chap020ise.docx

1、chap020iseCHAPTER 20: OPTIONS MARKETS: INTRODUCTION1.CostPayoffProfita.Call option, X = $80.00$4.40$5.00$0.60b.Put option, X = $80.00$0.75$0.00-$0.75c.Call option, X = $85.00$1.35$0.00-$1.35d.Put option, X = $85.00$2.90$0.00-$2.90e.Call option, X = $90.00$0.25$0.00-$0.25f.Put option, X = $90.00$6.80

2、$5.00-$1.802. In terms of monetary returns, based on a 1,000 investment:Price of Stock 6 Months from NowStock Price4567All stocks (200 shares)8001,0001,2001,400All options (2,000 options)002,0004,000MM Fund + 200 options9369361,1361,336In terms of rate of return, based on a 1,000 investment:Price of

3、 Stock 6 Months from NowStock Price4567All stocks (200 shares)-20%0%20%40%All options (2,000 options)-100%-100%100%300%MM Fund + 200 options-6.4%-6.4%13.6%33.6% 3. a. From put-call parity:P = C S0 + X/(1 + rf )T = 2 20 + 20/(1.10)1/4 = C$1.53b. Purchase a straddle, i.e., both a put and a call on the

4、 stock. The total cost of the straddle is: C$2 + C$1.53 = C$3.53This is the amount by which the stock would have to move in either direction for the profit on the call or put to cover the investment cost (not including time value of money considerations). Accounting for time value, the stock price w

5、ould have to move in either direction by: C$3.53 1.101/4 = C$3.624. a. From put-call parity:C = P + S0 X/(l + rf )T = 560 + 7,000 7,000/(1.10)1/4 = 724.82b. Sell a straddle, i.e., sell a call and a put to realize premium income of:724.82 + 560 = 1,284.82If the stock ends up at 7,000, both of the opt

6、ions will be worthless and your profit will be 1,284.82. This is your maximum possible profit since, at any other stock price, you will have to pay off on either the call or the put. The stock price can move by 1,284.82 in either direction before your profits become negative.c. Buy the call, sell (w

7、rite) the put, lend: 7,000/(1.10)1/4The payoff is as follows:PositionImmediate CFCF in 3 monthsS T XS T XCall (long)C = 724.820S T 7,000Put (short)P = 560.00 (7,000 S T)0Lending position7,0007,000TotalC P + S TS TBy the put-call parity theorem, the initial outlay equals the stock price:S0 = 7,000In

8、either scenario, you end up with the same payoff as you would if you bought the stock itself.5. a.OutcomeS T XS T XStockS T + DS T + DPutX S T0TotalX + DS T + Db.OutcomeS T XS T XCall0ST XZerosX + DX + DTotalX + DST + DThe total payoffs for the two strategies are equal regardless of whether S T exce

9、eds X.c. The cost of establishing the stock-plus-put portfolio is: S0 + PThe cost of establishing the call-plus-zero portfolio is: C + PV(X + D)Therefore:S0 + P = C + PV(X + D)This result is identical to equation 20.2.6. a. By writing covered call options, Jones receives premium income of 30,000. If

10、, in January, the price of the stock is less than or equal to 45, then Jones will have his stock plus the premium income. But the most he can have at that time is (450,000 + 30,000) because the stock will be called away from him if the stock price exceeds 45. (We are ignoring here any interest earne

11、d over this short period of time on the premium income received from writing the option.) The payoff structure is:Stock price Portfolio valueless than 45 10,000 times stock price + 30,000greater than 45 450,000 + 30,000 = 480,000This strategy offers some extra premium income but leaves Jones subject

12、 to substantial downside risk. At an extreme, if the stock price fell to zero, Jones would be left with only 30,000. This strategy also puts a cap on the final value at 480,000, but this is more than sufficient to purchase the house.b. By buying put options with a 35 strike price, Jones will be payi

13、ng 30,000 in premiums in order to insure a minimum level for the final value of his position. That minimum value is: (35 10,000) 30,000 = 320,000This strategy allows for upside gain, but exposes Jones to the possibility of a moderate loss equal to the cost of the puts. The payoff structure is:Stock

14、price Portfolio valueless than 35 350,000 30,000 = 320,000greater than 35 10,000 times stock price 30,000c. The net cost of the collar is zero. The value of the portfolio will be as follows:Stock price Portfolio value less than 35 350,000between 35 and 45 10,000 times stock pricegreater than 45 450,

15、000If the stock price is less than or equal to 35, then the collar preserves the 350,000 principal. If the price exceeds 45, then Jones gains up to a cap of 450,000. In between 35 and 45, his proceeds equal 10,000 times the stock price.The best strategy in this case would be (c) since it satisfies t

