Question 1

Which of the following statements regarding American puts is/are true?

Accepted Answer

A) An American put can be exercised any time before expiration. 
B) An American put is always at least as valuable as an equivalent European put. 
C) A multi-period binomial model can be used to value an American put. 
D) All of the options are true. 
A) An American put can be exercised any time before expiration. 
B) An American put is always at least as valuable as an equivalent European put. 
C) A multi-period binomial model can be used to value an American put. 
D) All of the options are true.

Question 2

If u equals the quantity (1 + upside change), then the quantity (1 + downside change)is equal to

Accepted Answer

A) −u. 
B) −1/u. 
C) 1/u. 
D) 1 − u. 
A) −u. 
B) −1/u. 
C) 1/u. 
D) 1 − u.

Question 3

Why does a discounted cash-flow approach to options valuation not work?

Accepted Answer

A) It is impossible to estimate expected cash flows. 
B) One cannot find the appropriate interest rate for an infinitely small interval. 
C) Finding the opportunity cost of capital is impossible as the risk of options changes every time the stock price moves. 
D) The strike price of options changes. 
A) It is impossible to estimate expected cash flows. 
B) One cannot find the appropriate interest rate for an infinitely small interval. 
C) Finding the opportunity cost of capital is impossible as the risk of options changes every time the stock price moves. 
D) The strike price of options changes.

Question 4

If the value of d is −0.75, calculate the value of N(d).

Accepted Answer

A) 0.2266 
B) 0.6914 
C) 0.7734 
D) 0.5987 
A) 0.2266 
B) 0.6914 
C) 0.7734 
D) 0.5987

Question 5

If the standard deviation of the continuously compounded returns on the asset is 20 percent and the interval is one half of a year, then the downside change is equal to

Accepted Answer

A) −37.9 percent. 
B) −19.3 percent. 
C) −20.1 percent. 
D) −13.2 percent. 
A) −37.9 percent. 
B) −19.3 percent. 
C) −20.1 percent. 
D) −13.2 percent.

Question 6

Give an example of an option equivalent investment using common stock and borrowing.

Accepted Answer

The current price of a stock is $40. The

Question 7

The option delta for a put option is always positive.

Accepted Answer

A) True 
 B)False

Question 8

Suppose ABC's stock price is currently $25. In the next six months it will either fall to $15 or rise to $40. What is the current value of a six-month call option with an exercise price of $20? The six-month risk-free interest rate is 5 percent (periodic rate). [Use the risk-neutral valuation method.]

Accepted Answer

A) $20.00 
B) $8.57 
C) $9.52 
D) $13.10 
A) $20.00 
B) $8.57 
C) $9.52 
D) $13.10

Question 9

Suppose ACC's stock price is currently $25. In the next six months it will either fall to $15 or rise to $40. What is the current value of a six-month call option with an exercise price of $20? The six-month risk-free interest rate is 5 percent per six-month period. (Use the replicating portfolio method.)

Accepted Answer

A) $20.00 
B) $8.57 
C) $9.52 
D) $13.10 
A) $20.00 
B) $8.57 
C) $9.52 
D) $13.10

Question 10

Considering the standard deviation of returns in option pricing,
1 + upside change = u = e^(σ   
).

Accepted Answer

A) True 
 B)False

Question 11

Explain what implied volatility, as measured by the VIX, may mean to the overall stock market.

Accepted Answer

The VIX measures the standard deviation

Question 12

A stock is currently selling for $50. The stock price could go up by 10 percent or fall by 5 percent each month. The monthly risk-free interest rate is 1 percent. Calculate the price of an American put option on the stock with an exercise price of $55 and a maturity of two months. (Use the two-stage binomial method.)

Accepted Answer

A) $5.10 
B) $3.96 
C) $4.78 
D) $1.19 
A) $5.10 
B) $3.96 
C) $4.78 
D) $1.19

Question 13

Briefly explain how to choose the up and down values for the binomial method.

Accepted Answer

[1 + upside change] = e^σ (SQRT(h))and [1

Question 14

Suppose Ralph's stock price is currently $50. In the next six months it will either fall to $30 or rise to $80. What is the option delta of a call option with an exercise price of $50?

Accepted Answer

A) 0.375 
B) 0.500 
C) 0.600 
D) 0.750 
A) 0.375 
B) 0.500 
C) 0.600 
D) 0.750

Question 15

Cola Company options have an exercise price of $45 and expire in 156 days. The current price of Cola Company stock is $44.375. The (annually compounded)risk-free rate is 7 percent per year and the standard deviation of Cola Company's stock returns is 0.31. Calculate d1.

