Question 1

If the stock makes a dividend payment before the expiration date, then the put-call parity relation 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 correct put-call parity relation, accounting for dividends, is: Value of call = value of put + share price - present value (PV) of dividend - PV of exercise price. This accounts for the fact that owning a call option does not entitle the holder to dividends paid during the option's life, hence the need to subtract the PV of dividends from the equation.

Question 2

All else equal, as the underlying stock price increases:
A)the call price decreases.
B)the call price increases.
C)there is no effect on call price.
D)the call price can either increase, decrease, or remain the same.

Accepted Answer

All else equal, as the underlying stock price increases, the call option becomes more valuable as it gives the holder the right to buy the stock at a lower price than the current market price. Therefore, the call price increases.

Question 3

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 on the stock.
B)short-selling the stock and buying a call option on the stock.
C)writing (selling)a put option and buying a call option on the stock.
D)a T-bill.

Accepted Answer

Investing the present value of the exercise price in T-bills and buying the call option on the stock is equivalent to buying the stock and the put option on the stock. They both provide the same payoff because the stock and the put option provide downside protection while investing in T-bills provides risk-free return. Buying the call option on the stock allows for upside potential, completing the equivalent payoff.

Question 4

Suppose the underlying stock pays a dividend before the expiration of options on that stock. This will:
I.increase the value of a call option;
II.increase the value of a put option;
III.decrease the value of a call option;
IV.decrease the value of a 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, its price typically decreases by the amount of the dividend, which decreases the value of call options (III) and increases the value of put options (II).

Question 5

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

The value of both put and call options generally decreases with a decrease in the volatility of the underlying asset because lower volatility means less chance of large price movements, making both types of options less valuable.

Question 6

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 tend to have a higher beta and a higher standard deviation of return compared to the underlying stock. This is because options leverage the movement of the underlying stock, amplifying both the potential returns and the risk (volatility).

Question 7

A call option has an exercise price of $150. At the option expiration 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 can replicate the payoff of owning the stock. If the stock price is $200, the calls will be exercised, and you will have a payoff equivalent to owning the stock. If the stock price is $100, the calls will not be exercised, and you will have the $100 lent.

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 simultaneously buying a put option and selling a call option with the same exercise price, the investor has created a synthetic long position. The value of this investment on the final exercise date will be equal to the exercise price regardless of the stock price. This is because if the stock price rises, the call option will be exercised and the investor will sell the stock for the exercise price. If the stock price falls, the put option will be exercised and the investor will buy the stock for the exercise price. In either case, the investor will end up with the stock at the exercise price, which is the same value as the investment.

Question 9

Which of the following investors would be happy to see the stock price rise sharply?
I.An investor who owns the stock and a put option;
II.An investor who has sold a put option and bought a call option;
III.correct for projects that have average risk compared to the firm's other assets. An investor who owns the stock and has sold a call option
IV.An 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

I. An investor who owns the stock benefits from a price increase. Owning a put option doesn't change the benefit of the stock price rising, as the option would simply become less valuable or expire worthless, but the gain on the stock outweighs this.II. An investor who has sold a put option benefits from the stock price rising because the option is less likely to be exercised, leading to profit. Buying a call option also benefits from a stock price increase, making this combination favorable.

Question 10

All else equal, as the underlying stock price increases:
A)the put price increases.
B)the put price decreases.
C)there is no effect on put price.
D)the put price can either increase, decrease, or remain the same.

Accepted Answer

When the underlying stock price increases, the probability of the stock price falling below the strike price decreases. Therefore, the option becomes less likely to be exercised and the put price decreases.

Question 11

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 given by the present value of the stock price minus the present value of the exercise price. The value of a put option is given by the present value of the exercise price minus the present value of the stock price. Therefore, the value of a call minus the value of a put is the present value of the stock price minus the present value of the exercise price minus (the present value of the exercise price minus the present value of the stock price), which simplifies to the value of a share minus the present value of the exercise price. Therefore, the correct answer is D.

Question 12

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 13

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

By definition, the value of a European call option is the present value of the expected payoff at expiration, which is the maximum of zero and the difference between the stock price and the exercise price. Therefore, the value of a call plus the present value of the exercise price is equal to the value of the stock (i.e. the current stock price). 
On the other hand, the value of a European put option is the present value of the expected payoff at expiration, which is the maximum of zero and the difference between the exercise price and the stock price. Therefore, the value of a put plus the present value of the exercise price is equal to the strike price. 
Combining these two, we get the value of a put plus the value of a call plus the present value of the exercise price is equal to the stock price plus the strike price, which is equivalent to the value of a put plus the value of a share. Therefore, the correct choice is C.

Question 14

Consider the following data for a European option: Expiration = 6 months; Stock price = $80; Exercise price = $75; Call option price = $12; Risk-free rate = 5 percent per year. Using put-call parity, calculate the price of a put option having the same exercise price and expiration date.
A)$3.07
B)$5.19
C)$11.43
D)$3.42

Accepted Answer

The answer of Consider the following data for a European...

Question 15

Put-call parity can be used to show
A)how valuable in-the-money put options can get.
B)how valuable 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 establishes a relationship between the prices of European call options and put options with the same strike price and expiration date. Specifically, it states that the sum of the price of a call option and the present value of the exercise price must be equal to the sum of the price of a put option and the current price of the underlying asset. This parity holds true in a theoretical, frictionless market and can be used to check for mispricings in options or to help determine the fair value of an option. It does not relate to the value of in-the-money options or the relative values of calls and puts.

Question 16

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 strategy, 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, similar to the payoff from buying a call and lending the present value of the exercise price.

Question 17

Which of the following features increase(s)the value of a call option?
I.A high interest rate;
II.A long time to maturity;
III.A higher volatility of the underlying stock price
A)I only
B)II only
C)III only
D)I, II, and III

Accepted Answer

All three features increase the value of a call option. A high interest rate increases the present value of the expected payoff, a long time to maturity gives the stock more time to increase in value, and higher volatility increases the potential for the stock to reach a higher price, all of which are beneficial for a call option holder.

Question 18

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 value of a call.

Accepted Answer

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

Question 19

If the risk-free interest rate increases, then
A)call option prices increase.
B)call option prices decrease.
C)call option prices remain the same.
D)call option prices can either increase, decrease, or remain the same.

Accepted Answer

The answer of If the risk-free interest rate increases, then
A)call...

Question 20

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 will sell the stock at the exercise price. Therefore, the value of her investment will be equal to the exercise price.

Quiz 20: Understanding Options

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

All else equal, as the underlying stock price increases:

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

Suppose the underlying stock pays a dividend before the expiration of options on that stock. This will: I.increase the value of a call option; II.increase the value of a put option; III.decrease the value of a call option; IV.decrease the value of a put option

If the volatility of the underlying asset decreases, then the

Relative to the underlying stock, a call option always has

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

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?

All else equal, as the underlying stock price increases:

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

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

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

Consider the following data for a European option: Expiration = 6 months; Stock price = $80; Exercise price = $75; Call option price = $12; Risk-free rate = 5 percent per year. Using put-call parity, calculate the price of a put option having the same exercise price and expiration date.

Put-call parity can be used to show

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

Which of the following features increase(s) the value of a call option? I.A high interest rate; II.A long time to maturity; III.A higher volatility of the underlying stock price

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

If the risk-free interest rate increases, then

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.)