16、he two requirements of preserving the 350,000 in principal while offering a chance of getting 450,000. Strategy (a) should be ruled out since it leaves Jones exposed to the risk of substantial loss of principal.Our ranking would be: (1) strategy c; (2) strategy b; (3) strategy a.7. a.PositionS T X1X

17、1 S T X2X2 S T X3X3 S T Long call (X1)0S T X1S T X1S T X1Short 2 calls (X2)002(S T X2)2(S T X2)Long call (X3)000S T X3Total0S T X12X2 X1 S T (X2 X1) (X3 X2) = 0 b.PositionS T X1X1 S T X2 X2X2XX2X2X2X2X2X2 S TBuy call (X2)00S T X2Buy put (X1)X1 S T 00TotalX1 S T 0S T X2 8.PositionS T X1X1 S T X2 XX2X

18、2 S TBuy call (X2)00S T X2Sell call (X1)0(S T X1)(S T X1)Total0X1 S T X1 X2 9. The farmer has the option to sell the crop to the government for a guaranteed minimum price if the market price is too low. If the support price is denoted PS and the market price Pm then the farmer has a put option to se

19、ll the crop (the asset) at an exercise price of PS even if the price of the underlying asset (Pm) is less than PS.10. The bondholders have, in effect, made a loan which requires repayment of B dollars, where B is the face value of bonds. If, however, the value of the firm (V) is less than B, the loa

20、n is satisfied by the bondholders taking over the firm. In this way, the bondholders are forced to “pay” B (in the sense that the loan is cancelled) in return for an asset worth only V. It is as though the bondholders wrote a put on an asset worth V with exercise price B. Alternatively, one might vi

21、ew the bondholders as giving the right to the equity holders to reclaim the firm by paying off the B dollar debt. The bondholders have issued a call to the equity holders.11. a. & b. The Excel spreadsheet for both parts (a) and (b) is shown on the next page, and the profit diagrams are on the follow

22、ing page.12. The manager gets a bonus if the stock price exceeds a certain value and gets nothing otherwise. This is the same as the payoff to a call option.13. i. Equity index-linked note: Unlike traditional debt securities that pay a scheduled rate of coupon interest on a periodic basis and the pa

23、r amount of principal at maturity, the equity index-linked note typically pays little or no coupon interest; at maturity, however, a unit holder receives the original issue price plus a supplemental redemption amount, the value of which depends on where the equity index settled relative to a predete

24、rmined initial level.ii. Commodity-linked bear bond: Unlike traditional debt securities that pay a scheduled rate of coupon interest on a periodic basis and the par amount of principal at maturity, the commodity-linked bear bond allows an investor to participate in a decline in a commoditys price. I

25、n exchange for a lower than market coupon, buyers of a bear tranche receive a redemption value that exceeds the purchase price if the commodity price has declined by the maturity date.Spreadsheet for Problem 11:Stock PricesBeginning Market Price116.5Ending Market Price130X 130 StraddleEndingProfitBu

26、ying Options:Stock Price-37.20Call Options StrikePricePayoffProfitReturn %5042.8011022.8020.00-2.80-12.28%6032.8012016.8010.00-6.80-40.48%7022.8013013.600.00-13.60-100.00%8012.8014010.300.00-10.30-100.00%902.80100-7.20Put Options StrikePricePayoffProfitReturn %110-17.2011012.600.00-12.60-100.00%120-

27、27.2012017.200.00-17.20-100.00%130-37.2013023.600.00-23.60-100.00%140-27.2014030.5010.00-20.50-67.21%150-17.20160-7.20StraddlePricePayoffProfitReturn %1702.8011035.4020.00-15.40-43.50%18012.8012034.0010.00-24.00-70.59%19022.8013037.200.00-37.20-100.00%20032.8014040.8010.00-30.80-75.49%21042.80Sellin

28、g Options:BullishCall Options StrikePricePayoffProfitReturn %EndingSpread11022.80-202.8012.28%Stock Price6.8012016.80-106.8040.48%50-3.213013.60013.60100.00%60-3.214010.30010.30100.00%70-3.280-3.2Put Options StrikePricePayoffProfitReturn %90-3.211012.60012.60100.00%100-3.212017.20017.20100.00%110-3.213023.60023.60100.00%120-3.214030.501040.50132.79%1306.81406.8Money SpreadPricePayoffProfit1506.8Bullish Spread1606.8Purchase 120 Call16.8010.00-6.801706.8Sell 130 Call13.60013.601806.8Combined Profit10.006.8019