for homework help1234 wk7

Here is what we discussed. Will see you on Friday to retrieve the work and do the other as we agreed. ok thank you so much

I even added chapt 8 school presentation to help you as a guide if you need it.

Ch08 P08 Build a Model

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Spring 2, 2013

7/22/12

Chapter 8. Ch 08 P08 Build a Model

Except for charts and answers that must be written, only Excel formulas that use cell references or functions will be accepted for credit.

Numeric answers in cells will not be accepted.

You have been given the following information on a call option on the stock of Puckett Industries:

P

=

$65

X =

$70

t =

0.5

rRF =

4%

s =

50.00%

a. Using the Black-Scholes Option Pricing Model, what is the value of the call option?

First, we will use formulas from the text to solve for d1 and d2.

Hint: use the NORMSDIST function.

(d1)

N(d1) =

(d2)

N(d2) =

Using the formula for option value and the values of N(d) from above, we can find the call option value.

VC

b. Suppose there is a put option on Puckett’s stock with exactly the same inputs as the call option. What is the value of the put?

Put option using Black-Scholes modified formula

Put option using put-call parity

Sheet2

7/22/12

Week 7 Cengage Homework

1. Deeble Construction Co.’s stock is trading at $30 a share. Call options on the company’s stock are also available, some with a strike price of $25 and some with a strike price of $35. Both options expire in three months. Which of the following best describes the value of these options?

a. The options with the $25 strike price have an exercise value greater than $5.

b. The options with the $35 strike price have an exercise value greater than $0.

c. The options with the $25 strike price will sell for less than the options with the $35 strike price.

d. If Deeble’s stock price rose by $5, the exercise value of the options with the $25 strike price would also increase by $5.

e. The options with the $25 strike price will sell for $5.

2. Suppose you believe that Delva Corporation’s stock price is going to decline from its current level of $82.50 sometime during the next 5 months. For $510.25 you could buy a 5-month put option giving you the right to sell 100 shares at a price of $85 per share. If you bought this option for $510.25 and Delva’s stock price actually dropped to $60, what would your pre-tax net profit be?

a. $1,989.75

b. $2,193.70

c. $510.25

d. $2,089.24

e. $2,303.38

3. Problem 8-2
Options

The exercise price on one of Flanagan Company’s options is $15, its exercise value is $23, and its time value is $4. What are the option’s market value and the price of the stock?

Market value	$
Price of the stock	$

4. Which of the following statements is CORRECT?

a. An option holder is not entitled to receive dividends unless he or she exercises their option before the stock goes ex dividend.

b. Put options give investors the right to buy a stock at a certain strike price before a specified date.

c. LEAPS are very short-term options that were created relatively recently and now trade in the market.

d. Call options give investors the right to sell a stock at a certain strike price before a specified date.

e. Options typically sell for less than their exercise value.

5. Which of the following statements is CORRECT?

a. An option’s value is determined by its exercise value, which is the market price of the stock less its striking price. Thus, an option can’t sell for more than its exercise value.

b. Issuing options provides companies with a low cost method of raising capital.

c. The market value of an option depends in part on the option’s time to maturity and also on the variability of the underlying stock’s price.

d. As the stock’s price rises, the time value portion of an option on a stock increases because the difference between the price of the stock and the fixed strike price increases.

e. The potential loss on an option decreases as the option sells at higher and higher prices because the profit margin gets bigger.

6. Problem 8-1
Options

A call option on the stock of Bedrock Boulders has a market price of $6. The stock sells for $30 a share, and the option has an exercise price of $25 a share.What is the exercise value of the call option?
$  

What is the option’s time value?
$  

7. Call options on XYZ Corporation’s common stock trade in the market. Which of the following statements is most correct, holding other things constant?

a. Assuming the same strike price, an XYZ call option that expires in one month will sell at a higher price than one that expires in three months.

b. The price of these call options is likely to rise if XYZ’s stock price rises.

c. If XYZ pays a dividend, then its option holders will not receive a cash payment, but the strike price of the option will be reduced by the amount of the dividend.

d. The higher the strike price on XYZ’s options, the higher the option’s price will be.

e. If XYZ’s stock price stabilizes (becomes less volatile), then the price of its options will increase.

8. The current price of a stock is $50, the annual risk-free rate is 6%, and a 1-year call option with a strike price of $55 sells for $7.20. What is the value of a put option, assuming the same strike price and expiration date as for the call option?

a. $7.71

b. $8.12

c. $8.55

d. $7.33

e. $9.00

9. An option that gives the holder the right to sell a stock at a specified price at some future time is

a. a call option.

b. a covered option.

c. an out-of-the-money option.

d. a put option.

e. a naked option.

