The following option prices were observed for calls and puts on a stock for the trading day of July 6 of particular year. Use this information in problems through 14. The stock was priced at 165.13. The expirations were July 17, August 21, and October 16. The continuously compounded risk-free rates asso- ciated with the three expirations were 0.0503, 0.0535, and 0.0571, respectively. Unless otherwise indicated, assume that the options are European.
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Let the standard deviation of the continuously compounded return on the stock is 21 percent. Ignore dividends. Respond to the following.
a) What is the theoretical fair value of the October 165 call?
b) Based on your answer in part a, recommend a riskless strategy.
c) If the stock price decreases by $1, how will the option position offset the loss on the stock
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- The data below consist of the closing price of the common stock of the American Telephone and Telegraph Corporation on 10 recent trading days. Time(t) Price Time(t) Price 1 $24.10 6 $22.73 2 23.80 7 22.60 3 23.39 8 21.76 4 22.90 9 22.14 5 22.10 10 21.69 a. Using a five-period moving average, forecast the price of the stock for period 10. b. What is the error of the forecast in #1-a? c. Using a five-period moving average, forecast the price of the stock for period 11.The following are the end-of-month prices for both the Standard & Poor's 500 Index and Nike's common stock. a. Using the data in the popup window, calculate the holding-period returns for each of the months. b. Calculate the average monthly return and the standard deviation for both the S&P 500 and Nike. c. Develop a graph that shows the relationship between the Nike stock returns and the S&P 500 Index. (Show the Nike returns on the vertical axis and the S&P 500 Index returns on the horizontal axis.) d. From your graph, describe the nature of the relationship between Nike stock returns and the returns for the S&P 500 Index.Use the data in the figure 20.1 and calculate thepayoff and the profits for investments in each ofthe following January expiration options, assumingthat the stock price on the expiration date is $125.a. Call option, X=$120b. Put option, X=$120c. Call option, X=$125d. Put option, X=$125e. Call option, X=$130f. Put option, X=$130
- Which of the following call options on XYZ stock is most valuable? 1. Strike price = $ 40, 3 months to expiration 2. Strike price = $ 40, 3 months to expiration 3. Strike price = $ 50, 6 months to expiration 4. Strike price = $ 50, 6 months to expirationUse this information for problems through 24. The stock was priced at 165.13. The expirations are July 17, August 21, and October 16. The continuously compounded risk-free rates associated with the three expirations are 0.0503, 0.0535, and 0.0571, respectively. The standard deviation is 0.21. a. Construct a bear money spread using the Octo- ber 165 and 170 calls. Hold the position until the options expire. Determine the profits and graph the results. Identify the breakeven stock price at expiration and the maximum and minimum profits. Discuss any special considerations asso- ciated with this strategy. b. Repeat problem "a.", but close the position on September 20. Use the spreadsheet to find the profits for the possible stock prices on September Generate a graph and use it to identify the approximate breakeven stock price.Consider a particular stock with call and put options. The date is January 12, and the price of the stock is P185. The table below shows the closing prices of four options, two of which expire in February and May and have exercise prices of 175 and 205, respectively. The February options will expire on February 16th, while the May options will expire on October 20th. These specific selections are of the American style. Exercise Price February Calls May Calls February Puts May Puts 175 25.00 33.50 18.00 26.75 205 18.20 20.22 25.25 32.18 Consider the February call. Explain (with supporting calculations) that the option holder has no reason the option right now. When is the purchased justified? Explain (with supporting calculations) that, given February call at an exercise price is less likely also to be exercised. Suppose that the option buyer has an alternative to purchase May call instead of February call. Explain why May options are more…
- A stock has had returns of 16.72 percent, 12.20 percent, 5.90 percent, 26.86 percent, and −13.49 percent over the past five years, respectively. What was the holding period return for the stock? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)On a particular day, the September S&P 500 stock index futures was priced at 960.50. The S&P 500 index was at 956.49. The contract expires 73 days later. Assuming continuous compounding, suppose the risk-free rate is 5.96 percent and the dividend yield on the index is 2.75 percent. Is the futures overpriced or underpriced? Assuming annual compounding, suppose the risk-free rate is 5.96 percent and the future value of dividends on the index is $5.27. Is the futures overpriced or underpriced?The following prices are available for call and put options on a stock priced at $50. The risk-free rate is 6 percent and the volatility is 0.35. The March options have 90 days remaining and the June options have 180 days remaining. The Black-Scholes model was used to obtain the prices. Calls Puts Strike March June March June 45 6.84 8.41 1.18 2.09 50 3.82 5.58 3.08 4.13 55 1.89 3.54 6.08 6.93 Assume that each transaction consists of one contract (for 100 shares) unless otherwise indicated. What is the cost of the box spread if we are constructing a long box spread using the June 50 and 55 options? A. $76 B. $484 C. $2,018 D. $500
- Consider a December 310 call and a December 310 put, both on a stock that is currently selling for $340/share. Calculate how much these options are in or out of the money.You find a certain stock that had returns of 16 percent, −23 percent, 24 percent, and 9 percent for four of the last five years. The average return of the stock over this period was 10.2 percent. a. What was the stock’s return for the missing year? (Do not round intermediate calculations and enter your answer as a percent rounded to 1 decimal place, e.g., 32.1.) b. What is the standard deviation of the stock’s returns? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)A stock currently trades for $115. January call options with a strike price of $100 sell for $16, and January put options a strike price of $100 sell for $5. Estimate the price of a risk-free bond.