Data attached on file

Questions:

1-3: Annualized stock volatility (Standard deviation of continuously compounded rate of return) for the 3 stocks

4-6: Fair Values of 3 calls on 3 stocks

7-9: Fair Valus of 3 puts on 3 stocks

10-12: Trades for calls (write 1 for buy and 0 for short-sell

13-15: Trades for puts (write 1 for buy and 0 for short-sell)

16-18: Profits from 3 call trades

19-21: Profits from 3 put trades

22: Total Profit from all trades

Take the following data generated for 3 calls and 3 puts with strike prices, rates of interest and years to maturity, and market prices of options on the opening day or trade day (first day of holding period) and the market prices of the options on the end of the closing period. Following these data are 32 prices of 3 underlying stocks on which the 3 pairs of calls and puts are written. These prices are prior to the trading date with the 32nd stock price (on row 32) as the price as of the close of the day before the trading date and the 1st stock price (on first row) as the price as of 32 days prior to the trading date. The data needed to calculate fair value of an option include the following: i) Strike price. There are 3 strike prices for each of the 3 pairs of calls and puts. ii) Years to maturity (Mat), the same for the call and put written on the same stock. iii) Yield to maturity (Rate) on a T-bill or any other zero-coupon Treasury bond with a date of maturity close to maturity of the option. 3 such interest rates are given. iv) Market prices of the options on the day of opening (Call0, Put0) and on closing (CallM and PutM) of trades. v) Daily stock prices (the 32 prices given). The 32nd stock price is as of close prior to trading day and the 1st stock price is as of 32 days prior to trading day. vi) The stock goes ex-dividend every quarter starting at 0.25 years from trading date over the life of the option. The amount of quarterly dividend is 5% of the (32nd) stock price just prior to the trading date. vii) An estimate of annual stock volatility (standard deviation of stock's 31 daily continuously compounded rate of return) based on 32 daily stock prices including and prior to trading day, using the procedure discussed in class. The annual volatility is 252 times the estimated standard deviation obtained from daily stock prices, because there are approximately 252 trading days in a year. The 32nd day stock price is exdividend price. Method of Calculating Fair Option Value: Follow the step-by-step procedure used in class to determine fair value of each option using a 5-step binomial tree. Trading, holding, and closing options: Compare the fair price of an option (obtained by using all information as of trading day) with the market price of the option on that day to determine the trade (buy or sell). Note that the trade is actually for the open on the following day, based on information as of close of the trading day. Ideally, you should base your trade on opening market price on the trading day. Decide a trade for each of the chosen 6 options. Hold your trades over the holding period and close the trades at the end of the holding period by selling the options bought and by buying the options soldshort. Profits: Calculate profits from trading, equal to selling market price of an option minus buying market price of the same option. Questions: 1 - 3: Annualized stock volatility (standard deviation of continuously compounded rate of return) for the 3 stocks. 4 - 6: Fair values of 3 calls on 3 stocks. 7 - 9: Fair values of 3 puts on 3 stocks. 10 - 12: Trades for calls (write 1 for buy and 0 for short-sell). 13 - 15: Trades for puts (write 1 for buy and 0 for short-sell). 16 - 18: Profits from 3 call trades. 19 - 21: Profits from 3 put trades. 22: Total profit from all trades. DATA: Stock Strike Mat Rate Call0 Put0 CallM PutM 1 30.50 0.300 0.1570 89.76 32.36 18.70 6.74 2 31.50 0.350 0.1590 146.94 27.91 30.61 5.81 3 32.50 0.400 0.1610 82.33 49.00 17.15 10.21 32 Prices of 3 stocks in 3 columns 34.40 29.88 30.44 26.35 27.84 37.88 30.47 25.91 37.28 27.11 46.34 28.11 23.07 29.67 33.36 26.89 31.29 27.97 23.43 25.47 28.51 23.95 27.34 27.11 44.39 36.08 32.56 30.30 30.32 44.43 27.45 29.44 20.08 27.83 27.74 30.60 25.99 25.62 19.87 41.46 18.15 19.77 60.71 14.21 17.04 23.45 30.59 28.19 15.72 35.20 31.70 26.79 46.93 14.44 41.43 21.80 39.20 25.77 20.17 24.01 8.04 57.00 14.66 24.90 32.46 33.60 28.67 23.04 20.97 54.54 29.16 22.57 37.42 50.79 17.86 43.39 12.15 39.98 32.69 16.92 37.00 35.40 14.32 9.53 25.76 35.40 10.52 10.80 17.20 24.42 25.54 29.12 22.14 41.06 54.59 37.42