Sheet1

$  

$  

$  

1.     Deeble Construction Co.’s stock is trading at $30 a share. Call options on the company’s stock are also available, some with a strike price of $25 and some with a strike price of $35. Both options expire in three months. Which of the following best describes the value of these options?
2. Suppose you believe that Delva Corporation’s stock price is going to decline from its current level of $82.50 sometime during the next 5 months. For $510.25 you could buy a 5-month put option giving you the right to sell 100 shares at a price of $85 per share. If you bought this option for $510.25 and Delva’s stock price actually dropped to $60, what would your pre-tax net profit be?
3. The exercise price on one of Flanagan Company’s options is $15, its exercise value is $23, and its time value is $4. What are the option’s market value and the price of the stock?
Market value
			$
Price of the stock
4.     Which of the following statements is CORRECT?
5.  Which of the following statements is CORRECT?
6. A call option on the stock of Bedrock Boulders has a market price of $6. The stock sells for $30 a share, and the option has an exercise price of $25 a share.What is the exercise value of the call option?
What is the option’s time value?
7.  Call options on XYZ Corporation’s common stock trade in the market. Which of the following statements is most correct, holding other things constant?
8. The current price of a stock is $50, the annual risk-free rate is 6%, and a 1-year call option with a strike price of $55 sells for $7.20. What is the value of a put option, assuming the same strike price and expiration date as for the call option?
9.  An option that gives the holder the right to sell a stock at a specified price at some future time is

1

Chapter 8

Financial Options and

Applications in Corporate Finance

2

Topics in Chapter

Financial Options Terminology

Option Price Relationships

Black-Scholes Option Pricing Model

Put-Call Parity

3

Stock Price = + + +
D1
D2
D∞
(1 + rs )1
(1 + rs)∞
(1 + rs)2

Dividends (Dt)
Risk-free bond
Portfolio of stock and
risk-free bond that
replicates cash flows
of the option
Value of option must
be the same as the
replicating portfolio
Cost of
equity (rs)
The Big Picture:
The Value of a Stock Option
…

For value box in Ch 4 time value FM13.
‹#›

4
What is a financial option?
An option is a contract which gives its holder the right, but not the obligation, to buy (or sell) an asset at some predetermined price within a specified period of time.

5
What is the single most important
characteristic of an option?
It does not obligate its owner to take any action. It merely gives the owner the right to buy or sell an asset.

6
Option Terminology
Call option: An option to buy a specified number of shares of a security within some future period.
Put option: An option to sell a specified number of shares of a security within some future period.

7
Option Terminology
Strike (or exercise) price: The price stated in the option contract at which the security can be bought or sold.
Expiration date: The last date the option can be exercised.

8
Option Terminology (Continued)
Exercise value: The value of a call option if it were exercised today =
Max[0, Current stock price – Strike price]
Note: The exercise value is zero if the stock price is less than the strike price.
Option price: The market price of the option contract.

9
Option Terminology (Continued)
Time value: Option price minus the exercise value. It is the additional value because the option has remaining time until it expires.

10
Option Terminology (Continued)
Writing a call option: For every new option, there is an investor who “writes” the option.
A writer creates the contract, sells it to another investor, and must fullfill the option contract if it is exercised.
For example, the writer of a call must be prepared to sell a share of stock to the investor who owns the call.

11
Option Terminology (Continued)
Covered option: A call option written against stock held in an investor’s portfolio.
Naked (uncovered) option: An option written without the stock to back it up.

12
Option Terminology (Continued)
In-the-money call: A call whose strike price is less than the current price of the underlying stock.
Out-of-the-money call: A call option whose strike price exceeds the current stock price.

13
Option Terminology (Continued)
LEAPS: Long-term Equity AnticiPation Securities that are similar to conventional options except that they are long-term options with maturities of up to 2 ½ years.

