The following prices are available for call and put options on a stock priced at
ID: 2782619 • Letter: T
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 .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 45 50 March 6.84 3.82 1.89 une 8.41 5.58 3.54 March 1.18 3.08 6.08 June 2.09 4.13 6.93 Use this information to answer questions 1 through 20. Assume that each transaction consists of one contract (100 options) unless otherwise indicated. For questions 1 through 6, consider a bull money spread using the March 45/50 calls. 1. How 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 aboveExplanation / Answer
In a bull money spread, the investor buys the option at a lower strike price and sells the option at a higher strike price. In our case, he would buy the 100 March call options with strike price of 45 @6.84 premium and sell 100 call options with stike price of 50 @3.82 premium.
1) Cost of spread = Premium paid - Premium received = $6.84 x 100 - $3.82 x 100 = $302 (option b)
2) Maximum profit is reached for the bull call spread options strategy when the stock price move above the higher strike price of the two calls and it is equal to the difference between the strike price of the two call options minus the initial debit taken to enter the position. It is given by -
Maximum Profit = (Strike price of short call - Strike Price of long call) x No. of Options - Net premium Paid
Maximum profit = (50 - 45) x 100 - $302 = $198 (Option c)
3) The bull call spread strategy will result in a loss if the stock price declines at expiration. Maximum loss cannot be more than the initial debit taken to enter the spread position.
Maximum Loss = Net Premium paid
Maximum Loss = $302 (Option e - none of the above)
4) If the stock price at expiry is $47, we will exercise the options bought and buy shares @45 and sell @47. But, the other buyer will not exercise his options as he would incur a loss at this price which is lower than the stike price of 50.
Profit = (47 - 45) x 100 - $302 = (-)$102 (option a)
5) Break-even point of a bull money spread is given by -
Break-Even Point = Strike Price of Long call + Net premium paid = $45 + ($6.84 - $3.82) = $48.02 (Option a)
6) If the stike price is 50, we will exercise options bought @45 and sell these shares @50 and other option buyer will be indifferent to this situation, as he has no gain or loss at this price.
Profit = ($50 - $45) x 100 - $302 = $198 (Option b)
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