Question 1

In a two-period binomial world, a mispriced call will lead to an arbitrage profit if

Accepted Answer

A)  the proper hedge ratio is maintained over the two periods 
B)  the hedge portfolio is terminated after one period 
C)  the option goes from over- to underpriced or vice versa 
D)  the option remains mispriced over both periods 
E)  none of the above 
A)  the proper hedge ratio is maintained over the two periods 
B)  the hedge portfolio is terminated after one period 
C)  the option goes from over- to underpriced or vice versa 
D)  the option remains mispriced over both periods 
E)  none of the above

Question 2

Which of the following statements about the binomial model is incorrect?

Accepted Answer

A)  it converges to the Black-Scholes-Merton model 
B)  it can accommodate early exercise 
C)  it allows only two stock prices at expiration 
D)  it can be extended to a large number of time periods 
E)  none of the above 
A)  it converges to the Black-Scholes-Merton model 
B)  it can accommodate early exercise 
C)  it allows only two stock prices at expiration 
D)  it can be extended to a large number of time periods 
E)  none of the above

Question 3

What is the value of the call if the stock goes up, then down?

Accepted Answer

A)  0.96 
B)  16.80 
C)  8.00 
D)  0.00 
E)  none of the above 
A)  0.96 
B)  16.80 
C)  8.00 
D)  0.00 
E)  none of the above

Question 4

The binomial option pricing formula will conform to the European lower bound.

Accepted Answer

A) True 
 B)False

Question 5

When the number of time periods in a binomial model is large, a European call option value does what?

Accepted Answer

A)  fluctuates around its intrinsic value 
B)  converges to a specific value 
C)  increases without limit 
D)  converges to the European lower bound 
E)  none of the above 
A)  fluctuates around its intrinsic value 
B)  converges to a specific value 
C)  increases without limit 
D)  converges to the European lower bound 
E)  none of the above

Question 6

If the binomial model is extended to multiple periods for a fixed option life, which of the following adjustments must be made?

Accepted Answer

A)  the up and down factors must be increased 
B)  the risk-free rate must be increased 
C)  the up and down factors and the risk-free rate must be decreased 
D)  the initial stock price must be proportionately reduced 
E)  none of the above 
A)  the up and down factors must be increased 
B)  the risk-free rate must be increased 
C)  the up and down factors and the risk-free rate must be decreased 
D)  the initial stock price must be proportionately reduced 
E)  none of the above

Question 7

The single period binomial hedge ratio for stock call options could be computed by equating the two future cash flows -- from a portfolio of long h shares of stock and short one call -- and solve for the number of underlying stocks to hold.

Accepted Answer

A) True 
 B)False

Question 8

What would be the call's price if the stock goes up?

Accepted Answer

A)  3.60 
B)  8.00 
C)  5.71 
D)  4.39 
E)  none of the above 
A)  3.60 
B)  8.00 
C)  5.71 
D)  4.39 
E)  none of the above

Question 9

One way to model an option with dividends in the binomial framework is for the stock price minus the present value of the dividends to grow by the up and down factors.

Accepted Answer

A) True 
 B)False

Question 10

In a binomial model, if the call price in the market is higher than the call price given by the model, you should

Accepted Answer

A)  sell the call and sell short the stock 
B)  buy the call and sell short the stock 
C)  buy the stock and sell the call 
D)  buy the call and buy the stock 
E)  none of the above 
A)  sell the call and sell short the stock 
B)  buy the call and sell short the stock 
C)  buy the stock and sell the call 
D)  buy the call and buy the stock 
E)  none of the above

Question 11

If the binomial model is used with a specific dollar dividend and the stock price follows the up and down parameters, the tree will explode and end up with far more outcomes than time periods.

Accepted Answer

A) True 
 B)False

Question 12

What is the hedge ratio?

Accepted Answer

A)  0.429 
B)  0.714 
C)  0.571 
D)  0.823 
E)  none of the above 
A)  0.429 
B)  0.714 
C)  0.571 
D)  0.823 
E)  none of the above

Question 13

The binomial probabilities are probabilities if investors were risk neutral.

Accepted Answer

A) True 
 B)False

Question 14

The binomial model assumes that investors are risk neutral.

Accepted Answer

A) True 
 B)False

Question 15

The binomial model for foreign currency options is similar to the binomial model for stock options except the risk-free discount rate is adjusted.

Accepted Answer

A) True 
 B)False

Question 16

When the hedge ratio is adjusted in the binomial model, the transactions must be done in the option.

Accepted Answer

A) True 
 B)False

Question 17

What is the theoretical value of the call?

Accepted Answer

A)  8.00 
B)  4.39 
C)  5.15 
D)  5.36 
E)  none of the above
Now extend the one-period binomial model to a two-period world. Answer questions 16 through 18. 
A)  8.00 
B)  4.39 
C)  5.15 
D)  5.36 
E)  none of the above
Now extend the one-period binomial model to a two-period world. Answer questions 16 through 18.

Question 18

In a one-period binomial model with Su = 49.5, Sd = 40.5, p = 0.8, r = 0.06, S = 45 and X = 50, what is a European put worth?

