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1. For Natural Resource Partners LP (NRP), what were the adjustments to the terms of a $1strike March 2016 call option that resulted from the 1-10 reverse stock split? What about the $1.5-strike March put option? When will the adjustments take place? (Note: The stock once traded for over $35 a share, in early 2011, and closed at $0.85 per share before the split.) 2. Suppose the following call and put prices on XYZ stock with expiration in April. You buy a $41-strike put and write (short) a $43-strike put. Assume you buy at the ask price and sell at the bid. XYZ Corporation Option Prices Calls Open Strike Last Bid Ask Change %Change Volume Interest 2.86 2.99 3.2 0 0.00% 1 1 2.29 2.57 2.75 0 0.00% 1 12 2.25 2.19 2.35 0 0.00% 20 412 1.88 1.83 1.99 0 0.00% 2 630 1.55 1.51 1.63 -0.23 -13.94% 9 852 1.27 1.21 1.33 -0.08 -6.40% 3 174 0.99 0.98 1.03 -0.19 -17.76% 497 1340 0.82 0.74 0.81 -0.04 -5.33% 109 920 0.58 0.57 0.6 0.06 13.33% 244 1243 0.43 0.4 0.46 0 0.00% 109 735 45 0.32 0.29 0.33 -0.06 -17.14% 365 448 Puts Open Strike Last Bid Ask Change %Change Volume Interest 0.26 0.3 0.34 -0.2 -32.79% 10 206 0.37 0.35 0.43 -0.23 -30.67% 2 149 0.5 0.49 0.53 0.06 10.53% 165 1442 0.78 0.58 0.68 0.07 9.86% 59 1865 0.73 0.78 0.82 -0.4 -28.99% 1574 767 1.16 0.96 1.05 0.09 8.41% 5 546 1.25 1.21 1.25 0 0.00% 35 496 1.39 1.46 1.57 -0.48 -22.12% 33 93 1.8 1.76 1.86 0.17 9.04% 90 143 2.02 2.1 2.25 0 0.00% 88 93 45 2.39 2.48 2.62 -0.51 -15.41% 352 147 1 a) Draw the payoff at expiration and profit at expiration (on the same graph) for your vertical put spread. At what stock price will the profit be zero? b) Describe two other trading strategies which, in the absence of arbitrage opportunities (and no transaction costs), will have the same profit diagram (if we account for interest on the initial investment). XYZ will pay no dividends before April expiration. 3. What strategy using a put option will have the same payout as a covered call on XYZ stock, where the written call expires in April and has a strike price of $44? Ignore the possibility of early exercise of the put. (Hint: The cost of the covered call is S – C. Use put call parity to find the alternative strategy that should have the same price, if there were no bid-ask spreads.) Assume the options expire in one month and the appropriate repo rate is 0.20% APR with continuous compounding. Use the XYZ option prices from problem 2 to compare the net investments of the two strategies. Assume that the share price is $42.88, and, for the options, that you will buy at the ask price and sell at the bid. 4. What position in call options (only) will have the same payoff as the variable prepaid forward contract we covered in class (PP slide 16)? 5. On a per-share based, determine the number (or proportion) of shares delivered to the bank in each region to construct a variable prepaid collar with the following payouts to the executive: i) zero dollar payout for ST between $0 and $80 ii) a $ payout of ST-$80 for ST between $80 and $95 iii) a $ payout of $15+(ST-$95)(3/19) for ST above $95 (Note that the payoff is continuous.) Suppose S= $80.07, C(80) = $3.35 (that is, the $80-strike call is $3.35) and C(95) = $0.15, and that there are no dividends before expiration. Then what is the fair fraction ? of the current stock price that the bank should pay up front to the executive for the deal? Hint: The PV of the executive’s position under the variable prepaid collar is ?S0 plus the cost of replicating (using call options) the resulting payout to the executive. 2 6. Suppose a stock is priced at $51, and European options on the stock, both expiring in one year with a strike price of $52.50, are priced at $4.25 for the call and $3.75 for the put. Assume a continuously compounded interest rate of 4.879% (which corresponds to 5% APR with annual compounding). The stock will pay no dividends over the next year. Carefully show the arbitrage strategy, using numbers where possible, using a payoff table. 7. Suppose employees of Google are given call options to buy the stock for $10 per share; the options expire in 2 months. Google is trading at $726.82 per share and will not pay a dividend before the options expire. Assume the interest rate is 1% continuously compounded, and that there is no chance that the share price of Google will fall below $10 before expiration. a) Provide a numerical expression for the value of each call assuming they are European style. b) Provide a numerical expression for the value of each call assuming they are American style. 8. Find the lower bound for the price of a 6-month call option on a non-dividend-paying stock when the stock price is $80, the strike price is $75, and the riskless interest rate is 10% c.c. Suppose the European call premium were $8. What is the arbitrage strategy? 9. The price of a 1-month European put option on a non-dividend-paying stock is $2.50. The stock price is $47, the strike price is $50, and the riskless interest rate is 6% c.c. Show the arbitrage trade and payouts using a payout table. 10. Show that it would it never be optimal to exercise an American put option early if interest rates were always less than or equal to zero. Hint: Use the lower bound on the European put option, and show that it must exceed the intrinsic value if r=0. 3

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