Question

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.

	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

Use this information to answer the following questions. Assume that each transaction consists of one contract for 100 shares. Consider a bull call spread using the March 45/50 calls. A bull call spread consists of one long call with a lower strike price and one short call with a higher strike price. Also, Briefly discuss why you would use a bull call spread in terms of risk?

1. How much will the spread cost?
2. What is the maximum profit on the spread? Maximum loss?
3. What is the profit or loss if the stock price at expiration is $47?
4. What is the breakeven point?

Answer 1

A bull call spread is executed when the view on the underlying asset is bullish but one does not see the underlying breach a particular level on the up side. It is a cost reduction structure. It is a net premium paying structure. If the stock price at maturity is below the level of Buy Call, then one loses only to the extent of the net premium paid for going long the Bull Call Spread

a. 6.84 - 3.82 = USD 3.02

b. The maximum profit on the spread: SC strike - BC strike - net premium = 50 - 45 - 3.02 = USD 1.98.

Maximum Loss = Net premium paid = USD 3.02

c. If stock price at expiration = 47, payoff = 47 - 45 - 3.02 = Loss of USD 1.02

d. Break even point is where one would recoup the net premium paid = 45 + 3.02 = USD 48.02