Finance

Finance
1. An investor believes that there will be a big jump in a stock price, but is uncertain as to the direction. Identify the different strategies (about 4) the investor can follow and briefly explain the differences among them. (Hint: There are potentially six different strategies)

2. Three call options on a stock have the same expiration date and strike prices of $55, $60, and $65. The market prices are $8, $5, and $3, respectively. Explain how a butterfly spread can be created. Construct a table showing the profit from the strategy. For what range of stock prices would the butterfly spread lead to a loss?Plot a graph of the final profits (after excluding cost) from the strategy (Y axis) for a closing stock price range of $0 to $100 in increments of $5, on the X-axis.

3. Suppose that c1, c2, and c3 are the prices of European call options with strike prices K1, K2, and K3, respectively, where K3>K2>K1 and K3¬– K2 = K2 – K1. All options have the same maturity. Assuming no arbitrage, what is the relation between c1, c2, and c3?

4. The price of a stock is $40. The price of a one-year European put option on the stock with a strike price of $30 is quoted as $7 and the price of a one-year European call option on the stock with a strike price of $50 is quoted as $5. Suppose that an investor buys 100 shares, shorts 100 call options, and buys 100 put options. Draw a diagram (to scale) illustrating how the investor’s profit or loss varies with the stock price over the next year. How does the answer change if the investor buys 100 shares, shorts 200 call options, and buys 200 put options? Clearly show the payoffs using different graphs for each of the securities (for example — for calls, ___for stock, … for puts, and ___for the overall payoff). Note: I expect is 2 diagrams, one for each scenario.

5. You are given the following information from the WSJ and the Cumulative normal distribution tables. The option matures in 0.5 years and is at the money. The current stock price of the underlying stock is $90.00, and the annualized 365 day t-bill rate is 2.0%. Compute the following:
a) Use the stock price and strike price information from above. Assume that the stock price can either go up by 10% or go down by 10% eachperiod. Assume that each period lasts 0.5 years. Set up a replicating portfolio of the stock and a risk free bond and use a two-period binomial model. Assume that the risk free rate is 1.0% per period.
b) Show CLEARLY the payoffs for the Stock, Bond and the Call for both periods.
c) Calculate the Number of Stocks and Bonds in both periods required to replicate the call.
d) Using no Arbitrage, compute the price of the Call option using this replicating portfolio.
e) Compute the probability (implied) that the stock price will go up.
f) Compute the annualized variance of the stock.
g) Compute the Black- Scholes- theoretical option price for a European Call option on the stock using the above
h) Using Put –Call Parity, compute the price of a European Put option on a share of the stock.

Questions 1 through 4 carry 15 points each and question 5 carries 30 points.