[2008]Topic 16: Properties of Stock Options相关习题 stock, following, increase, discuss

Baran

AIM 1: Identify the six factors that affect an option’s price and discuss how these six factors affect the price for both European and American options.

1、Which of the following has the same impact on both American call and put option prices?

      I. An increase in volatility.
     II. An increase in the stock price.
    III. An increase in the risk-free rate.
    IV. A decrease in time to expiration.

A) I only.
 
B) I and IV.
 
C) I and II.
 
D) I and III.

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AIM 5: Discuss the effects dividends have on the put-call parity, the bounds of put and call option prices, and on the early exercise feature of American options.

1、Rachel Barlow is a recent graduate of Columbia University with a Bachelor’s degree in finance. She has accepted a position at a large investment bank, but first must complete an intensive training program to gain experience in several of the investment bank’s areas of operations. Currently, she is spending three months at her firm's Derivatives Trading desk. One of the traders, Jason Coleman, CFA, is acting as her mentor, and will be giving her various assignments over the three month period.

One of the first projects he asks her to do is to compare different option trading strategies. Coleman would like Barlow to pay particular attention to strategy costs and their potential payoffs. Barlow is not very comfortable with option models, and knows she needs to be able to fully understand the most basic concepts in order to move on. She decides that she must first investigate how to properly price European and American style equity options. Coleman has given her software that provides a variety of analytical information using three valuation approaches: the Black-Scholes model, the Binomial model, and Monte Carlo simulation. Barlow has decided to begin her analysis using a variety of different scenarios to evaluate option behavior. The data she will be using in her scenarios is provided in Exhibits 1 and 2. Note that all of the rates and yields are on a continuous compounding basis.

Exhibit 1

Stock Price (S)	$100
Strike Price (X)	$100
Interest Rate (r)	7%
Dividend Yield (q)	0%
Time to Maturity (years)	0.5
Volatility (Std. Dev.)	20%

Exhibit 2

Stock Price (S)	$110
Strike Price (X)	$100
Interest Rate (r)	7%
Dividend Yield (q)	0%
Time to Maturity (years)	0.5
Volatility (Std. Dev.)	20%
Value of European Call	$14.8445

Barlow notices that the stock in Exhibit 1 does not pay dividends. If the stock begins to pay a dividend, how will the price of a call option on that stock be affected?

A) Increase.

B) Be unchanged.

C) Increase or decrease.

D) Decrease.

Baran

 

The  correct answer is D

The call option value will decrease since the payment of dividends reduces the value of the underlying, and the value of a call is positively related to the value of the underlying.

Baran

 The  correct answer is A

It can be shown that American put options on non-dividend paying stocks may be exercised early if the underlying stock price is sufficiently low. The owner of the option would essentially receive the strike price, which is the maximum value of the option, and could reinvest the proceeds at the risk-free rate, which would generate a payoff received today as opposed to in the future.

Baran

The  correct answer is D

According to put-call parity we can write a riskless pure-discount bond position as:
X/(1+Rf)T = P0 + S0 – C0.
We can then read off the right-hand side of the equation to create a synthetic position in the riskless pure-discount bond. We would need to buy the European put, buy the same underlying stock, and sell the European call.

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AIM 4: Explain the early exercise features of American call and put options on a nondividend-paying stock and the price effect early exercise may have.

 

1、For American options prior to maturity, the difference between the price of a call option and the price of a put option with the same underlying stock, strike price, and maturity must be less than or equal to the:

A) stock price minus the exercise price.
 
B) stock price minus the present value of the exercise price.
 
C) present value of exercise price minus stock price.
 
D) exercise price minus stock price.

Baran

 The  correct answer is B

The following relationship must hold for American options:
S0 - X ≤ C - P ≤ S0 - Xe-rt

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2、It may be attractive to exercise an American put option prior to expiration when the underlying stock price is:

A) much lower than the exercise price and risk-free rates are positive. 
 
B) close to the strike price and risk-free rates are positive. 
 
C) above the strike price and risk-free rates are close to zero. 
 
D) close to the strike price and risk-free rates are close to zero.

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10、Referring to put-call parity, which one of the following alternatives would allow you to create a synthetic riskless pure-discount bond?

A) Buy a European put option; sell the same stock; sell a European call option. 
 
B) Sell a European put option; buy the same stock; buy a European call option.
 
C) Sell a European put option; sell the same stock; buy a European call option.
 
D) Buy a European put option; buy the same stock; sell a European call option.

Baran

 The  correct answer is B

According to put-call parity we can write a stock position as: S0 = C0 – P0 + X/(1+Rf)T

We can then read off the right-hand side of the equation to create a synthetic position in the stock. We would need to buy the European call, sell the European put, and invest the present value of the exercise price in a riskless pure-discount bond.