1. Consider a two-period binomial tree model with the following information of the stocks: stock price = $50, up factor = 1.238, down factor = 0.795, risk-free rate = 0.05. If a call option has a strike price of $60, then what is the probability of the call expiring in the money based on the risk-neutral probability?

A. 33.13%

B. 40.98%

C. 24.43%

D. None of above

2. Consider a three-period binomial tree model with the following information of the stocks: stock price = $50, up factor = 1.238, down factor = 0.795, risk-free rate = 0.05. If a call option has a strike price of $60, then what I the probability of the call expiring in the money based on the risk-neutral probability? (hint: if there are more than one node, the probability should be added)

A. 19.07%

B. 42.18%

C. 61.25%

D. None of above

3. Which of the following regarding hedge ratio is NOT correct?

A. The hedge ratio for put option is always non-positive and the hedge ratio for call option is always non-negative.

B. The hedge ratio for call option is always between 0 and 1.

C. The hedge ratio for call option can be higher than 1. It happens when both the up state and the down state yielda stock price that's higher than the strike price.

D. For a call option, the hedge is zero if, in both the up and down states, the stock price is lower than the strike price.

4. A non-dividend-paying stock is trading at $45. We consider a PUT option in a one-period binomial tree model. The periodically compounded risk- free interest rate is 4%, the exercise price is also $45, u = 1.21, and d = 0.77. Assume the call option is European- style. The hedge ratio at the beginning of the binomial tree is close to

A. 0.5

B. -0.5

C. 1

D. -1

5. We consider a four-period binomial tree model for a call option. Suppose the risk- free interest rate is 4%, the up-factor u = 1.125, and down-factor d = 0.812. The probability of the stock price ends at the second to the lowest level (after four periods), based on the risk-neutral probability, is closest to

A. 6.0%

B. 16.0%

C. 26.0%

D. 36.0%