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Chapter 20, Problem 5, Parts a, b, c, Page 760 5. The common stock of Company XYZ is currently trading at a price of $42, Both a put and a call option are available for XYZ stock, each having an exercise price of $40 and an expiration date in exactly six months. The current market prices for the put and call are $1.45 and $3.90, respectively. The risk-free holding period return for the next six months is 4 percent, which corresponds to an 8 percent annual rate. a. For each possible stock price in the following sequence, calculate the expiration date payoffs (net of the initial purchase price) for the following positions: (1) buy one XYZ call option, and (2) short one XYZ call option. (1) Buy One XYZ Call Option Enter Exercise Price of Option 40.00 Enter Correct Data from Problem Enter Price of Call Option 3.90 Initial Stock Payoff Premium Price Net Profit 0 3.90 20 (3.90) 0 3.90 25 (3.90) 0 3.90 30 (3.90) 0 3.90 35 (3.90) 0 3.90 40 (3.90) 5 3.90 45 1.10 10 3.90 50 6.10 15 3.90 55 11.10 20 3.90 60 16.10 Draw a graph of these payoff relationships, using net profit on the vertical axis. Be sure to specify the prices at which these respective positions will break even (i.e., produce a net profit of zero). Buy One XYZ Call Option 20.00 15.00 10.00 Net Profit 5.00 0.00 0 10 20 30 40 50 60 (5.00) (10.00) Stock Price (2) Short One XYZ Call Option Enter Exercise Price of Option Enter Correct Data from Problem Enter Price of Call Option Initial Stock Payoff Premium Price Net Profit 0 0.00 20 0.00 0 0.00 25 0.00 0 0.00 30 0.00 0 0.00 35 0.00 0 0.00 40 0.00 45 0.00 45 (45.00) 50 0.00 50 (50.00) 55 0.00 55 (55.00) 60 0.00 60 (60.00) Short One XYZ Call Option 10.00 0.00 (10.00) 0 10 20 30 40 50 60 70 (20.00) Net Profit (30.00) (40.00) (50.00) (60.00) (70.00) Stock Price b. Using the same potential stock prices as in Part a, calculate the expiration date payoffs and profits (Net of initial purchase price) for the following positions: (1) buy one XYZ put option, and (2) short one XYZ put option. Draw a graph of these relationships, labeling the prices at which these investments will break even. (1) Buy One XYZ Put Option Enter Exercise Price of Option Enter Correct Data from Problem Enter Price of Put Option Initial Stock Payoff Premium Price Net Profit -20 0.00 20 (20.00) -25 0.00 25 (25.00) -30 0.00 30 (30.00) -35 0.00 35 (35.00) 0 0.00 40 0.00 0 0.00 45 0.00 0 0.00 50 0.00 0 0.00 55 0.00 0 0.00 60 0.00 Buy One XYZ Put Option 5.00 0.00 (5.00) 0 10 20 30 40 50 60 70 (10.00) Net Profit (15.00) (20.00) (25.00) (30.00) (35.00) (40.00) Stock Price (2) Short One XYZ Put Option Enter Exercise Price of Option Enter Correct Data from Problem Enter Price of Put Option Initial Stock Payoff Premium Price Net Profit 0 0.00 20 0.00 0 0.00 25 0.00 0 0.00 30 0.00 0 0.00 35 0.00 0 0.00 40 0.00 0 0.00 45 0.00 0 0.00 50 0.00 0 0.00 55 0.00 0 0.00 60 0.00 Short One XYZ Put Option 1.00 1.00 0.80 Net Profit 0.60 0.40 0.20 0.00 0 10 20 30 40 50 60 70 Stock Price c. Determine whether the $2.45 difference in the market prices between the call and put options is consistent with the put-call parity relationship for European-style contracts. Enter Call Premium Enter Correct Data from Problem Enter Put Premium Enter Exercise Price Enter Risk-free Rate Enter Stock Price Enter Number of Months to Maturity Call - Put = Stock Price - PV Exercise Price 0.00 0.00 0.00 0.00 0.00 0.00 Put Call Parity holds 70 70 70 70 ptions is consistent with PV Exercise Price Chapter 21, Problem 2, Page 796 You are a coffee dealer anticipating the purchase of 82,000 pounds of coffee in three months. You are concerned that the price of coffee will rise, so you take a position in coffee futures. Each contract covers 37,500 pounds, and so, rounding to the nearest contract, you decide to go long in two contracts. The futures price at the time you initiate your hedge is 55.95 cents per pound. Three months later, the actual spot price of coffee turns out to be 58.56 cents per pound and the futures price is 59.20 cents per pound. a. Determine the effective price at which you purchased your coffee? How do you account for the difference n amounts for the spot and hedge positions? * Determining Effective Price Futures Contract Beginning Price of Coffee per