Question 1

What is the primary potential for error when using the Cox-Ross-Rubenstein binomial tree?

Accepted Answer

When either the time period or standard deviation is large,it is possible for eʳʰ > $ e^{\sigma \sqrt{h}} $ ,which is not possible for a valid binomial tree.

Question 2

Consider a one-period binomial model of 6 months.Assume the stock price is $45.00,σ = 0.20,r = 0.06 and the stock's expected return is 12.0%.What is the discount rate for a $45.00 strike European call option (Y)?

Accepted Answer

A)  38.2% 
B)  39.1% 
C)  42.5% 
D)  45.6% 
A)  38.2% 
B)  39.1% 
C)  42.5% 
D)  45.6% B

Question 3

Consider a one-period binomial model of 12 months.Assume the stock price is $54.00,σ = 0.25,r = 0.04 and the exercise price of a call option is $55.What is the forecasted price of the stock given a downward movement during the year?

Accepted Answer

A)  $43.77 
B)  $ 45.28 
C)  $48.98 
D)  $51.84 
A)  $43.77 
B)  $ 45.28 
C)  $48.98 
D)  $51.84 A

Question 4

Ask the class to prove that option pricing is consistent with standard discounted cash flow calculations.Propose that students form groups and develop two binomial trees for the same set of data.One tree should use real probabilities as defined in chapter 11 and the other as defined in chapter 10.

Accepted Answer

To prove that option pricing is consiste

Question 5

Consider a two-period binomial model,where each period is 6 months.Assume the stock price is $75.00,σ = 0.35,and r = 0.05.An American call option with a strike price of $80 would be exercised early at what dividend yield?

Accepted Answer

A)  5.0% 
B)  7.0% 
C)  9.0% 
D)  Never exercise early 
A)  5.0% 
B)  7.0% 
C)  9.0% 
D)  Never exercise early

Question 6

Why is an American call option rarely exercised early,and thus priced similar to European options?

Accepted Answer

A)  Early exercise requires purchasing the stock 
B)  Most option sellers cannot deliver the stock 
C)  Option prices usually exceed intrinsic values 
D)  Short sellers disrupt delivery 
A)  Early exercise requires purchasing the stock 
B)  Most option sellers cannot deliver the stock 
C)  Option prices usually exceed intrinsic values 
D)  Short sellers disrupt delivery

Question 7

Consider a two-period binomial model,where each period is 6 months.Assume the stock price is $60.00,σ = 0.30,r = 0.05.An American put option with a strike price of $65 would be exercised early at what dividend yield?

Accepted Answer

A)  5.0% 
B)  6.0% 
C)  11.0% 
D)  Never exercised early 
A)  5.0% 
B)  6.0% 
C)  11.0% 
D)  Never exercised early

Question 8

What economic concept is central to proving that risk neutral pricing functions in the establishing of option prices?

Accepted Answer

A)  Consumption possibilities 
B)  Factor analysis 
C)  Marginal average cost 
D)  Declining marginal utility 
A)  Consumption possibilities 
B)  Factor analysis 
C)  Marginal average cost 
D)  Declining marginal utility

Question 9

Using a binomial pricing model,what is the impact on the price of a call option if the company increases the dividend paid to shareholders? The call option price:

Accepted Answer

A)  Will drop 
B)  Will increase 
C)  Will remain constant 
D)  Impact cannot be determined 
A)  Will drop 
B)  Will increase 
C)  Will remain constant 
D)  Impact cannot be determined

Question 10

Consider a two-period binomial model,where each period is 6 months.Assume the stock price is $50.00,σ = 0.20,r = 0.06 and the dividend yield = 3.5%.What is the lowest strike price where early exercise would occur with an American put option?

Accepted Answer

A)  $50 
B)  $55 
C)  $60 
D)  $65 
A)  $50 
B)  $55 
C)  $60 
D)  $65

Question 11

What is the relationship between dividends and the forecasted stock price in a binomial model?

Accepted Answer

The dividend acts to

Question 12

In a binomial pricing model,what is the lowest price of an option at any node and why?

Accepted Answer

Zero,because the price of the

Question 13

A stock price is $85.00.Assume r = 0.07 and there is no dividend.What is the 6-month forward price?

Accepted Answer

A)  $88.03 
B)  $89.16 
C)  $90.26 
D)  $92.33 
A)  $88.03 
B)  $89.16 
C)  $90.26 
D)  $92.33

Question 14

Consider a one-period binomial model of 6 months.Assume the stock price is $63.00,σ = 0.28,r = 0.05 and the stock's expected return is 14.0%.What is the true probability of the stock going up?

Accepted Answer

A)  56.6% 
B)  52.4% 
C)  48.2% 
D)  46.4% 
A)  56.6% 
B)  52.4% 
C)  48.2% 
D)  46.4%

Question 15

Consider a three-period binomial model of 12 months.Assume the stock price is $37.50,σ = 0.20,r = 0.05 and the exercise price of a call option is $35.What is the forecasted price of the stock at the node after two consecutive upward movements of the stock price?

