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t1-370-07-sol

# t1-370-07-sol - ACT370H1S TEST 1 Write name and student...

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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 . O O  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).