See hw 2.xlsx

please see attached for class "Options, Futures and other Derivatives"

SPDR S&P 500 ETF (SPY) Watchlist 205.74 +0.47(+0.23%) NYSEArca - As of 4:00PM EDT | After Hours: 205.85 +0.11 (0.05%) 07:59pm EDT June 30, 2015 List Straddle In The Money Show Me Strikes From $ to $ Apply Filter Clear Filter Calls Strike Filter Contract Name Last Bid Ask Change Showing strikes at 205 205 SPY150630C00205000 6.47 6.46 6.64 %Change [modify] -0.11 -1.67% Volume Open Interest Implied Volatility 87 3524 15.05% Implied Volatility 16.07% Show Me Strikes From $ to $ Apply Filter Clear Filter Puts Strike Filter Contract Name Last Bid Ask Change %Change Volume Open Interest 422 6926 Showing strikes at 205 205 SPY150630P00205000 6.22 6.53 6.37 [modify] 0.33 5.32% Today is April 1. The spot price of SPY, S=205. the interest rate per annum for different maturities are given in Table I. Table II includes option prices for three different strike prices and two maturities, May 1, 2015 and June 30, 2015. Strike 200 200 200 200 205 205 205 205 210 210 210 210 215 215 Contract Name SPY150501C00200000 SPY150501P00200000 SPY150630C00200000 SPY150630P00200000 SPY150501C00205000 SPY150501P00205000 SPY150630C00205000 SPY150630P00205000 SPY150501C00210000 SPY150501P00210000 SPY150630C00210000 SPY150630P00210000 SPY150630C00215000 SPY150630P00215000 Table II Last transaction price Bid 7.74 7.4 1.91 1.91 10 9.91 4.72 4.66 3.98 3.88 3.38 3.33 6.46 6.47 6.53 6.22 1.37 1.32 5.8 5.75 3.61 3.6 8.78 8.41 1.6 1.56 12.58 11.41 Table I Ask 7.52 1.98 10.18 4.73 3.95 3.41 6.64 6.37 1.37 5.89 3.75 8.64 1.67 11.72 1-month 3-months 6-months 1-year t 0.083333 0.25 0.5 1 r 0.02 0.04 0.12 0.27 Date Open High Low Close Volume Adj Close 3/27/2015 205.13 205.95 204.9 205.74 1.1E+008 205.74 3/26/2015 204.96 206.37 204.12 205.27 1.5E+008 205.27 3/25/2015 209.07 209.35 205.71 205.76 1.6E+008 205.76 3/24/2015 209.85 210.4 208.74 208.82 77805300 208.82 3/23/2015 210.42 211.11 210 210 71784500 210 3/20/2015 209.71 211.02 209.49 210.41 1.8E+008 210.41 3/19/2015 209.96 210.47 209.03 209.5 1.2E+008 208.57 3/18/2015 207.39 211.27 206.62 210.46 2.3E+008 209.52 3/17/2015 207.69 208.42 206.98 207.96 94510400 207.04 3/16/2015 206.71 208.69 205.86 208.58 1.4E+008 207.65 3/13/2015 206.77 207.93 204.58 205.83 1.6E+008 204.92 3/12/2015 205.26 207.18 205.2 207.1 93993500 206.18 3/11/2015 205.29 205.5 204.4 204.5 1.1E+008 203.59 3/10/2015 206.71 206.81 204.93 204.98 1.6E+008 204.07 3/9/2015 207.74 208.79 207.55 208.36 89818900 207.43 3/6/2015 210.46 210.46 207.1 207.5 1.9E+008 206.58 3/5/2015 210.62 210.8 209.85 210.46 76873000 209.52 3/4/2015 210.4 210.49 209.06 210.23 1.1E+008 209.3 3/3/2015 211.47 212.05 210.08 211.12 1.1E+008 210.18 3/2/2015 210.78 212.06 210.72 211.99 87491400 211.05 2/27/2015 211.26 211.58 210.6 210.66 1.1E+008 209.72 2/26/2015 211.52 211.71 210.65 211.38 72697900 210.44 2/25/2015 211.66 212.24 211.22 211.63 73061700 210.69 2/24/2015 211.12 212.05 210.76 211.81 72472300 210.87 2/23/2015 210.94 211.21 210.48 211.21 74411100 210.27 2/20/2015 209.48 211.33 208.73 211.24 1.4E+008 210.3 2/19/2015 209.41 210.42 209.24 209.98 91462500 209.05 2/18/2015 209.66 210.22 209.34 210.13 80652900 209.2 2/17/2015 209.4 210.32 209.1 210.11 76968200 209.18 2/13/2015 209.07 209.84 208.76 209.78 93670400 208.85 2/12/2015 207.89 208.99 206.97 208.92 97545900 207.99 2/11/2015 206.61 207.45 205.83 206.93 91087800 206.01 2/10/2015 205.88 207.12 204.68 206.81 96164200 205.89 2/9/2015 204.77 205.64 204.14 204.63 87219000 203.72 2/6/2015 206.56 207.24 204.92 205.55 1.2E+008 204.64 2/5/2015 204.86 206.3 204.77 206.12 97953200 205.2 2/4/2015 203.92 205.38 203.51 204.06 1.3E+008 203.15 2/3/2015 203 204.85 202.55 204.84 1.2E+008 203.93 2/2/2015 200.05 202.03 197.86 201.92 1.6E+008 201.02 1/30/2015 200.57 202.17 199.13 199.45 2.0E+008 198.56 1/29/2015 200.38 202.3 198.68 201.99 1.7E+008 201.09 