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?

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

The  correct answer is B

Increased volatility positively influences put and call option values, while a decrease in time to expiration will negatively influence call and put prices. Note that an increase in the stock price and an increase in the risk-free rate will cause the price of an American call to increase but will cause the price of an American put to decrease.

2、Put option values increase as a result of increases in which of the following factors?

  I. Volatility.
 II. Dividends.
III. Stock Price.
IV. Time to expiration.
A) I, III, and IV only. 
 
B) I, II, and IV only. 
 
C) II and IV only. 
 
D) I and III only. 

AIM 2: Identify, interpret and compute upper and lower bounds for option prices.

A) Because the American and European options have identical terms and are written against the same common stock, they will have identical option premiums.
 
 
B) The American option will have a higher option premium, because the American security markets are larger than the European markets.
 
 
C) The greater flexibility allowed in exercising the American option will normally result in a higher market value relative to an otherwise identical European option.
 
 
D) The European option will normally have a higher option premium because of their relative scarcity compared to American options.

The  correct answer is C

Trading in European options is considerably less than trading in American options, because demand for them is much lower. This is due to their relative inflexibility regarding when they can be exercised. The greater exercising flexibility of American options gives them increased value to traders, which normally results in a greater market value relative to an otherwise identical European option.

2、What is the primary difference between an American and a European option?

A) The European option can only be traded on overseas markets. 
 
B) The American option can be exercised at anytime on or before its expiration date.
 
C) American and European options always have different strike prices when written on the same underlying asset. 
 
D) American and European options are never written on the same underlying asset. 

The  correct answer is B

American and European options are virtually identical, except exercising the European option is limited to its expiration date only. The American option can be exercised at anytime on or before its expiration date. For the exam, the key concept relating to this difference is the value of the American option must be equal or greater than the value of the corresponding European option, all else being equal.

3、Consider a call option on a stock currently priced at $50 with a strike price of $55. Which of the following CANNOT be the price of the call option?

A) $10.
 
B) $15.
 
C) $55.
 
D) $50.

The  correct answer is C

The upper bound on a European call option is the stock price, so it can’t be worth $55.

AIM 3: Explain put-call parity and calculate, using the put-call parity on a nondividend-paying stock, the value of a European and American option, respectively.

1、A put option on DCY stock matures six months from today and sells for $0.49. A call option on DCY stock with the same strike price sells for $4.52. Both the put and the call are European options. DCY stock is priced at $55 and the risk-free rate of interest is 4 percent. The strike price of the put and call options is closest to:

A) $51.
 
B) $53.
 
C) $52.
 
D) $50.

The  correct answer is C

This question can be answered with the put-call parity relation. The relation is p+S0=c+Xe-rT, so rearranging gives X=(p+S0-c)/e-rT=(0.49+55-4.52)/e-0.04(.5)=52.

2、A European put option on a stock can be replicated with which of the following combined postions?

A) Long a European call, long a zero-coupon bond, and short the stock.
 
B) Long a European call, short a zero-coupon bond, and long the stock.
 
C) Short a European call, long a zero-coupon bond, and short the stock.
 
D) Short a European call, short a zero-coupon bond, and long the stock.

 The  correct answer is A

Using put-call parity, the value of a put is: p=c+Xe-rT-S0. Thus a put is equivalent to being long a call, long a zero-coupon bond, and short the stock.

3、Ronald Franklin, CFA, has recently been promoted to junior portfolio manager for a large equity portfolio at Davidson-Sherman (DS), a large multinational investment-banking firm. He is specifically responsible for the development of a new investment strategy that DS wants all equity portfolio managers to implement. Upper management at DS has instructed its portfolio managers to begin overlaying option strategies on all equity portfolios. The relatively poor performance of many of their equity portfolios has been the main factor behind this decision. Prior to this new mandate, DS portfolio managers had been allowed to use options at their own discretion, and the results were somewhat inconsistent. Some portfolio managers were not comfortable with the most basic concepts of option valuation and their expected return profiles, and simply did not utilize options at all. Upper management of DS wants Franklin to develop an option strategy that would be applicable to all DS portfolios regardless of their underlying investment composition. Management views this new implementation of option strategies as an opportunity to either add value or reduce the risk of the portfolio.

Franklin gained experience with basic options strategies at his previous job. As an exercise, he decides to review the fundamentals of option valuation using a simple example. Franklin recognizes that the behavior of an option's value is dependent on many variables and decides to spend some time closely analyzing this behavior. His analysis has resulted in the information shown in Exhibits 1 and 2 for European style options.

