The following prices are available for call and put options on a stock priced at $50. The risk-free rate is 6 percent and the volatility is 0.35. The March options have 90 days remaining and the June options have 180 days remaining. The Black-Scholes model was used to obtain the prices.

	Calls		Puts
Strike	March	June	March	June
45	6.84	8.41	1.18	2.09
50	3.82	5.58	3.08	4.13
55	1.89	3.54	6.08	6.93

1. Suppose you closed the spread 60 days later. What will be the profit if the stock price is still at $50

a. $41

b. $198

c. $302

d. $102

e. none of the above

2. Suppose you wish to construct a ratio spread using the March and June 50 calls. You want to buy 100 June 50 call contracts. How many March 50 calls would you sell?

a. 105

b. 95

c. 100

d. 57

e. none of the above

3.What is the profit if the position is held for 90 days and the stock price is $55?

a. -$971

b. -$58

c. -$109

d. -$471

e. none of the above