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J Speculative premium per day 1'. Assume on May 1 you are considering a stock with three different expiration dates for the on call options. The percentage of the speculative premium for each date is as follows: lvlay 2.3% August 6.7 November 10.9 Each contract expires at 11:59 pm. Eastern time on the Saturday immediately following the third Friday of the expiration month. For purposes ofthis problem, assume the May option has 21 days to run, the August option has 112 days, and the November option has 203 days. 3. Compute the percentage speculative premium per day for each of the three dates. a. From the viewpoint of a call option purchaser. which expiration date appears most attractive {all else being equal)? 0. From the viewpoint of a call option writer, which expiration date appears most attractive {all else being equal)? Covered call options 10. Assume you purchase 100 shares of stock at $44 per share and wish to hedge your position by writing a 100-share call option on your holdings. The option has a 40 strike price and a premium of 8.50. If the stock is selling at 38 at the time of expiration, what will be the overall dollar gain or loss on this covered option play? (Consider the change in stock value as well as the gain or loss on the option.) Note that the stock does not pay a cash dividend.J l Protecting a short position with options 14. Assume you sell 100 shares of Bowie Corporation short at $2. You also buy a F0 call option for 5.25 to protect against the stock price going up. a. If the stock ends up at $90, what will be your overall gain or loss? b. If the stock ends up at 350, what will be your overall gain or loss? o. If you have an unprotected short sale position {no call option), what is the most you could lose? Protecting a short position with options 15. Assume you sell 100 shares of Alston Corporation short at $43. You also buy a 40 call option for $4.30 to protect against the stock price going up. a. If the stock ends up at $60. what will be your overall gain or loss? a. If the stock ends up at $20, what will be your overall gain or loss? :2. What is the most you can lose under this short salecall option plan? of If you have an unprotected short sale position {no call option}, what is the most you could lose? e. Under the conditions described in part at if you had a limit order to buy the stock and close out the position at $54, what is the most you could lose? Question 2.18 Near market closing time on a given day, you lose access to stock prices, but some European call and put prices for a stock are available as follows: Strike Price Call Price Put Price $45 $12 $4 $55 $7 $60 $4 $12 All 6 options have the same expiration date. The risk-free interest rate is zero. After reviewing the information above, Jill tells Sabrina and Kelly that one could use the following zero-cost portfolio to obtain arbitrage profit: Short one put option with strike price 45; long 3 put options with strike price 55; lend $1; and short some number of put options with strike price 60. Sabrina claims that the following zero-cost portfolio can produce arbitrage profit: Long one call option with strike price 45; short 3 call options with strike price 55; lend $1; and long some number of call options with strike price 60. Kelly claims that the following zero-cost portfolio can produce arbitrage profit: Long 2 calls and short 2 puts with strike price 60; long 1 call and short 1 put with strike price 45; lend $2; and short some calls and long the same number of puts with strike price 55. Which of the following statements is correct? A Only Jill is correct. B Only Sabrina is correct. C Only Kelly is correct. D Only Sabrina and Kelly are correct. E None of them is correct. ActuarialBrew.com 2015 Page 2.03 Exam MFE/3F Questions Chapter 2- Comparing Options Question 2.19 You are given: (i) C(K,T) denotes the current price of a K-strike T-year European call option on a nondividend-paying stock. (ii) P(K,T) denotes the current price of a K-strike T-year European put option on the same stock. (iii) S denotes the current price of the stock. (iv) The continuously compounded risk-free interest rate is r, and r > 0. Which of the following is (are) correct? I O S P(85, T) - P(80, T) 5 5e FT II 75e-FT s P(75, T) - C(80,T) + SS 80e-TT III 80e- s P(75,T) - C(80,T) + Ss 85 A I only B II only C III only D I and II only E I and III only