1/28/2015 204.17 204.29 199.91 200.14 1.7E+008 199.25 1/27/2015 202.97 204.12 201.74 202.74 1.3E+008 201.84 1/26/2015 204.71 205.56 203.85 205.45 92009700 204.54 1/23/2015 205.79 206.1 204.81 204.97 1.2E+008 204.06 1/22/2015 203.99 206.26 202.33 206.1 1.7E+008 205.18 1/21/2015 201.5 203.66 200.94 203.08 1.2E+008 202.18 1/20/2015 202.4 202.72 200.17 202.06 1.3E+008 201.16 1/16/2015 198.77 201.82 198.55 201.63 2.1E+008 200.73 1/15/2015 201.63 202.01 198.88 199.02 1.8E+008 198.14 1/14/2015 199.65 201.1 198.57 200.86 1.9E+008 199.97 1/13/2015 204.12 205.48 200.51 202.08 2.1E+008 201.18 1/12/2015 204.41 204.6 201.92 202.65 1.4E+008 201.75 1/9/2015 206.4 206.42 203.51 204.25 1.6E+008 203.34 1/8/2015 204.01 206.16 203.99 205.9 1.5E+008 204.98 1/7/2015 201.42 202.72 200.88 202.31 1.3E+008 201.41 1/6/2015 202.09 202.72 198.86 199.82 2.1E+008 198.93 1/5/2015 204.17 204.37 201.35 201.72 1.7E+008 200.82 1/2/2015 206.38 206.88 204.18 205.43 1.2E+008 204.52 Date 1/2/2015 1/5/2015 1/6/2015 1/7/2015 1/8/2015 1/9/2015 1/12/2015 1/13/2015 1/14/2015 1/15/2015 1/16/2015 1/20/2015 1/21/2015 1/22/2015 1/23/2015 1/26/2015 1/27/2015 1/28/2015 1/29/2015 1/30/2015 2/2/2015 2/3/2015 2/4/2015 2/5/2015 2/6/2015 2/9/2015 2/10/2015 2/11/2015 2/12/2015 2/13/2015 2/17/2015 2/18/2015 2/19/2015 2/20/2015 2/23/2015 2/24/2015 2/25/2015 2/26/2015 2/27/2015 3/2/2015 3/3/2015 3/4/2015 3/5/2015 3/6/2015 3/9/2015 3/10/2015 3/11/2015 3/12/2015 3/13/2015 3/16/2015 3/17/2015 3/18/2015 3/19/2015 3/20/2015 3/23/2015 3/24/2015 3/25/2015 3/26/2015 3/27/2015 SPY SPY_RET 204.52 200.82 -0.018091 198.93 -0.009411 201.41 0.012467 204.98 0.017725 203.34 -0.008001 201.75 -0.007819 201.18 -0.002825 199.97 -0.006015 198.14 -0.009151 200.73 0.013072 201.16 0.002142 202.18 0.005071 205.18 0.014838 204.06 -0.005459 204.54 0.002352 201.84 -0.0132 199.25 -0.012832 201.09 0.009235 198.56 -0.012581 201.02 0.012389 203.93 0.014476 203.15 -0.003825 205.2 0.010091 204.64 -0.002729 203.72 -0.004496 205.89 0.010652 206.01 0.000583 207.99 0.009611 208.85 0.004135 209.18 0.00158 209.2 9.6E-005 209.05 -0.000717 210.3 0.005979 210.27 -0.000143 210.87 0.002853 210.69 -0.000854 210.44 -0.001187 209.72 -0.003421 211.05 0.006342 210.18 -0.004122 209.3 -0.004187 209.52 0.001051 206.58 -0.014032 207.43 0.004115 204.07 -0.016198 203.59 -0.002352 206.18 0.012722 204.92 -0.006111 207.65 0.013322 207.04 -0.002938 209.52 0.011978 208.57 -0.004534 210.41 0.008822 210 -0.001949 208.82 -0.005619 205.76 -0.014654 205.27 -0.002381 205.74 0.00229 Answer the following questions based on the information in the data sheet assuming that options are Eoropeans and dividend yield is zero. (a)A3A16 Based on the last transaction prices Compute for each strike price=200,205, and 210 and each maturity, (i) The cost of a strategy that buys a call and lends the present value of the exercise price; (ii) The cost of buying a put and one share of the underlying stock provide your answers by filling in the following table: Strike 200 200 205 205 210 210 Maturity C P S r C+Kexp(-rt) P+S (b) If you can trade at the last transaction prices, determine whether each option is under-priced or over priced. For a strike price 200 and June 30 maturity describe an arbitrage strategy that can take advantage of existing mispricing (c ) If you can't trade at last transaction prices and you have to buy at the ask price and sell at the bid price, what happens to your arbitrage profit. Discuss your ability to execute your transaction simultaneously and how that may impact your arbitrage profit. (d) Suppose that you manage a 10.25m portfolio invested in S&P ETF, SPY. Assume that you want to insure that your portfolio will not fall significantly from its current level on 20150501. Using options and each option gives you the right to buy or sell 100 shares. (i) Desctibe a strategies that can achieve this objective.; (ii) Demonstrate that the value