Pound Futures Contract Ending Price of Coffee per Pound Spot Price of Coffee in 3 Months (cents per pound) Pounds of Coffee in 1 Futures Contract Number of Futures Contracts Purchased Total Number of Pounds of Coffee to be Purchased Number of Pounds of Coffee Covered by Futures Contracts 0 Initial Cost of Futures Contract 0.00 Ending Value of Futures Contract 0.00 Gain or Loss on Futures Contract 0.00 Cash Cost for First 0 Pounds 0.00 Net Cost for First 0 Pounds 0.00 Cash Cost Less Futures Contract Gain or Loss Effective Per Pound Cost for First 0 Pounds #DIV/0! Cost to Purchase Remaining 0 Pounds 0.00 Total Cost for 0 Pounds 0.00 Excluding Gain/Loss on Futures Contract Effective Cost per Pound for 0 Pounds #DIV/0! Excluding Gain/Loss on Futures Contract Effective Cost per Pound for 0 Pounds #DIV/0! Including Gain/Loss on Futures Contract b. Describe the nature of basis risk in this long hedge. hs. You are wo contracts. s 59.20 cents Less Futures Contract Gain or Loss Gain/Loss on Futures Contract Gain/Loss on Futures Contract Gain/Loss on Futures Contract Chapter 21, Problem 7, Page 797 Suppose that one day in early April, you observe the following prices on futures contracts maturing in June: 93.35 for Eurodollar and 94.07 for T-bill. These prices imply three-month LIBOR and T-bill settlement yields of 6.65 percent and 5.93, respectively. You think that over the next quarter the general level of interest rates will rise while the credit spread built into LIBOR will widen. Demonstrate how you can use a TED (Treasury/Eurodollar) spread, which is a simultaneous long (short) position in a Eurodollar contract and short (long) position in the T-bill contract, to create a position that will benefit from these views. (Note: See discussion of TED spread on pages 780-781.) T-Bill and Eurodollar Futures Contracts Spread Settlemen Settlemen (Basis t Yield T- t Yield T-bill Eurodollar Points) bill Eurodollar June Contracts 0.00 100.00 100.00 September Contracts (Estimated) 0.00 100.00 100.00 Position = Long T-bill Contract; Short Eurodollar Contract Profit on Transaction is Caculated as: Evaluating the Position (New TED spread) - (Original TED spread) Total Gain Change in TED spreads 0.00 - 0.00 = 0.00 Returns on Components 0.00 - 0.00 = 0.00 Loss on Long Gain on Position in Short T-Bill Position in Eurodollar Basis Points Basis Points Chapter 22, Problem No. 5, Page 842 Consider the following questions on the pricing of options on the stock of ARB Inc.: a. A share of ARB stock sells for $75 and has a standard deviation of returns equal to 20 percent per year. The current risk-free rate is 9 percent and the stock pays two dividends: (1) a $2 dividend just prior to the option's expiration day, which is 91 days from now (i.e., exactly one-quarter of a year); and, (2) a $2 dividend 182 days from now (i.e., exactly one-half year). Calculate the Black-Scholes value for a European-style call option with an exercise price of $70. The attached model will calculate the Black-Scholes and Binominal Option Pricing Model values for the call option. b. What would be the price of a 91-day European-style put option on ARB stock having the same exercise price: The attached model automatically calculates the Black-Scholes and Binomial Option Pricing Model values for the put option. Alternatively, Put-Call Parity can be used to solve for the value of the put option. Enter Call Premium Enter Exercise Price Enter Risk-free Rate Enter Stock Price Dividend Payment Enter Number of Months to Maturity exp Value is 2.7183 Call - Stock Price + PV Exercise Price = Put 0.00 - 0.00 + #NUM! = #NUM! c. Calculate the change in the call option's value that would occur if ARB's management suddenly decided to suspend dividend payments and this action had no effect on the price of the company's stock. The new call option price is , which is 0.00 greater than the initial value of d. Briefly describe (without calculations) how your answer in Part a would differ under the following separate circumstances: Note: See page 819 to learn how changes in factors affect Black-Scholes Option Values. rcent per year. tion Pricing Model ddenly decided than the initial value of 0.00 . following separate circumstances: Chapter 22, Problem 11, Page 844 In mid-May, there are two outstanding call option