Question 1

For a call and a put written on the same underlying but at at possibly different strike prices,

Accepted Answer

A call and a put option can both be in-the-money simultaneously if the underlying asset's price is between the two strike prices, assuming the call's strike price is lower than the put's strike price.

Question 2

You have a long position in a stock that you purchased for $100, and a short position in a put option on the same stock at strike K = 100. At maturity the stock price is $95, and you liquidate your stock and option positions. Your gross payoff (cash flow) is

Accepted Answer

The long underlying stock position will generate a cash flow of -$100 (since the stock is sold for $95, resulting in a loss of $5).
The short put option position will generate a cash flow of +$5 (since the holder of the put option will exercise it and sell the stock to the writer of the put option at the strike price of $100, resulting in a gain of $5 for the writer).
Therefore, the net cash flow is -$100 + $5 = -$95. Since this is the gross payoff, the answer is C ($90) after taking into account the initial investment of $100.

Question 3

Which of the following is a valid completion of the sentence-"An American option ..."?

Accepted Answer

An American option is exercisable prior to maturity whereas European options are not. This is the key distinguishing feature between the two options. A reflects a potential behavioral explanation for the naming of the option, and B is incorrect as European options can also be traded in America.

Question 4

The value of the following position for options at the same strike price is always zero:

Accepted Answer

The value of a position with both a long call and a long put (a) or both a short call and a short put (b) at the same strike price is not always zero. The value depends on the underlying asset's price relative to the strike price.

Question 5

You have a portfolio with long positions in both puts and calls. The volatility in the market rises.

Accepted Answer

When market volatility rises, both puts and calls generally increase in value because the potential for large price swings makes these options more valuable. This is due to the fact that options are priced based on volatility among other factors; higher volatility increases the likelihood of an option ending in the money.

Question 6

If you believe that stock prices are going to fall for sure, then given a fixed amount of capital, you should

Accepted Answer

Buying put options allows an investor to profit from a decline in the underlying stock without having to sell the stock directly. This strategy limits potential losses to the cost of the put option while offering unlimited profit potential as the stock continues to decline. Selling stock or selling call options may also be viable strategies, but they involve greater risks and potentially unlimited losses. Therefore, the best choice in this scenario is to buy put options.

Question 7

You have $100 to invest in a stock (or options on the stock). The stock is trading for $100. The three-month 100-strike calls on the stock are trading at $4 each. The minimum stock price you expect to see after three months is $60. What is the worst case return on investment you can possibly end up with using stock and/or options?

Accepted Answer

If you invest in the stock directly and the price drops to $60, you lose $40 on a $100 investment, which is a -40% return. However, if you buy the call option for $4 and the stock price drops below $100, you would let the option expire worthless, losing only the $4 premium paid. This results in a -100% loss on the option investment, but because the option investment was only $4, the actual dollar loss is much smaller compared to investing directly in the stock. The worst case return on investment, considering the options available, is -100% if you choose to invest in the options and they expire worthless.

Question 8

If your directional view is that stock prices are going to fall, you should

Accepted Answer

Selling stock now allows you to profit from a decline in stock prices. Selling call options generates income and profits if the stock price falls or stays below the strike price. Buying put options gives you the right to sell the stock at a predetermined price, which can be profitable if the stock price falls below that level. All these strategies are profitable if your directional view that stock prices are going to fall is correct.

Question 9

You hold the following portfolio: a long position in a European call option on gold with a strike of $975 per oz, a short position in a European put option on gold with a strike of $975 per oz, and a short forward position in gold with a delivery price of $1,000 per oz. All three contracts expire in one month. The value of your position is

Accepted Answer

The answer of You hold the following portfolio: a long...

Question 10

You sold a call option at strike 105 for a price of $3 and sold a put option at strike 95 for a price of $2, both options with the same maturity. In what range of stock prices at maturity will you make money or not lose (on your net payoff)?

Accepted Answer

The answer of You sold a call option at strike...

Question 11

The premium of an option is

Accepted Answer

The premium of an option is the price of the option, which represents the value of the right but not the obligation to undertake a purchase or sale of the underlying asset. Additionally, the premium is always non-negative. Therefore, all of the above choices are correct.

Question 12

You have $100 to invest. You can invest it in one of two alternatives. The first is to invest it in a stock that is trading for $100. The second is to buy three-month 100-strike calls on the stock that are currently trading at $4 each. You expect the stock price to appreciate with a maximum price after three months of $110. What is the maximum return on investment you can generate using stock and options?

Accepted Answer

- If you invest all $100 in the stock, and the stock price increases to $110, then your return on investment is: (110-100)/100 = 10%.
- If you buy three-month 100-strike calls on the stock, each costing $4, then you can buy 25 calls with $100 ($100/($4 x 25) = 100/100). Each call option gives you the right to buy one share of the stock at $100 within the next three months. If the stock price increases to $110, then each call option is worth: max(0, 110-100) = $10. Therefore, your return on investment is: (25 x $10 - $100)/$100 = 150%.
Thus, buying three-month call options is the better choice as it gives a higher potential return on investment.

Question 13

If you expect stock volatility to fall but have no particular view of direction, then you should

Accepted Answer

Selling call options is a strategy that benefits from decreasing volatility, as it typically leads to a decrease in option prices, allowing the seller to potentially buy back the option at a lower price or profit from the option expiring worthless.

Question 14

The largest markets for derivatives based on notional outstandings are

Accepted Answer

According to the Bank for International Settlements, as of June 2019, interest-rate derivatives accounted for 76% of the total notional amount outstanding for all derivatives globally. This is followed by foreign exchange derivatives at 15%, credit derivatives at 4%, and equity derivatives at 3%. Commodity derivatives make up only a small fraction of the market. Therefore, the best choice is Interest-rate derivatives.

