1, stock 2 and the portfolio
respectively, all with same X and T.
(1) Which option is the most expensive?
(2) Which option is the least expensive?
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• Assigned problems: #23.3, 5-7, 10, 13, 14, 17, 19, 21, 24, 25,
26, 29, 32, 33
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Myron S. Scholes
The Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel 1997
Autobiography
I was born in Timmins, Ontario, Canada on July 1, 1941. My father had ventured to Timmins, a relatively prosperous goldmining region, to practice dentistry during the depression. My mother and her uncle established a chain of small
department stores in and around Timmins. The death of her uncle resulted in a family dispute, my first exposure to
agency and contracting problems. To my benefit, my mother then devoted her time to raising her two sons. At the age of
ten, we moved 500 miles south to Hamilton, Ontario.
I was a good student, ranking near the top of my class. Soon after we arrived in Hamilton, my life changed dramatically.
My mother developed cancer. She died a few days after my sixteenth birthday. Another shock awaited me. I developed
scar tissue on each of my corneas that impaired my eyesight. It was difficult to read for extended periods of time. I
learned to think abstractly and to conceptualize the solution to problems. Out of necessity, I became a good listener --a
quality appreciated by subsequent associates and students. Luckily, at age twenty-six, a successful cornea transplant
greatly improved my vision.
……
For a full autobiography, go to http://nobelprize.org/nobel_prizes/economics/laureates/1997/scholes-autobio.html.
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