1.Roslin Robotics stock has a volatility of 30% and a current stock price of $60 per share. Roslin pays no dividends. The risk-free interest is 5%. Determine the Black-Scholes value of a one-year,at-the-money call option on Roslin stock.
2.Rebecca is interested in purchasing a European call on a hot new stock, Up, Inc. The call has a strike price of $100 and expires in 90 days. The current price of Up stock is $120, and the stock has a standard deviation of 40% per year. The risk-free interest rate is 6.18% per year.
a. Using the Black-Scholes formula, compute the price of the call.
b. Use put-call parity to compute the price of the put with the same strike and expiration date.
3.Using the data in Table 21.1, compare the price on July 24, 2009, of the following options on JetBlue stock to the price predicted by the Black-Scholes formula. Assume that the standard deviation of JetBlue stock is 65% per year and that the short-term risk-free rate of interest is 1% per year.
a. December 2009 call option with a $5 strike price
b. December 2009 put option with a $6 strike price
c. March 2010 put option with a $7 strike price
4.Using the market data in Figure 20.10 and a risk-free rate of 1% per annum, calculate the implied volatility of Google stock in July 2009, using the 320 January 2011 call option.
5.Using the implied volatility you calculated in Problem 14, and the information in that problem,use the Black-Scholes option pricing formula to calculate the value of the 340 January 2011 call option.
6.Plot the value of a two-year European put option with a strike price of $20 on World Wide Plants as a function of the stock price. Recall that World Wide Plants has a constant dividend yield of 5% per year and that its volatility is 20% per year. The two-year risk-free rate of interest is 4%. Explain why there is a region where the option trades for less than its intrinsic value.
7.Consider the at-the-money call option on Roslin Robotics evaluated in Problem 11. Suppose the call option is not available for trade in the market. You would like to replicate a long position in 1000 call options.
a. What portfolio should you hold today?
b. Suppose you purchase the portfolio in part (a). If Roslin stock goes up in value to $62 per share today, what is the value of this portfolio now? If the call option were available for trade, what would be the difference in value between the call option and the portfolio (expressed as percent of the value of the call)?
c. After the stock price changein part (b), how should you adjust your portfolio to continue to replicate the options?
8.Consider again the at-the-money call option on Roslin Robotics evaluated in Problem 11. What is the impact on the value of this call option of each of the following changes (evaluated separately)?
a. The stock price increases by $1 to $61.
b. The volatility of the stock goes up by 1% to 31%.
c. Interest rates go up by 1% to 6%.
d. One month elapses, with no other change.
e. The firm announces a $1 dividend, paid immediately.
9.Harbin Manufacturing has 10 million shares outstanding with a current share price of $20 per share. In one year, the share price is equally likely to be $30 or $18. The risk-free interest rate is 5%.
a. What is the expected return on Harbin stock?
b. What is the risk neutral probability that Harbin’s stock price will increase?
10.Using the information on Harbin Manufacturing in Problem 19, answer the following:
a. Using the risk neutral probabilities, what is the value of a one-year call option on Harbin stock with a strike price of $25?
b. What is the expected return of the call option?
c. Using the risk neutral probabilities, what is the value of a one-year put option on Harbin stock with a strike price of $25?
d. What is the expected return of the put option?