Question 15

A call option with a strike of K = 100 is purchased at a premium of $4. The stock price at maturity is $105. The net payoff of the option is

Accepted Answer

The net payoff of the option is calculated by subtracting the premium paid for the option from the gross payoff. The gross payoff from the call option is the difference between the stock price at maturity ($105) and the strike price ($100), which is $5. After subtracting the premium paid ($4), the net payoff is $1.

Question 16

If you expect stock volatility to rise but have no particular view of direction, then you should

Accepted Answer

Buying put options is the best choice if you expect stock volatility to rise but have no particular view of direction. This is because put options increase in value as the stock price decreases, providing downside protection in the event of a market downturn. Selling stock now or selling call options both involve taking a bearish view of the market, which may not be accurate if volatility increases but the market doesn't necessarily move downwards. Therefore, buying put options is the most appropriate strategy for this scenario.

Question 17

You have a long position in a stock that you purchased for $100, a short position in a call and a long position in a put, both at strike K = 100. At maturity the stock price is S_T, and you liquidate your stock and option positions. Your gross payoff (cash flow) is

Accepted Answer

The answer of You have a long position in a...

Question 18

The writer of a put option on a stock

Accepted Answer

The writer of a put option has the obligation to buy the stock if the option is exercised by the holder.

Question 19

You anticipate that volatility will increase sharply and the stock price will fall. Select the most profitable of the following portfolios to hold, given your views:

Accepted Answer

If you anticipate that volatility will increase sharply and the stock price will fall, the most profitable portfolio to hold is a short stock and long puts. This is because shorting the stock will benefit from the anticipated price fall, while buying long puts will give you the right to sell the stock at a higher price, resulting in a profit. This combination will also limit your potential losses if the stock price were to rise instead of fall. The other options all include long calls, which would not be profitable in a falling market.

Question 20

Which of the following statements is true of an option's payoff?

Accepted Answer

The gross payoff of an option is the total amount received from exercise or sale of the option, while the net payoff is the gross payoff minus the cost of the option. Therefore, depending on the cost of the option, the gross payoff can be greater or less than the net payoff. Choice A is incorrect because the gross payoff could be less than the net payoff if the cost of the option is high. Choice B is incorrect because the gross payoff cannot be less than zero. Choice D is incorrect because there are some scenarios where the gross payoff is not equal to the net payoff.

Quiz 7: Options Markets

For a call and a put written on the same underlying but at at possibly different strike prices,

You have a long position in a stock that you purchased for $100, and a short position in a put option on the same stock at strike K = 100. At maturity the stock price is $95, and you liquidate your stock and option positions. Your gross payoff (cash flow) is

Which of the following is a valid completion of the sentence-"An American option ..."?

The value of the following position for options at the same strike price is always zero:

You have a portfolio with long positions in both puts and calls. The volatility in the market rises.

If you believe that stock prices are going to fall for sure, then given a fixed amount of capital, you should

If your directional view is that stock prices are going to fall, you should

You sold a call option at strike 105 for a price of $3 and sold a put option at strike 95 for a price of $2, both options with the same maturity. In what range of stock prices at maturity will you make money or not lose (on your net payoff) ?

The premium of an option is

If you expect stock volatility to fall but have no particular view of direction, then you should

The largest markets for derivatives based on notional outstandings are

A call option with a strike of K = 100 is purchased at a premium of $4. The stock price at maturity is $105. The net payoff of the option is

If you expect stock volatility to rise but have no particular view of direction, then you should

You have a long position in a stock that you purchased for $100, a short position in a call and a long position in a put, both at strike K = 100. At maturity the stock price is S_T, and you liquidate your stock and option positions. Your gross payoff (cash flow) is

The writer of a put option on a stock

You anticipate that volatility will increase sharply and the stock price will fall. Select the most profitable of the following portfolios to hold, given your views:

Which of the following statements is true of an option's payoff?

Quiz 7: Options Markets

For a call and a put written on the same underlying but at at possibly different strike prices,

You have a long position in a stock that you purchased for $100, and a short position in a put option on the same stock at strike K = 100. At maturity the stock price is $95, and you liquidate your stock and option positions. Your gross payoff (cash flow) is

Which of the following is a valid completion of the sentence-"An American option ..."?

The value of the following position for options at the same strike price is always zero:

You have a portfolio with long positions in both puts and calls. The volatility in the market rises.

If you believe that stock prices are going to fall for sure, then given a fixed amount of capital, you should

If your directional view is that stock prices are going to fall, you should

You sold a call option at strike 105 for a price of $3 and sold a put option at strike 95 for a price of $2, both options with the same maturity. In what range of stock prices at maturity will you make money or not lose (on your net payoff) ?

The premium of an option is

If you expect stock volatility to fall but have no particular view of direction, then you should

The largest markets for derivatives based on notional outstandings are

A call option with a strike of K = 100 is purchased at a premium of $4. The stock price at maturity is $105. The net payoff of the option is

If you expect stock volatility to rise but have no particular view of direction, then you should

You have a long position in a stock that you purchased for $100, a short position in a call and a long position in a put, both at strike K = 100. At maturity the stock price is ST, and you liquidate your stock and option positions. Your gross payoff (cash flow) is

The writer of a put option on a stock

You anticipate that volatility will increase sharply and the stock price will fall. Select the most profitable of the following portfolios to hold, given your views:

Which of the following statements is true of an option's payoff?

You have a long position in a stock that you purchased for $100, a short position in a call and a long position in a put, both at strike K = 100. At maturity the stock price is S_T, and you liquidate your stock and option positions. Your gross payoff (cash flow) is