1. The profit for a short position in a call option is always negative or zero. (a)True
   2. False

2. As the time to expiration becomes longer, an American call option always becomes more valuable.

(a)True

2. False

3. Consider two European put options with the same expiration dates and the same strike prices. The underlying assets of the two options are different. One option is for stock A whose current price is $50 and has the volatility of 30%. The other is for stock B whose current price is $45 and has the volatility of 25%. Both stock A and B will pay no dividends. The price of put A is always higher than the price of put B.

1. True (b)False

4. The put-call parity holds only when future stock price changes as described in a binomial tree. (a)True

2. False

5. To find the option price in a binomial tree, we need an assumption regarding the probability of the increase/decrease in the stock price.

(a)True (b)False

6. Suppose that risk-averse investors expect the return on a stock to be per annum and the risk-free rate is r per annum. In a binomial tree, if < r, the real probability of an increase in the stock price is lower than the risk-neutral probability of the increase.

(a)True (b)False

7. Consider an American put option on a non-dividend paying stock. The option will expire on date T . On date t(< T ), the option payoff from the immediate exercise is always lower than the value that results from not exercising and holding the contract.

(a)True (b)False

8. In risk-neutral valuation, we recognize that investors are risk-averse and thus modify the probability of an increase in a stock price from the real probability.

(a)True (b)False

9. In the Discounted Cash Flow, the required return on a European option should be higher than the risk-free rate. Otherwise, an arbitrage exists.

(a)True (b)False

10. An investor wants to construct a bull spread using put options with the same expiration dates. The investor needs to long the put with strike price K₁ and short the put with strike price K₂(> K₁).

(a)True (b)False

1. The profit for a short position in a call option is always negative or zero. (a)True
   2. False

2. As the time to expiration becomes longer, an American call option always becomes more valuable.

(a)True

2. False

3. Consider two European put options with the same expiration dates and the same strike prices. The underlying assets of the two options are different. One option is for stock A whose current price is $50 and has the volatility of 30%. The other is for stock B whose current price is $45 and has the volatility of 25%. Both stock A and B will pay no dividends. The price of put A is always higher than the price of put B.

1. True (b)False

4. The put-call parity holds only when future stock price changes as described in a binomial tree. (a)True

2. False

5. To find the option price in a binomial tree, we need an assumption regarding the probability of the increase/decrease in the stock price.

(a)True (b)False

6. Suppose that risk-averse investors expect the return on a stock to be per annum and the risk-free rate is r per annum. In a binomial tree, if < r, the real probability of an increase in the stock price is lower than the risk-neutral probability of the increase.

(a)True (b)False

7. Consider an American put option on a non-dividend paying stock. The option will expire on date T . On date t(< T ), the option payoff from the immediate exercise is always lower than the value that results from not exercising and holding the contract.

(a)True (b)False

8. In risk-neutral valuation, we recognize that investors are risk-averse and thus modify the probability of an increase in a stock price from the real probability.

(a)True (b)False

9. In the Discounted Cash Flow, the required return on a European option should be higher than the risk-free rate. Otherwise, an arbitrage exists.

(a)True (b)False

10. An investor wants to construct a bull spread using put options with the same expiration dates. The investor needs to long the put with strike price K₁ and short the put with strike price K₂(> K₁).

(a)True (b)False

1. The profit for a short position in a call option is always negative or zero. (a)True
   2. False

2. As the time to expiration becomes longer, an American call option always becomes more valuable.

(a)True

2. False

3. Consider two European put options with the same expiration dates and the same strike prices. The underlying assets of the two options are different. One option is for stock A whose current price is $50 and has the volatility of 30%. The other is for stock B whose current price is $45 and has the volatility of 25%. Both stock A and B will pay no dividends. The price of put A is always higher than the price of put B.

1. True (b)False

4. The put-call parity holds only when future stock price changes as described in a binomial tree. (a)True

2. False

5. To find the option price in a binomial tree, we need an assumption regarding the probability of the increase/decrease in the stock price.

(a)True (b)False

6. Suppose that risk-averse investors expect the return on a stock to be per annum and the risk-free rate is r per annum. In a binomial tree, if < r, the real probability of an increase in the stock price is lower than the risk-neutral probability of the increase.

(a)True (b)False

7. Consider an American put option on a non-dividend paying stock. The option will expire on date T . On date t(< T ), the option payoff from the immediate exercise is always lower than the value that results from not exercising and holding the contract.

(a)True (b)False

8. In risk-neutral valuation, we recognize that investors are risk-averse and thus modify the probability of an increase in a stock price from the real probability.

(a)True (b)False

9. In the Discounted Cash Flow, the required return on a European option should be higher than the risk-free rate. Otherwise, an arbitrage exists.

(a)True (b)False

10. An investor wants to construct a bull spread using put options with the same expiration dates. The investor needs to long the put with strike price K₁ and short the put with strike price K₂(> K₁).

(a)True (b)False