Using the information in Exhibit 1, Franklin wants to compute the value of the corresponding European call option. Which of the following is the closest to Franklin's answer?

A) $4.78.

B) $5.55.

C) $11.54.

D) $12.07.

The  correct answer is C

This result can be obtained using put-call parity in the following way:

Call Value = Put Value – Xe^-rt + S = $4.78 - $100.00e^{(-0.07 * 1.0)} + 100 = $11.54

The incorrect value of $4.78 does not discount the strike price in the put-call parity formula. The value $12.07 results from using the binomial model.

Franklin is interested in the sensitivity of the European call option to changes in the volatility of the underlying equity's returns. What happens to the value of the call option if the volatility of the underlying equity's returns decreases?

The call option value:

A) decreases.

B) increases.

C) stays the same.

D) increases or decreases.

The  correct answer is A

Due to the limited potential downside loss, changes in volatility directly affect option value. Vega measures the option’s sensitivity relative to volatility changes.

4、Which of the following best explains put-call parity?

A) A stock can be replicated using any call option, put option and bond.
 
B) No arbitrage requires that using any three of the four instruments (stock, call, put, bond) the fourth can be synthetically replicated.
 
C) A stock can be replicated using any at the money call and put options and a bond.
 
D) No arbitrage requires that only the underlying stock can be synthetically replicated using at the money call and put options and a zero coupon bond with a face value equal to the strike price of the options.

The  correct answer is B

A portfolio of the three instruments will have the identical profit and loss pattern as the fourth instrument and therefore the same value by no arbitrage. So the fourth security can be synthetically replicated using the remaining three.

5、Assume that the value of a call option with a strike price of $100 and six months remaining to maturity is $5. For a stock price of $100 and an interest rate of 6 percent, what is the value of the corresponding put option with the same strike price and expiration as the call option?

A) $1.78.
 
B) $2.87.
 
C) $5.00.
 
D) $2.13.

The  correct answer is D

The formula for put-call parity is: Call – Put = Stock – X/(1+r)t  

Solving for the put results in: Call – Stock + X/(1+r)t = Put 

Rearranging the variables: P = C – S + X/(1+r)t   

Put value = $5 - $100 + $100/1.060.5 = $2.13

6、Which of the following is the expression for put-call parity (ct = call price, pt = put price, St = stock price (all at time t), X = exercise price of call and put, r = interest rate, T = time at expiration of the options)?

A) St + ct = pt + Xe-r(T-t)
 
 
B) St + pt = ct + Xe-r(T-t)
 
 
C) St + pt = ct - Xe-r(T-t)
 
 
D) St - pt = ct + Xe-r(T-t)

7、A security sells for $40. A 3-month call with a strike of $42 has a premium of $2.49. The risk-free rate is 3 percent. What is the value of the put according to put-call parity?

A) $1.89.
 
B) $3.45.
 
C) $4.18.
 
D) $6.03.

The  correct answer is C

p = c + Xe–rt – S = 2.49 + 42 e –0.03 × 0.25 – 40 = $4.18

8、Referring to put-call parity, which one of the following alternatives would allow you to create a synthetic European call option?

A) Buy the stock; sell a European put option on the same stock with the same exercise price and the same maturity; short an amount equal to the present value of the exercise price worth of a pure-discount riskless bond. 
 
B) Buy the stock; buy a European put option on the same stock with the same exercise price and the same maturity; short an amount equal to the present value of the exercise price worth of a pure-discount riskless bond.
 
C) Sell the stock; buy a European put option on the same stock with the same exercise price and the same maturity; invest an amount equal to the present value of the exercise price in a pure-discount riskless bond.
 
D) Sell the stock; sell a European put option on the same stock with the same exercise price and the same maturity; invest an amount equal to the present value of the exercise price in a pure-discount riskless bond.

The  correct answer is B

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

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

9、Referring to put-call parity, which one of the following alternatives would allow you to create a synthetic stock position?

A) Buy a European call option; buy a European put option; invest the present value of the exercise price in a riskless pure-discount bond. 
 
B) Buy a European call option; short a European put option; invest the present value of the exercise price in a riskless pure-discount bond.
 
C) Sell a European call option; buy a European put option; short the present value of the exercise price worth of a riskless pure-discount bond.
 
D) Sell a European call option; sell a European put option; invest the present value of the exercise price in a riskless pure-discount bond.

 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.

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.

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.

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.

 The  correct answer is B

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

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.

 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.

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

Exhibit 2

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.

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.