*I need step by step explanation on how the answer in bold were gotten.* The fol

Question

*I need step by step explanation on how the answer in bold were gotten.* 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 180ys remaining. The Black-Scholes model was used to obtain the prices. Calla Puts Sirike 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 Use this information to answer questions 1 through 3. Assume that each transaction consists of one contract (for 100 shares) unless otherwise indicated. For questions 1 through 3, consider a bull money spread using the March 45/50 calls. 1 low much will the spread cost? a. $986 b. $302 c. $283 d. $193 e. none of the above 2. What is the maximum profit on the spread? a. $500 b. $802 c. $198 d. $302 e. none of the above 3. What is the maximum loss on the spread? a. $500 b. $698 c. $198 d. $802 e. none of the above

Explanation / Answer

1. A bull spread in calls means you buy the lower strike and sell the higher strike. So you are buying one March 45 call for 6.84 and selling one March 50 call for 3.82, for a net cash outlay of 3.02 or $302 (for one contract, buying and selling).

2. The highest value the spread can ever get to is 5 so the most you can make is $198. Consider where the options will be at expiration if the stock is at or above 50:

stock at 50, 45 call worth 5, 50 call worth 0

stock at 55, 45 call worth 10, 50 call worth 5

stock at 100, 45 all worth 55, 50 call worth 50

... so you see the spread will be worth 5 no matter what, if the stock is above 50. So the most you can make is 5 - 3.02 = 1.98, or $198.

3. And the most you can lose is the $302 you paid. If the stock closes at or below 45, both options go to zero.

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