The following prices are available for call and put options on a stock priced at
ID: 2635276 • 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 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. Use this information to answer questions 1 through 20. Assume that each transaction consists of one contract (for 100 shares) unless otherwise indicated. For questions 7 and 8. suppose an investor expects the stock price to remain at about $50 and decides to execute a butterfly spread using the June calls. 7. What will be the cost of the butterfly spread? 8. What will be the profit if the stock price at expiration is $52.50? 9. 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?Explanation / Answer
7. The butterfly spread will be formed by:
a. Long 1 call with strike price $45
b. Short 2 calls with strike price $50
c. long 1 call with strike price $55
Thus, total cost of the spread (1 contract = 100 shares) = 100 * (8.41 - 2*5.58 + 3.54) = 100 * 0.79 = $79 i.e choice c.
8. Stock price at expiration = $52.50
a.payoff from Long 1 call with strike price $45 = 52.50 - 45 = $7.50
b.payoff from Short 2 calls with strike price $50 = 2 * (50-52.50) = -5
c.payoff from long 1 call with strike price $55 = 0
Thus total profit = 100 * (7.50 -5 - 0.79) = 100 * 1.71 = $171 i.e choice a
9. typically involves shorting options of shorter dated call and going long in options of longer dated call.
Value of 100 June contracts = 100 * 100 * 5.58 = 55800
Let no of March contracts be x. Value of x Mar contracts = x * 100 * 3.82 = 382x
Ratio = 382x : 55800
Incomplete question as we are not given the ratio that should be used.
Using the most typical 3:2 & 2:1 ratios:
3:2 = 382x:55800
382x = 55800*1.5= 83700
x = 111600/382 = 219
2:1 = 382x:55800
382x = 55800*2 = 111600
x = 111600/382 = 292
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