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

The answer of If the volatility of the underlying asset...

Question 2

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 the investment will be the exercise price, which is the value of the put option. The value of the stock is not relevant in this scenario.

Question 3

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

The answer of A call option has an exercise price...

Question 4

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

The answer of Which of the following investors would be...

Question 5

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

The answer of If the risk-free interest rate increases:
A) the...

Question 6

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

This is known as put-call parity and is a fundamental relationship in option pricing theory. The value of a call minus the value of a put is equal to the value of a share minus the present value of the exercise price. Therefore, the correct choice is D, which states that the value of a share minus the present value of the exercise price.

Question 7

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 concept in options trading that shows the relationship between put and call option prices given equal exercise prices and equal expiration dates. It states that the price of a call option plus the present value of the exercise price is equal to the price of a put option plus the stock price. This relationship must hold in order to avoid arbitrage opportunities by traders. Therefore, put-call parity can be used to determine the fair price of options in the market. Option traders can also use this concept to construct synthetic positions or hedge their existing positions.

Question 8

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

The answer of Suppose you buy a call and lend...

Question 9

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 10

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 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

The answer of For European options, the value of a...

Question 12

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

According to put-call parity, C + Ke^(-rt) = P + S
where C is the price of the call option, K is the exercise price, r is the risk-free rate, t is the time to expiration, P is the price of the put option, and S is the spot price.

We can rearrange the formula to solve for P:
P = C + Ke^(-rt) - S
Substituting the given values, we get:
P = 12 + 75e^(-0.05*0.5) - 80
P = 5.19

Therefore, the price of an equivalent put option is $5.19.

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

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 15

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

The answer of Relative to the underlying stock, a call...

Question 16

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 answer of For European options, the value of a...

Question 17

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 18

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

Since the investor has bought a share of stock and a put option on the stock, he has the right to sell the stock at the exercise price in case the stock price falls. Along with this, he has sold a call option on the stock with the same exercise price. This means that he has the obligation to sell the stock at the exercise price in case the stock price rises. Therefore, no matter what happens to the stock price, he will always be able to sell the stock at the exercise price. Hence, the value of his investment will be equal to the exercise price regardless of the stock price.

Question 19

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

A high interest rate increases the value of the option because it increases the present value of the option. A long time to maturity gives the underlying stock more time to increase in value, increasing the potential payoff of the option. A higher volatility of the underlying stock price increases the potential magnitude of the stock's movement, providing more opportunity for the option to be profitable. Therefore, all three features increase the value of a call option.

Question 20

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

The answer of If the underlying stock pays a dividend...

Quiz 16: Understanding Options

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

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 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?

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

If the risk-free interest rate increases:

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

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:

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

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

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

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:

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:

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

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

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

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 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?

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