1. Suppose you hold LLL employee stock options representing options to buy 10,400 shares of LLL stock. You wish to hedge your position by buying put options with three-month expirations and a $28.85 strike price. LLL accountants estimated the value of these options using the Black-Scholes-Merton formula and the following assumptions:

S = current stock price = $27.07

K = option strike price = $29.5

r = risk-free interest rate = 0.055

= stock volatility = 0.2

T = time to expiration = 3.5 years

How many put option contracts are required? (Note that such a trade may not be permitted by the covenants of many ESO plans. Even if the trade were permitted, it could be considered unethical.) (Round your answer to the nearest whole number.)

2. A stock is currently priced at $68 and has an annual standard deviation of 48 percent. The dividend yield of the stock is 3.5 percent, and the risk-free rate is 6.5 percent. What is the value of a call option on the stock with a strike price of $65 and 55 days to expiration? (Round your answer to 2 decimal places. Omit the "$" sign in your response.)

3. You are managing a pension fund with a value of $410 million and a beta of 1.8. You are concerned about a market decline and wish to hedge the portfolio. You have decided to use SPX calls. How many contracts do you need if the delta of the call option is 0.64 and the S&P Index is currently at 1,230? (Writing options should be indicated by a minus sign. Round your answer to the nearest whole number.)

4. A stock has a price of $27 and an annual return volatility of 46 percent. The risk-free rate is 2.91 percent. Perform calculations in Excel.

	a. Calculate the call and put option prices with a strike price of $23 and a 90-day expiration. (Round your answers to 2 decimal places. Omit the "$" sign in your response.)

Call premium: $
Put premium: $

b. Calculate the deltas of the call and put. (Negative amounts should be indicated by a minus sign. Round your answers to 4 decimal places.)

Call delta
Put delta

5. A stock with an annual standard deviation of 41 percent currently sells for $68. The risk-free rate is 6.1 percent. What is the value of a put option with a strike price of $81 and 62 days to expiration? (Round your answer to 2 decimal places. Omit the "$" sign in your response.)

6. You have a stock market portfolio with a beta of 0.9 that is currently worth $145 million. You wish to hedge against a decline using index options. Suppose you decide to use SPX calls. Calculate the number of contracts needed if the call option you pick has a delta of 0.4, and the S&P 500 Index is at 1,160. (Writing options should be indicated by a minus sign. Round your answer to the nearest whole number.)

7. A stock is currently priced at $49 and will move up by a factor or 1.23 or down by a factor of 0.89 each period over each of the next two periods. The risk-free rate of interest is 3 percent. Calculate the value of a put by solving for the value of a call and then using put-call parity. (Round your answer to 2 decimal places. Omit the "$" sign in your response.)

8. A stock is currently selling for $43. In one period, the stock will move up by a factor of 1.26 or down by a factor of 0.59. A call option with a strike price of $53 is available. If the risk-free rate of interest is 2.5 percent for this period, what is the value of the call option? (Round your answer to 2 decimal places. Omit the "$" sign in your response.)

9. A stock is currently priced at $50. A call option with an expiration of one year has an exercise price of $55. The risk-free rate is 16 percent per year, compounded continuously, and the standard deviation of the stocks return is infinitely large. What is the price of the call option? (Omit the "$" sign in your response.)

10. In its 10-Q dated February 4, 2010, LLL, Inc., had outstanding employee stock options representing over 295 million shares of its stock. LLL accountants estimated the value of these options using the Black-Scholes-Merton formula and the following assumptions:

S = current stock price = $26.84

K = option strike price = $29.27

r = risk-free interest rate = 0.055

= stock volatility = 0.3

T = time to expiration = 3.5 years

What was the estimated value of these employee stock options per share of stock? (Note: LLL pays no dividends.) (Round your answer to 2 decimal places. Omit the "$" sign in your response.)