Question 1

If the volatility of the underlying asset decreases, then the:
A) Value of the put option will increase, but the value of the call option will decrease
B) Value of the put option will decrease, but the value of the call option will increase
C) Value of both the put and call option will increase
D) Value of both the put and call option will decrease

Accepted Answer

Volatility is a key factor in option pricing; higher volatility increases the potential for larger price swings, which increases the value of both call and put options. Conversely, a decrease in volatility reduces the potential for price swings, thus decreasing the value of both call and put options.

Question 2

The higher the underlying stock price: (everything else remaining the same)
A) higher the call price
B) lower the call price
C) has no effect on call price
D) none of the above

Accepted Answer

The answer of The higher the underlying stock price: (everything...

Question 3

Suppose an investor buys one share of stock and a put option on the stock. What will be the value of her investment on the final exercise date if the stock price is below the exercise price? (Ignore transaction costs)
A) The value of two shares of stock
B) The value of one share of stock plus the exercise price
C) The exercise price
D) The value of one share of stock minus the exercise price

Accepted Answer

If the stock price is below the exercise price, the put option will be exercised, and the investor can sell the stock at the exercise price. Therefore, the value of the investment will be equal to the exercise price. The value of the stock itself is irrelevant in this scenario since the put option protects the investor from downside risk.

Question 4

If the risk-free interest rate increases:
A) the direct effect of it on the call option price is positive
B) the direct effect of it on the call option price is negative
C) the direct effect of it on the call option price is unknown
D) none of the above

Accepted Answer

An increase in the risk-free interest rate generally increases the call option price because the present value of the exercise price decreases, making the option more attractive.

Question 5

Given the following data: Expiration = 6 months; Stock price = $80; exercise price = $75; call option price = $12; risk-free rate = 5% per year. Calculate the price of an equivalent put option using put-call parity:
A) $3.07
B) $5.19
C) $11.43
D) none of the above

Accepted Answer

The answer of Given the following data: Expiration = 6...

Question 6

If the underlying stock pays a dividend before the expiration of the options that will have the following effect on the price of the options:
I. increase the value of the call option II) increase the value of the put option
III. decrease the value of the call option
IV. decrease the value of the put option
A) I and II only
B) III and IV only
C) I and IV only
D) II and III only

Accepted Answer

When a stock pays a dividend, the stock price typically drops by the dividend amount, which decreases the value of call options (III) and increases the value of put options (II).

Question 7

For European options, the value of a put is equal to:
A) The value of a call minus the value of a share plus the present value of the exercise price
B) The value of a call plus the value of a share plus the present value of the exercise price
C) The value of the share minus the value of a call plus the present value of the exercise price
D) The value of the share minus the present value of the exercise price plus the valued of a call

Accepted Answer

The value of a put is equal to the value of a call minus the value of a share plus the present value of the exercise price.

Question 8

Suppose an investor buys one share of stock and a put option on the stock and simultaneously sells a call option on the stock with the same exercise price. What will be the value of his investment on the final exercise date?
A) Above the exercise price if the stock price rises and below the exercise price if it falls
B) Equal to the exercise price regardless of the stock price
C) Equal to zero regardless of the stock price
D) Below the exercise price if the stock price rises and above if it falls

Accepted Answer

By buying one share of stock and a put option on the stock while selling a call option on the same stock with the same exercise price, the investor has created a synthetic long position. This means that they will earn a profit if the stock price rises and will not lose any money if the stock price falls. Therefore, the value of their investment on the final exercise date will be equal to the exercise price regardless of the stock price.

Question 9

Relative to the underlying stock, a call option always has:
A) A higher beta and a higher standard deviation of return
B) A lower beta and a higher standard deviation of return
C) A higher beta and a lower standard deviation of return
D) A lower beta and a lower standard deviation of return

Accepted Answer

Call options have a higher beta and higher standard deviation of return compared to the underlying stock because they are leveraged instruments, amplifying both potential returns and risks.

