Microsoft Word - Homework2-2016

1. A 10-month European call option on a stock is currently selling for $5. The stock price is $64, the strike price is $60. The continuously-compounded risk-free interest rate is 5% per annum for all maturities.

1. 1) Suppose that the stock pays no dividend in the next ten months, and that the price of a 10-month European put with a strike price of $60 on the same stock is trading at $1. Is there an arbitrage opportunity? If yes, how can you take advantage of it to make profit?
2. 2) Now suppose instead that a dividend of $10 will be paid in six months. What price do you expect a 10-month European put with a strike price of $60 on the same stock to be trading at?

2. 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 illustrating how the investors profit or loss varies with the stock price over the next year. How does your answer change if the investor buys 100 shares, shorts 200 call options, and buys 200 put options?

3. Three-month European put options with strike prices of $50, $55, and $60 cost $2, $4, and $7, respectively.

1. 1) How can one create a butterfly spread using these options?
2. 2) Please draw the payoff and profit diagrams of this butterfly strategy.
3. 3) What are the maximum gain and maximum loss of the butterfly spread created using these put options?
4. 4) For which two values of ST does the holder of the butterfly spread break even (with a profit of zero), where ST is the stock price in three months?
5. 5) If you use call options to create a butterfly spread that has the same payoff structure as this one, what would be the upfront cost? Why? (Hint: for 3) and 4), the easiest way to proceed is to work with the profit diagram. You can start with the payoff to the holder ignoring the initial cost, and then subtract the net initial cost from the payoff to get the profit.)