14
Consider the following data:
Strike price = $25.
Stock Price Call Option Price
$25 $3.00
30 7.50
35 12.00
40 16.50
45 21.00
50 25.50

15
Exercise Value of Option
Price of
stock (a) Strike
price (b) Exercise value
of option (a)–(b)
$25.00 $25.00 $0.00
30.00 25.00 5.00
35.00 25.00 10.00
40.00 25.00 15.00
45.00 25.00 20.00
50.00 25.00 25.00

16
Market Price of Option
Price of
stock (a) Strike
price (b) Exer.
val. (c) Mkt. Price
of opt. (d)
$25.00 $25.00 $0.00 $3.00
30.00 25.00 5.00 7.50
35.00 25.00 10.00 12.00
40.00 25.00 15.00 16.50
45.00 25.00 20.00 21.00
50.00 25.00 25.00 25.50

17
Time Value of Option
Price of
stock (a) Strike
price (b) Exer.
Val. (c) Mkt. P of
opt. (d) Time value
(d) – (c)
$25.00 $25.00 $0.00 $3.00 $3.00
30.00 25.00 5.00 7.50 2.50
35.00 25.00 10.00 12.00 2.00
40.00 25.00 15.00 16.50 1.50
45.00 25.00 20.00 21.00 1.00
50.00 25.00 25.00 25.50 0.50

18

5 10 15 20 25 30 35 40
Stock Price
Option value
30
25
20
15
10
5

Market price
Exercise value
Call Time Value Diagram

19
Option Time Value Versus Exercise Value
The time value, which is the option price less its exercise value, declines as the stock price increases.
This is due to the declining degree of leverage provided by options as the underlying stock price increases, and the greater loss potential of options at higher option prices.

20
The Binomial Model
Stock assumptions:
Current price: P = $27
In next 6 months, stock can either
Go up by factor of 1.41
Go down by factor of 0.71
Call option assumptions
Expires in t = 6 months = 0.5 years
Exercise price: X = $25
Risk-free rate: rRF = 6%

21
Binomial Payoffs at Call’s Expiration
Current
stock price
P = $27
Ending “up” stock price = P(u) = $38.07
Option payoff: Cu = MAX[0,P(u)−X] = $13.07
Ending “down” stock price = P(d) = $19.17
Option payoff: Cd = MAX[0,P(d)−X] = $0.00
u = 1.41
d = 0.71
X = $25

22
Create portfolio by writing 1 option and buying Ns shares of stock.
Portfolio payoffs:
Stock is up: Ns(P)(u) − Cu
Stock is down: Ns(P)(d) − Cd

23
The Hedge Portfolio with a Riskless Payoff
Set payoffs for up and down equal, solve for number of shares:
Ns= (Cu − Cd) / P(u − d)
In our example:
Ns= ($13.07 − $0) / $27(1.41 − 0.71)
Ns=0.6915

24
Riskless Portfolio’s Payoffs at Call’s Expiration: $13.26
Current
stock price
P = $27
Ending “up” stock price = P(u) = $38.07
Ending “up” stock value = NsP(u) = $26.33
Option payoff: Cu = MAX[0,P(u)−X] = $13.07
Portfolio’s net payoff = P(u)Ns – Cu = $13.26
Ending “down” stock price = P(d) = $19.17
Ending “down” stock value = NsP(d) = $13.26
Option payoff: Cd = MAX[0,P(d)−X] = $0.00
Portfolio’s net payoff = P(d)Ns – Cd = $13.26
u = 1.41
d = 0.71
X = $25
Ns = 0.6915

25
Riskless payoffs earn the risk-free rate of return.
Discount at risk-free rate compounded daily.
VPortfolio = PV of riskless payoff
VPortfolio = Payoff / (1 + rRF/365)365*t
VPortfolio = $13.26 / (1 + 0.06/365)365*0.5
VPortfolio = $12.87

26
The Value of the Call Option
Because the portfolio is riskless:
VPortfolio = PV of riskless payoff
By definition, the value of the portfolio is:
VPortfolio = Ns(P) − VC
Equating these and rearranging, we get the value of the call:
VC = Ns(P) − PV of riskless payoff

27
Value of Call
VC = Ns(P) − Payoff / (1 + rRF/365)365*t
VC = 0.6915($27)
− $13.26 / (1 + 0.06/365)365*0.5
= $18.67 − $12.87
= $5.80
(VC = $5.81 if no rounding in any intermediate steps.)

28
Multi-Period Binomial Pricing
If you divided time into smaller periods and allowed the stock price to go up or down each period, you would have a more reasonable outcome of possible stock prices when the option expires.
This type of problem can be solved with a binomial lattice.
As time periods get smaller, the binomial option price converges to the Black-Scholes price, which we discuss in later slides.