Question 10

Suppose you buy a call and lend the present value of its exercise price. You could match the payoffs of this strategy by:
A) Buying the underlying stock and selling a call
B) Selling a put and lending the present value of the exercise price
C) Buying the underlying stock and buying a put
D) Buying the underlying stock and selling a put

Accepted Answer

This strategy is equivalent to a protective put, where you buy the underlying stock and buy a put option. This combination ensures that you have the right to sell the stock at the exercise price, matching the payoff of buying a call and lending the present value of the exercise price.

Question 11

For European options, the value of a call plus the present value of the exercise price is equal to:
A) The value of a put minus the value of a share
B) The value of a share minus the value of a call
C) The value of a put plus the value of a share
D) The value of a share minus the value of a put

Accepted Answer

This is based on the put-call parity relationship for European options, which states that the value of a call option plus the present value of the exercise price is equal to the value of a put option plus the value of the underlying share.

Question 12

The higher the underlying stock price: (everything else remaining the same)
A) higher the put price
B) lower the put price
C) has no effect on put price
D) none of the above

Accepted Answer

The answer of The higher the underlying stock price: (everything...

Question 13

Buying a call option, investing the present value of the exercise price in T-bills, and short selling the underlying share is the same as:
A) Buying a call and a put
B) Buying a put and a share
C) Buying a put
D) Selling a call

Accepted Answer

The answer of Buying a call option, investing the present...

Question 14

Which of the following features increase(s) the value of a call option?
A) A high interest rate
B) A long time to maturity
C) A higher volatility of the underlying stock price
D) All of the above

Accepted Answer

All of the above features increase the value of a call option. 
A high interest rate increases the cost of borrowing and hence the cost of buying the underlying stock, which in turn increases the call option price. 
A long time to maturity gives the stock price more time to rise above the strike price, which increases the probability of the call option being exercised, hence increasing its price. 
A higher volatility of the underlying stock price increases the probability of the stock rising above the strike price, hence increasing the price of the call option.

Question 15

Put-call parity can be used to show:
A) How far in-the-money put options can get
B) How far in-the-money call options can get
C) The precise relationship between put and call option prices given equal exercise prices and equal expiration dates
D) That the value of a call option is always twice that of a put given equal exercise prices and equal expiration dates

Accepted Answer

Put-call parity is an important principle in options pricing. It states that the price of a call option plus the present value of the exercise price must equal the price of a put option plus the current stock price. This relationship holds true for options with equal exercise prices and equal expiration dates. Put-call parity can be used to determine the fair price of either a put or call option by comparing it to the other side of the equation. Therefore, the best choice is C, which states that put-call parity can be used to show the precise relationship between put and call option prices given equal exercise prices and equal expiration dates. Choices A, B, and D are incorrect because they do not accurately describe what put-call parity is used for.

Question 16

If the stock makes a dividend payment before the expiration date then the put-call parity is:
A) Value of call = value of put + share price - present value (PV) of dividend -PV of exercise price
B) Value of call = value of put - share price + PV of dividend - PV of exercise price
C) Value of call = value of put + share price + PV of dividend + PV of exercise price
D) Value of call = value of put + share price + PV of dividend - PV of exercise price

Accepted Answer

The put-call parity equation is: Value of Call + PV of Exercise Price = Value of Put + Share Price. 
However, if the stock pays a dividend before the expiration date, then the equation becomes: Value of Call + PV of Exercise Price = Value of Put + Share Price - PV of Dividend. 
So, rearranging this equation to solve for Value of Call, we get: Value of Call = Value of Put + Share Price - PV of Dividend - PV of Exercise Price (Option A).