Accepted Answer

A)  2.17 
B)  0.50 
C)  9.50 
D)  5.00 
E)  none of the above 
A)  2.17 
B)  0.50 
C)  9.50 
D)  5.00 
E)  none of the above

Question 19

In the binomial model, if a call is overpriced, investors should sell it and buy stock.

Accepted Answer

A) True 
 B)False

Question 20

What is the hedge ratio if the stock goes down one period?

Accepted Answer

A)  0.00 
B)  0.0725 
C)  1.00 
D)  0.73 
E)  none of the above 
A)  0.00 
B)  0.0725 
C)  1.00 
D)  0.73 
E)  none of the above

In a two-period binomial world, a mispriced call will lead to an arbitrage profit if

Which of the following statements about the binomial model is incorrect?

What is the value of the call if the stock goes up, then down?

The binomial option pricing formula will conform to the European lower bound.

When the number of time periods in a binomial model is large, a European call option value does what?

If the binomial model is extended to multiple periods for a fixed option life, which of the following adjustments must be made?

The single period binomial hedge ratio for stock call options could be computed by equating the two future cash flows -- from a portfolio of long h shares of stock and short one call -- and solve for the number of underlying stocks to hold.

What would be the call's price if the stock goes up?

One way to model an option with dividends in the binomial framework is for the stock price minus the present value of the dividends to grow by the up and down factors.

In a binomial model, if the call price in the market is higher than the call price given by the model, you should

If the binomial model is used with a specific dollar dividend and the stock price follows the up and down parameters, the tree will explode and end up with far more outcomes than time periods.

What is the hedge ratio?

The binomial probabilities are probabilities if investors were risk neutral.

The binomial model assumes that investors are risk neutral.

The binomial model for foreign currency options is similar to the binomial model for stock options except the risk-free discount rate is adjusted.

When the hedge ratio is adjusted in the binomial model, the transactions must be done in the option.

What is the theoretical value of the call?

In a one-period binomial model with S_u = 49.5, S_d = 40.5, p = 0.8, r = 0.06, S = 45 and X = 50, what is a European put worth?

In the binomial model, if a call is overpriced, investors should sell it and buy stock.

What is the hedge ratio if the stock goes down one period?

Introduction

Structure of Options Markets

Principles of Option Pricing

Option Pricing Models: The Black-Scholes-Merton Model

Basic Option Strategies

Advanced Option Strategies

Structure of Forward and Futures Markets

Principles of Pricing Forwards, Futures and Options on Futures

Futures Arbitrage Strategies

Forward and Futures Hedging, Spread, and Target Strategies

Swaps

Interest Rate Forwards and Options

Advanced Derivatives and Strategies

Financial Risk Management Techniques and Appplications

Managing Risk in an Organization

Filters

Exam 4: Option Pricing Models: The Binomial Model

In a two-period binomial world, a mispriced call will lead to an arbitrage profit if

Which of the following statements about the binomial model is incorrect?

What is the value of the call if the stock goes up, then down?

The binomial option pricing formula will conform to the European lower bound.

When the number of time periods in a binomial model is large, a European call option value does what?

If the binomial model is extended to multiple periods for a fixed option life, which of the following adjustments must be made?

The single period binomial hedge ratio for stock call options could be computed by equating the two future cash flows -- from a portfolio of long h shares of stock and short one call -- and solve for the number of underlying stocks to hold.

What would be the call's price if the stock goes up?

One way to model an option with dividends in the binomial framework is for the stock price minus the present value of the dividends to grow by the up and down factors.

In a binomial model, if the call price in the market is higher than the call price given by the model, you should

If the binomial model is used with a specific dollar dividend and the stock price follows the up and down parameters, the tree will explode and end up with far more outcomes than time periods.

What is the hedge ratio?

The binomial probabilities are probabilities if investors were risk neutral.

The binomial model assumes that investors are risk neutral.

The binomial model for foreign currency options is similar to the binomial model for stock options except the risk-free discount rate is adjusted.

When the hedge ratio is adjusted in the binomial model, the transactions must be done in the option.

What is the theoretical value of the call?

In a one-period binomial model with Su = 49.5, Sd = 40.5, p = 0.8, r = 0.06, S = 45 and X = 50, what is a European put worth?

In the binomial model, if a call is overpriced, investors should sell it and buy stock.

What is the hedge ratio if the stock goes down one period?

Introduction

Structure of Options Markets

Principles of Option Pricing

Option Pricing Models: The Black-Scholes-Merton Model

Basic Option Strategies

Advanced Option Strategies

Structure of Forward and Futures Markets

Principles of Pricing Forwards, Futures and Options on Futures

Futures Arbitrage Strategies

Forward and Futures Hedging, Spread, and Target Strategies

Swaps

Interest Rate Forwards and Options

Advanced Derivatives and Strategies

Financial Risk Management Techniques and Appplications

Managing Risk in an Organization

Filters

In a one-period binomial model with S_u = 49.5, S_d = 40.5, p = 0.8, r = 0.06, S = 45 and X = 50, what is a European put worth?