29
Replicating Portfolio
From the previous slide we have:
VC = Ns(P) − Payoff / (1 + rRF/365)365*t
The right side of the equation is the same as creating a portfolio by buying Ns shares of stock and borrowing an amount equal to the present value of the hedge portfolio’s riskless payoff (which must be repaid).
The payoffs of the replicating portfolio are the same as the option’s payoffs.

30
Replicating Portfolio Payoffs: Amount Borrowed and Repaid
Amount borrowed:
PV of payoff = $12.87
Repayment due to borrowing this amount:
Repayment = $12.87 (1 + rRF/365)365*t
Repayment = $13.26
Notice that this is the same as the payoff of the hedge portfolio.

31
Replicating Portfolio Net Payoffs
Stock up:
Value of stock = 0.6915($38.07) =$26.33
Repayment of borrowing = $13.26
Net portfolio payoff = $13.07
Stock down:
Value of stock = 0.6915($19.17) =$13.26
Repayment of borrowing = $13.26
Net portfolio payoff = $0
Notice that the replicating portfolio’s payoffs exactly equal those of the option.

32
Replicating Portfolios and Arbitrage
The payoff’s of the replicating portfolio exactly equal those of the call option.
Cost of replicating portfolio
= Ns(P) − Amount borrowed
= 0.6915($27) − $12.87
= $18.67 − $12.87
= $5.80
If the call option’s price is not the same as the cost of the replicating portfolio, then there will be an opportunity for arbitrage.

33
Arbitrage Example
Suppose the option sells for $6.
You can write option, receiving $6.
Create replicating portfolio for $5.80, netting $6.00 −$5.80 = $0.20.
Arbitrage:
You invested none of your own money.
You have no risk (the replicating portfolio’s payoffs exactly equal the payoffs you will owe because you wrote the option.
You have cash ($0.20) in your pocket.

34
Arbitrage and Equilibrium Prices
If you could make a sure arbitrage profit, you would want to repeat it (and so would other investors).
With so many trying to write (sell) options, the extra “supply” would drive the option’s price down until it reached $5.80 and there were no more arbitrage profits available.
The opposite would occur if the option sold for less than $5.80.

35
Assumptions of the
Black-Scholes Option Pricing Model
The stock underlying the call option provides no dividends during the call option’s life.
There are no transactions costs for the sale/purchase of either the stock or the option.
Risk-free rate, rRF, is known and constant during the option’s life.
(More…)

36
Assumptions (Continued)
Security buyers may borrow any fraction of the purchase price at the short-term risk-free rate.
No penalty for short selling and sellers receive immediately full cash proceeds at today’s price.
Call option can be exercised only on its expiration date.
Security trading takes place in continuous time, and stock prices move randomly in continuous time.

37
VC = P[N(d1)] – Xe -rRFt[N(d2)]
d1 =

 t 0.5
d2 = d1 –  t 0.5
ln(P/X) + [rRF + (2/2)]t
What are the three equations that make up the OPM?

38
What is the value of the following call option according to the OPM?
Assume:
P = $27
X = $25
rRF = 6%
t = 0.5 years
σ = 0.49

39
d1 = {ln($27/$25) + [(0.06 + 0.492/2)](0.5)}
÷ {(0.49)(0.7071)}
d1 = 0.4819
d2 = 0.4819 – (0.49)(0.7071)
d2 = 0.1355
First, find d1 and d2.

40
Second, find N(d1) and N(d2)
N(d1) = N(0.4819) = 0.6851
N(d2) = N(0.1355) = 0.5539
Note: Values obtained from Excel using NORMSDIST function. For example:
N(d1) = NORMSDIST(0.4819)

16

‹#›

41
Third, find value of option.
VC = $27(0.6851) – $25e-(0.06)(0.5)(0.5539)
= $19.3536 – $25(0.97045)(0.6327)
= $5.06

42
What impact do the following parameters have on a call option’s value?
Current stock price: Call option value increases as the current stock price increases.
Strike price: As the exercise price increases, a call option’s value decreases.

43
Impact on Call Value (Continued)
Option period: As the expiration date is lengthened, a call option’s value increases (more chance of becoming in the money.)
Risk-free rate: Call option’s value tends to increase as rRF increases (reduces the PV of the exercise price).
Stock return variance: Option value increases with variance of the underlying stock (more chance of becoming in the money).

44
Put Options
A put option gives its holder the right to sell a share of stock at a specified stock on or before a particular date.

45
Put-Call Parity
Portfolio 1:
Put option,
Share of stock, P
Portfolio 2:
Call option, VC
PV of exercise price, X

46
Portfolio Payoffs at Expiration Date T for PT