Question 17

For European options, the value of a call minus the value of a put is equal to:
A) The present value of the exercise price minus the value of a share
B) The present value of the exercise price plus the value of a share
C) The value of a share plus the present value of the exercise price
D) The value of a share minus the present value of the exercise price

Accepted Answer

The value of a call option is the maximum of either zero or the difference between the stock price and the exercise price, while the value of a put option is the maximum of either zero or the difference between the exercise price and the stock price. Therefore, the value of a call option minus the value of a put option is equal to the difference between the stock price and the exercise price, which is the same as the value of a share minus the exercise price. Taking the present value of the exercise price does not affect this relationship. Thus, the correct answer is the value of a share minus the present value of the exercise price.

Question 18

Buying the stock and the put option on the stock provides the same payoff as:
A) investing the present value of the exercise price in T-bills and buying the call option
B) on the stock
C) short selling the stock and buying a call option on the stock
D) writing (selling) a put option and buying a call option on the stock
E) none of above

Accepted Answer

Buying the stock and the put option on the stock provides the same payoff as investing the present value of the exercise price in T-bills and buying the call option on the stock. This is known as a synthetic call option. It is achieved by buying the underlying asset (stock) and purchasing a put option which provides downside protection, just like a call option. In contrast, short selling the stock and buying a call option on the stock is known as a synthetic long option, and writing a put option and buying a call option is known as a synthetic long stock position.

Question 19

Which of the following investors would be happy to see the stock price rise sharply? I) Investor who owns the stock and a put option
II) Investor who has sold a put option and bought a call option
III) Investor who owns the stock and has sold a call option
IV) Investor who has sold a call option
A) I and II only
B) III and IV only
C) III only
D) IV only

Accepted Answer

Investor I benefits from stock ownership as the stock price rises, and the put option provides downside protection. Investor II benefits from the call option as the stock price rises, and selling a put option is neutral or positive in this scenario.

Question 20

A call option has an exercise price of $150. At the final exercise date, the stock price could be either $100 or $200. Which investment would combine to give the same payoff as the stock?
A) Lend PV of $100 and buy two calls
B) Lend PV of $100 and sell two calls
C) Borrow $100 and buy two calls
D) Borrow $100 and sell two calls

Accepted Answer

By lending the present value of $100 and buying two call options, you replicate the payoff of owning the stock. If the stock price is $200, the calls will be exercised, and you will receive $100 per call, totaling $200. If the stock price is $100, the calls will not be exercised, and you will have the $100 from lending.

Quiz 20: Understanding Options

If the volatility of the underlying asset decreases, then the:

The higher the underlying stock price: (everything else remaining the same)

Suppose an investor buys one share of stock and a put option on the stock. What will be the value of her investment on the final exercise date if the stock price is below the exercise price? (Ignore transaction costs)

If the risk-free interest rate increases:

Given the following data: Expiration = 6 months; Stock price = $80; exercise price = $75; call option price = $12; risk-free rate = 5% per year. Calculate the price of an equivalent put option using put-call parity:

For European options, the value of a put is equal to:

Suppose an investor buys one share of stock and a put option on the stock and simultaneously sells a call option on the stock with the same exercise price. What will be the value of his investment on the final exercise date?

Relative to the underlying stock, a call option always has:

Suppose you buy a call and lend the present value of its exercise price. You could match the payoffs of this strategy by:

For European options, the value of a call plus the present value of the exercise price is equal to:

The higher the underlying stock price: (everything else remaining the same)

Buying a call option, investing the present value of the exercise price in T-bills, and short selling the underlying share is the same as:

Which of the following features increase(s) the value of a call option?

Put-call parity can be used to show:

If the stock makes a dividend payment before the expiration date then the put-call parity is:

For European options, the value of a call minus the value of a put is equal to:

Buying the stock and the put option on the stock provides the same payoff as:

Which of the following investors would be happy to see the stock price rise sharply? I) Investor who owns the stock and a put option II) Investor who has sold a put option and bought a call option III) Investor who owns the stock and has sold a call option IV) Investor who has sold a call option

A call option has an exercise price of $150. At the final exercise date, the stock price could be either $100 or $200. Which investment would combine to give the same payoff as the stock?