# Investment

3-Assuming that a one-year call option with an exercise price of \$38 is available for the stock of the DEW Corp., consider the following price tree for DEW stock over the next year:

a.         If the sequence of stock prices that DEW stock follows over the year is 40.00, 42.00, 40.32, and 38.71, describe the composition of the initial riskless portfolio of stock and options you would form and all the subsequent adjustments you would have to make to keep this portfolio riskless. Assume the one-year risk-free rate is 6 percent.

d. Calculate the value of a one-year put option on DEW stock having an exercise price of \$38; be sure your answer is consistent with the correct response to Part c.[Part c Use the binominal option model to calculate the present value of this call option. ]

5. Consider the following questions on the pricing of options on the stock of ARB Inc.:
a- A share of ARB stock sells for \$75 and has a standard deviation of returns equal to 20% per year. The current risk-free rate is 9% and the stock pays two dividends: (1) a 2% dividend just prior to the option’s expiration day, which is 91 days from now (i.e., exactly one half year). Calculate the black-Scholes value for European-style call option with an exercise price of \$70.
b- What would be the price of a 91-day European-style option on ARB stock having the same exercise price?
c- Calculate the change in the call option’s value that would occur if ARB’s management suddenly decided to suspend dividend payments and this action had no effect on the price of the company’s stock.
d- Briefly describe ( without calculations) how your answer in part a would differ under the following separate circumstances: (1) the volatility of ARB stock increases to 30%, and (2) the risk free rate decreases to 8%.

7- Suppose the current value of a popular stock index is 653.50 and the dividend yield on the index is 2.8%. Also, the yield curve is flat at a continuously compounded rate of 5.5%.
a. If you estimate the volatility factor for the index to be 16%, calculate the value of an index call option with an exercise price of 670 and an expiration date in exactly three months.
b. If the actual market price of this option is \$17.40, calculate its implied volatility coefficient.
c. Besides volatility estimation error, explain why your valuation and the option’s traded price might differ from one another.

10- Melissa Simmons is the chief investment officer of a hedge fund specializing in options trading. She is currently back testing various option trading strategies that will allow her to profit from large fluctuations-either up or down-in a stock’s price. An example of such typical trading strategy is straddle strategy that involves the combination of a long call and a long put with an identical strike price and time to maturity. She is considering the following pricing information on securities associated with friend work, a new internet start-up hosting a leading online social network:
Friend work stock: \$100
Call option with an exercise price of \$100 expiring in one year: \$9
Put option with an exercise price of \$100 expiring in one year: \$8
a. Use the above information on friend work and draw a diagram showing the net profit/loss position at maturity for the straddle strategy. Clearly label on the graph the break-even points of the position.
b. Melissa’s colleague proposes another lower-cost option strategy that would profit from a large fluctuation in friend work’s stock price:
Long call option with an exercise price of \$110 expiring in one year: \$6
Long put option with an exercise price of \$90 expiring in one year: \$5
Similar to part a, draw a diagram showing the net profit/loss position for the above alternative option strategy. Clearly label on the graph the breakeven points of the position.