contracts available on the stock of ARB Co.: Number Exercise Expiration Market Purchased Call # Price Date Price or Sold 1 50 Aug. 19 8.40 1 2 60 Aug. 19 3.34 2 a. Assuming that you form a portfolio consisting of one Call #1 held long, and two Calls #2 held short, complete the following table showing your intermediate steps. In calculating net profit, be sure to include the net initial cost of the options. Price of ARB Initial Cost Profit on Profit on Stock at Net Profit of Call #1 Call #2 Expiration on Total Portfolio Position Position ($) Portfolio (1.72) 0.00 0.00 40 (1.72) (1.72) 0.00 0.00 45 (1.72) (1.72) 0.00 0.00 50 (1.72) (1.72) 5.00 0.00 55 3.28 (1.72) 10.00 0.00 60 8.28 (1.72) 15.00 (10.00) 65 3.28 (1.72) 20.00 (20.00) 70 (1.72) (1.72) 25.00 (30.00) 75 (6.72) b. Graph the net profit relationship in Part a, using stock price on the horizontal axis. What is (are) the breakeven stock price(s)? What is the point of maximum profit? Net Profit on Total Portfolio 10 N 8 e 6 t 4 2 P r 0 o -2 40 45 50 55 60 65 70 75 80 f -4 i -6 t -8 Stock Price Stock Price Breakeven on Low Side: Occurs at Long Call Strike Price 50 plus 1.72 or total of, Breakeven on High Side: Occurs with the position's cost, (1.72), Profit on the Call (P - Strike), and loss on the short c c. Under what market conditions will this strategy (which is known as a call ratio spread ), generally make sense? Does the holder of this position have limited or unlimited liability? Enter correct data from problem! 51.72 ,to cover cost. , and loss on the short calls 2(Strike - P) equal zero: make sense? Week 11, Assignment No. 5, Essay Question, "Ethics and Regulation in the Professional Asset Management Industry" Chapter 24 identifies and discusses ethical conflicts that can arise between professional investment managers (e.g., financial advisors, investment counselors, etc.) and investors whose assets they are employed to manage. a. Describe at least three potential ethical conflicts that can arise between financial advisors and investors. This explanation should describe the basis for the conflict (what causes it?) and how it is potentially damaging to the investor? Be specific. b. How should government legislation (laws) and regulatory oversight (regulations) be structured to protect individual investors from such conflicts? Please be specific. set Management Industry" estment managers mployed to manage. s and investors. f2e30216-0460-43e0-8ec2-6b03ad6358d0.xlsx Black-Scholes-Merton and Binomial Option Pricing BSMbin7e.xls Inputs: Black-Scholes-Merton Model Binomial Model Run Binomial Model Asset price (S0) 75 European European Steps: 100 Exercise price (X) 70 Call Put European European Time to expiration (T) 0.2500 Price #NAME? #NAME? Call Put Standard deviation (s) 20.00% Delta (D) #NAME? #NAME? Price 5.6500 1.1135 discrete Gamma (G) Delta (D) Risk-free rate (r or rc) 9.00% #NAME? #NAME? 0.7542 -0.2458 continuous Dividends: 0.00% Theta (Q) #NAME? #NAME? Gamma (G) 0.0429 0.0429 continuous yield (dc) or discrete dividends below: Vega #NAME? #NAME? Theta (Q) -8.8598 -2.9559 Rho #NAME? #NAME? American American In lieu of a continuously compounded yield, place below Call Put up to fifty discrete dividends and the time in years to d1 #NAME? Price 7.1310 1.1135 each ex-dividend date. Leave all unused cells blank. Set the yield above to zero. If yield is not set to zero, d2 #NAME? Delta (D) 0.8361 -0.2458 all discrete dividends are disregarded. N(d1) #NAME? Gamma (G) 0.0338 0.0429 N(d2) #NAME? Theta (Q) -8.2735 -2.9559 Dividend # Dividend Time to ex Present 1 2.0000 0.2500 1.9555 2 0.0000 3 0.0000 4 0.0000 5 0.0000 6 0.0000 7 0.0000 8 0.0000 9 0.0000 10 0.0000 11 0.0000 12 0.0000 13 0.0000 14 0.0000 15 0.0000 16 0.0000 17 0.0000 18 0.0000 19 0.0000 20 0.0000 21 0.0000 22 0.0000 23 0.0000 24 0.0000 25 0.0000 26 0.0000 27 0.0000 28 0.0000 29 0.0000 30 0.0000 31 0.0000 32 0.0000 33 0.0000 34 0.0000 35 0.0000 36 0.0000 37 0.0000 38 0.0000 39 0.0000 40 0.0000 41 0.0000 42 0.0000 43 0.0000 Page 21 f2e30216-0460-43e0-8ec2-6b03ad6358d0.xlsx 44 0.0000 45 0.0000 46 0.0000 47 0.0000 48 0.0000 49 0.0000 50 0.0000 ========== ======== ======== ======= Sum 0.0000 Page 22 Instructions: Insert values in highlighted cells. Risk-free rate, standard deviation and yield can be entered as decimal or percentage (e.g., .052 or 5.2 for 5.2 %). Select form (discrete or continuous) for risk-free rate. Black-Scholes values automatically recalculate. Click on "Run Binomial Option Pricing Model" button to recalculate binomial values. Input cells have double borders. Output cells have single borders. Up to 1,000 time steps can be used in the binomial model. Input a continuous dividend yield or up to 50 discrete dividends. Do not enter both or the discrete dividends will be ignored. This spreadsheet can be used to calculate options on forwards or futures using the Black variation of the Black-Scholes model. Input the forward or futures price instead of the asset price and input the risk-free rate as both the risk-free rate and the dividend yield. Do not enter discrete dividends. To price foreign currency options, input the spot rate as the asset price, the domestic interest rate as the risk-free rate and the foreign interest rate as the dividend yield. Do not enter discrete dividends. Written by Don M. Chance and Robert E. Brooks For use with An Introduction to Derivatives and Risk Management, 7th ed. (Mason, Ohio: South-Western Thomson, Inc., 2007) Date: 9/02 Last updated: 12/28/05 f2e30216-0460-43e0-8ec2-6b03ad6358d0.xlsx Black-Scholes-Merton and Binomial Option Pricing BSMbin7e.xls Inputs: Black-Scholes-Merton Model Binomial Model Run Binomial Model Asset price (S0) 75 European European Steps: 100 Exercise price (X) 70 Call Put European European Time to expiration (T) 0.2500 Price #NAME? #NAME? Call Put Standard deviation (s) 20.00% Delta (D) #NAME? #NAME? Price 5.6500 1.1135 discrete Gamma (G) Delta (D) Risk-free rate (r or rc) 9.00% #NAME? #NAME? 0.7542 -0.2458 continuous Dividends: 0.00% Theta (Q) #NAME? #NAME? Gamma (G) 0.0429 0.0429 continuous yield (dc) or discrete dividends below: Vega #NAME? #NAME? Theta (Q) -8.8598 -2.9559 Rho #NAME? #NAME? American American In lieu of a continuously compounded yield, place below Call Put up to fifty discrete dividends and the time in years to d1 #NAME? Price 7.1310 1.1135 each ex-dividend date. Leave all unused cells blank. Set the yield above to zero. If yield is not set to zero, d2 #NAME? Delta (D) 0.8361 -0.2458 all discrete dividends are disregarded. N(d1) #NAME? Gamma (G) 0.0338 0.0429 N(d2) #NAME? Theta (Q) -8.2735 -2.9559 Dividend # Dividend Time to ex Present 1 0.0000 2 0.0000 3 0.0000 4 0.0000 5 0.0000 6 0.0000 7 0.0000 8 0.0000 9 0.0000 10 0.0000 11 0.0000 12 0.0000 13 0.0000 14 0.0000 15 0.0000 16 0.0000 17 0.0000 18 0.0000 19 0.0000 20 0.0000 21 0.0000 22 0.0000 23 0.0000 24 0.0000 25 0.0000 26 0.0000 27 0.0000 28 0.0000 29 0.0000 30 0.0000 31 0.0000 32 0.0000 33 0.0000 34 0.0000 35 0.0000 36 0.0000 37 0.0000 38 0.0000 39 0.0000 40 0.0000 41 0.0000 42 0.0000 43 0.0000 Page 26 f2e30216-0460-43e0-8ec2-6b03ad6358d0.xlsx 44 0.0000 45 0.0000 46 0.0000 47 0.0000 48 0.0000 49 0.0000 50 0.0000 ========== ======== ======== ======= Sum 0.0000 Page 27 Instructions: Insert values in highlighted cells. Risk-free rate, standard deviation and yield can be entered as decimal or percentage (e.g., .052 or 5.2 for 5.2 %). Select form (discrete or continuous) for risk-free rate. Black-Scholes values automatically recalculate. Click on "Run Binomial Option Pricing Model" button to recalculate binomial values. Input cells have double borders. Output cells have single borders. Up to 1,000 time steps can be used in the binomial model. Input a continuous dividend yield or up to 50 discrete dividends. Do not enter both or the discrete dividends will be ignored. This spreadsheet can be used to calculate options on forwards or futures using the Black variation of the Black-Scholes model. Input the forward or futures price instead of the asset price and input the risk-free rate as both the risk-free rate and the dividend yield. Do not enter discrete dividends. To price foreign currency options, input the spot rate as the asset price, the domestic interest rate as the risk-free rate and the foreign interest rate as the dividend yield. Do not enter discrete dividends. Written by Don M. Chance and Robert E. Brooks For use with An Introduction to Derivatives and Risk Management, 7th ed. (Mason, Ohio: South-Western Thomson, Inc., 2007) Date: 9/02 Last updated: 12/28/05

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