Accepted Answer

A)  $38.68 
B)  $42.80 
C)  $48.84 
D)  $50.06 
A)  $38.68 
B)  $42.80 
C)  $48.84 
D)  $50.06

Question 16

Consider a one-period binomial model of 12 months.Assume the stock price is $54.00,σ = 0.25,r = 0.04 and the exercise price of a call option is $55.What is the forecasted price of the stock given an upward movement during the year?

Accepted Answer

A)  $56.16 
B)  $61.01 
C)  $65.12 
D)  $72.16 
A)  $56.16 
B)  $61.01 
C)  $65.12 
D)  $72.16

Question 17

Consider a two-period binomial model,where each period is 6 months.Assume the stock price is $46.00,σ = 0.28,r = 0.06 and the dividend yield is 2.0%.What is the maximum approximate strike price where early exercise would occur with an American call option?

Accepted Answer

A)  $29 
B)  $33 
C)  $42 
D)  $46 
A)  $29 
B)  $33 
C)  $42 
D)  $46

Question 18

When developing a binomial tree model where stocks pay discrete dividends,what problem may occur?

Accepted Answer

Trees created with s

Question 19

Under what circumstances should an option be exercised early?

Accepted Answer

Whenever the dividend gain exc

Exam 11: Binomial Option Pricing: Selected Topics

What is the primary potential for error when using the Cox-Ross-Rubenstein binomial tree?

Consider a one-period binomial model of 6 months.Assume the stock price is $45.00,σ = 0.20,r = 0.06 and the stock's expected return is 12.0%.What is the discount rate for a $45.00 strike European call option (Y)?

Consider a one-period binomial model of 12 months.Assume the stock price is $54.00,σ = 0.25,r = 0.04 and the exercise price of a call option is $55.What is the forecasted price of the stock given a downward movement during the year?

Ask the class to prove that option pricing is consistent with standard discounted cash flow calculations.Propose that students form groups and develop two binomial trees for the same set of data.One tree should use real probabilities as defined in chapter 11 and the other as defined in chapter 10.

Consider a two-period binomial model,where each period is 6 months.Assume the stock price is $75.00,σ = 0.35,and r = 0.05.An American call option with a strike price of $80 would be exercised early at what dividend yield?

Why is an American call option rarely exercised early,and thus priced similar to European options?

Consider a two-period binomial model,where each period is 6 months.Assume the stock price is $60.00,σ = 0.30,r = 0.05.An American put option with a strike price of $65 would be exercised early at what dividend yield?

What economic concept is central to proving that risk neutral pricing functions in the establishing of option prices?

Using a binomial pricing model,what is the impact on the price of a call option if the company increases the dividend paid to shareholders? The call option price:

Consider a two-period binomial model,where each period is 6 months.Assume the stock price is $50.00,σ = 0.20,r = 0.06 and the dividend yield = 3.5%.What is the lowest strike price where early exercise would occur with an American put option?

What is the relationship between dividends and the forecasted stock price in a binomial model?

In a binomial pricing model,what is the lowest price of an option at any node and why?

A stock price is $85.00.Assume r = 0.07 and there is no dividend.What is the 6-month forward price?

Consider a one-period binomial model of 6 months.Assume the stock price is $63.00,σ = 0.28,r = 0.05 and the stock's expected return is 14.0%.What is the true probability of the stock going up?

Consider a three-period binomial model of 12 months.Assume the stock price is $37.50,σ = 0.20,r = 0.05 and the exercise price of a call option is $35.What is the forecasted price of the stock at the node after two consecutive upward movements of the stock price?

Consider a one-period binomial model of 12 months.Assume the stock price is $54.00,σ = 0.25,r = 0.04 and the exercise price of a call option is $55.What is the forecasted price of the stock given an upward movement during the year?

Consider a two-period binomial model,where each period is 6 months.Assume the stock price is $46.00,σ = 0.28,r = 0.06 and the dividend yield is 2.0%.What is the maximum approximate strike price where early exercise would occur with an American call option?

When developing a binomial tree model where stocks pay discrete dividends,what problem may occur?

Under what circumstances should an option be exercised early?

Introduction to Derivatives

An Introduction to Forwards and Options

Insurance, collars, and Other Strategies

Introduction to Risk Management

Financial Forwards and Futures

Commodity Forwards and Futures

Interest Rate Forwards and Futures

Swaps

Parity and Other Option Relationships

Binomial Option Pricing: Basic Concepts

The Black-Scholes Formula

Market-Making and Delta-Hedging

Exotic Options: I

Financial Engineering and Security Design

Corporate Applications

Real Options

The Lognormal Distribution

Monte Carlo Valuation

Brownian Motion and Itos Lemma

The Black-Scholes-Merton Equation

Risk-Neutral and Martingale Pricing

Exotic Options: 2

Volatility

Interest Rate and Bond Derivatives

Value at Risk

Credit Risk

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