Accepted Answer

A) 0.0226 
B) 0.1750 
C) −0.3157 
D) 0.3157 
A) 0.0226 
B) 0.1750 
C) −0.3157 
D) 0.3157

Question 16

Suppose VS's stock price is currently $20. In the next six months it will either fall to $10 or rise to $30. What is the current value of a put option with an exercise price of $15? The six-month risk-free interest rate is 5 percent per six-month period.

Accepted Answer

A) $5.00 
B) $2.14 
C) $0.86 
D) $7.86 
A) $5.00 
B) $2.14 
C) $0.86 
D) $7.86

Question 17

Assume the following data: Stock price = $50; Exercise price = $45; Risk-free rate = 6 percent per year; Continuously compounded variance = 0.2; Expiration = three months. Calculate the value of a European call option. (Use the Black-Scholes formula.)

Accepted Answer

A) $7.62 
B) $7.90 
C) $5 
D) $5.92 
A) $7.62 
B) $7.90 
C) $5 
D) $5.92

Question 18

Suppose VS's stock price is currently $20. In the next six months it will either fall by 50 percent or rise by 50 percent. What is the current value of a call option with an exercise price of $15 and expiration of one year? The six-month risk-free interest rate is 5 percent (periodic rate). Use the two-stage binomial method.

Accepted Answer

A) $5.00 
B) $2.14 
C) $7.86 
D) $8.23 
A) $5.00 
B) $2.14 
C) $7.86 
D) $8.23

Question 19

N(d1)and N(d2)represent cumulative probabilities and therefore take values between 0 and 1.

Accepted Answer

A) True 
 B)False

Question 20

If the value of d1 is 1.25, then the value of N(d1)is equal to

Accepted Answer

A) 0.1056. 
B) 1.2500. 
C) 0.2500. 
D) 0.8944. 
A) 0.1056. 
B) 1.2500. 
C) 0.2500. 
D) 0.8944.

Exam 21: Valuing Options

Which of the following statements regarding American puts is/are true?

If u equals the quantity (1 + upside change), then the quantity (1 + downside change)is equal to

Why does a discounted cash-flow approach to options valuation not work?

If the value of d is −0.75, calculate the value of N(d).

If the standard deviation of the continuously compounded returns on the asset is 20 percent and the interval is one half of a year, then the downside change is equal to

Give an example of an option equivalent investment using common stock and borrowing.

The option delta for a put option is always positive.

Considering the standard deviation of returns in option pricing, 1 + upside change = u = e^(σ ).

Explain what implied volatility, as measured by the VIX, may mean to the overall stock market.

Briefly explain how to choose the up and down values for the binomial method.

Suppose Ralph's stock price is currently $50. In the next six months it will either fall to $30 or rise to $80. What is the option delta of a call option with an exercise price of $50?

Cola Company options have an exercise price of $45 and expire in 156 days. The current price of Cola Company stock is $44.375. The (annually compounded)risk-free rate is 7 percent per year and the standard deviation of Cola Company's stock returns is 0.31. Calculate d1.

Suppose VS's stock price is currently $20. In the next six months it will either fall to $10 or rise to $30. What is the current value of a put option with an exercise price of $15? The six-month risk-free interest rate is 5 percent per six-month period.

Assume the following data: Stock price = $50; Exercise price = $45; Risk-free rate = 6 percent per year; Continuously compounded variance = 0.2; Expiration = three months. Calculate the value of a European call option. (Use the Black-Scholes formula.)

N(d1)and N(d2)represent cumulative probabilities and therefore take values between 0 and 1.

If the value of d1 is 1.25, then the value of N(d1)is equal to

Introduction to Corporate Finance

How to Calculate Present Values

Valuing Bonds

The Value of Common Stocks

Net Present Value and Other Investment Criteria

Making Investment Decisions With the Net Present Value Rule

Introduction to Risk and Return

Portfolio Theory and the Capital Asset Pricing Model

Risk and the Cost of Capital

Project Analysis

How to Ensure That Projects Truly Have Positive Npvs

Agency Problems and Investment

Efficient Markets and Behavioral Finance

An Overview of Corporate Financing

How Corporations Issue Securities

Payout Policy

Does Debt Policy Matter

How Much Should a Corporation Borrow

Financing and Valuation

Understanding Options

Real Options

Credit Risk and the Value of Corporate Debt

The Many Different Kinds of Debt

Leasing

Managing Risk

Managing International Risks

Financial Analysis

Financial Planning

Working Capital Management

Mergers

Corporate Restructuring

Governance and Corporate Control Around the World

Filters

N(d₁)and N(d₂)represent cumulative probabilities and therefore take values between 0 and 1.