t1-370-07-sol - ACT370H1S - TEST 1 - FEBRUARY 14, 2007...

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ACT370H1S - TEST 1 - FEBRUARY 14, 2007 Write name and student number on each page. Write your solution for each question in the space provided. 1. For each of the following payoff functions at time 1, find an appropriate combination of call options and zero coupon bonds (short or long) that replicates the payoff. 3 a) œ "& W Ÿ "& $!  W W   "& " "" 3 b) H & W Ÿ"( W  ## "(  W Ÿ #$ "W # $ if if if " " 4 c) H W Ÿ"& W  #! "&  W Ÿ #! #!  W #!  W Ÿ #& W #& if if if if " "
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2. A bull spread based on call options is the combination of a long call with strike price and O " a short call with strike price , where . Assume all options expire at time . OO O X #" # 4 (a) Show that the payoff on a bull spread can also be obtained using an appropriate combination of put options and zero coupon bond. 4 (b) Assuming European options and no dividends payable on the stock, use put-call parity to prove that bull spread price at time 0 is the same when constructed with calls as it is when constructed with the combination in part (a).
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6 3. A non-dividend paying stock has a current price of $50. A put option on the stock with a strike price $50 is currently selling for $5.50 and a call option on the stock with strike price $55 is currently selling for $5.25, with both options being European and expiring in one year. The one-year risk-free present value factor is .9. Construct an arbitrage strategy on one share of the stock, and indicate clearly the arbitrage profit.
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4. The price of XYZ stock at time 0 is 20. Annual effective interest is at rate 5%. Your are given that for put options (European) expiring in one year are, the prices are Strike Price Put Price 19 2.16 25 5.70 It is assumed that XYZ stock pays no dividends. 3 (a) Using the convexity relationship for put option prices, find the upper bound on a put option with a strike price of 21. 5 (b) Suppose that a buyer for a put option with a strike price of 21 is willing to pay 4 for the option. Construct and verify an arbitrage strategy.
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5. You are given the following two-period binomial tree for stock prices. The stock price is above the numbered node. The annual effective interest rate is 10%. Assume the stock pays no dividends for parts (a) to (d).
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This note was uploaded on 09/27/2009 for the course STA ACT370 taught by Professor Broverman during the Spring '07 term at University of Toronto- Toronto.

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t1-370-07-sol - ACT370H1S - TEST 1 - FEBRUARY 14, 2007...

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