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##### This problem set covers materials in Chapters 9-11 of Hull 2014.

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solution

**Question**

This problem set covers materials in Chapters 9-11 of Hull 2014.;Due on Monday, Nov 17th, 2014, at the beginning of the class.;Each group should submit one hard copy of the solution. The names (both the first;and last names) of each student in the group should be written clearly on the first page;of the hard copy.;Clarity will be rewarded and disorganization will be penalized. Show your detailed;work!;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) 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) 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 prot 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) How can one create a butterfly spread using these options?;2) Please draw the payoff and profit diagrams of this butterfly strategy.;3) What are the maximum gain and maximum loss of the butterfly spread created;using these put options?;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) 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.);FINA 471;Liang Ma;4. How would you create the following payoff by buying/selling calls? Could you do it;using only puts as well? Do you expect the net upfront cost of implementing this strategy;to be positive or negative? (Explain the type, the number, and the strike price of the;options you buy/sell. Note that the graph shows only the final payoff. No initial cost is;included.)

Paper#26006 | Written in 18-Jul-2015

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