of your portfolio excluding the cost of insurance does not lose value regardles of the change in the S&P level Chart Title 20000000 18000000 16000000 Column B 14000000 12000000 10000000 180 200 220 240 260 280 300 320 340 360 S Use prices in the data sheets assuming that all options are Eorpoean and zero dividend yield (a) Design and graph a bulll spread strategy using calls, June 30, maturity, last transaction prices, and Strike prices 205 and 210 and graph its profit. ( Ignore time value of money) (b) describe the investment objective of this strategy ( c ) Design a bull spread strategy using the strike prices in (a) and graph its profit (d) Graph the profit of the two strategies on the same horizontal stock price It is April 1, 2015 and you believe that the market will experience a big, roughly 2.5%, move in the next month. (a) Using option data in the data sheet, describe a strategy designed to make money if your expectation realize. Your answer should include contingent profit table and profit graph. (b) If you believe that the market will not experience high volatility in the next month, How can you act on this beieve trading some options in the data sheet. ( c ) Which strategy buys volatility and which sells volatility ? Under what conditions each strategy is profitable? Assume that the current stock price is $205. It may move up to $210 in the next three months and it may drop down to $200 in the next three months. Assume that the one month interest rate is 2% per annum. (a) The following tree describes two possible paths for the stock price. Please fill in the contingent call option value of in the green cells Now 3-months forward 210 0.87318 42.5941 200 0.8316 40.5658341463 208.9526 205 (c ) Describes a strategy that's writes 100 calls and buys X shares by writing its value ,contingent on the stock price, in the blue highted cells If we buy 100 calls we are actually shortening them or selling them so we would get 100 options per call contract or 10,000 options times their premium of 0.87318 so we would receive a premium of 8,731.796 and we want to invest them back into the shares so we will buy 42.59 shares premium collected= 8731.796125; 4259413 shares bought (d) How many shares you should buy to achieve a certain payoff regardless whether the price move is up or down (d) Given the interest rate, find the equilibrium price of the call and explain why the call's price can't be higher or lower. ( e) Calculate the risk nuetral probability and use them to calculate the price of a call and a price of a put of threemonths options on the above stock price (f) Use the probabilities in (e) to find the price of the call (g) Find the the price of a put with the same exercise price and the same maturity 199.0025 8315.996 (a) Using the return data in the SPY daily ret sheet, compute the the following: Daily std Annualized std Monthly std 3-months std (b) Assume all options in the spy options data are European. Use the estimated std in (a) to calculate the price of the call options in the SPY options data sheet (c) Assume all options in the spy options data are European. Use the estimated std in (a) and your answers in (b) to calculate the price of the put options (d) Considering the fact that the SPY dividend yield is 3.6 % per annum. Calculate the price of the 3-months call option with strike price 205. ( e) Use the call option at the money and the last transaction option price to calculate the impied volatility (std). What is the difference between this implied volatility and the volatility calculated in (a) and the implied volatility reported in sheet0 (f) Go to http://finance.yahoo.com/q/op?s=spy+options. Check the prices of options with strike price = 205 and May 1, Maturity. Find the price nad the implied volatility on April 20, 2015. Compare those to the prices and implied volatilities of March 27, 2015 in sheet0