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Unformatted text preview: Financial Economics V 3025 Fall 2009 Rajiv Sethi 5B Lehman Phone: 854 5140 [email protected] Problem Set 5 Solutions Due Date: Monday December 14 1. The payo&s are as follows: S T & X 1 X 1 < S T < X 2 S T ¡ X 2 Buy Shares 100 S T 100 S T 100 S T Buy put options, strike price X 1 100 ( X 1 ¢ S T ) Write call options, strike price X 2 100 ( X 2 ¢ S T ) Total 100 X 1 100 S T 100 X 2 The premium for the put is paid for by the premium received by writing the call, so the cost of the portfolio is just the cost of the shares. The pro¡t is therefore the payo& minus 100 S : This strategy is called a collar, and it brackets the value of the portfolio between 100 X 1 and 100 X 2 : The investor is protected from severe loss but gives up the possibility of substantial gain. 2. The value tree for the call option is t = 0 t = 1 2 t = 1 C ++ = 19 : 00 % C + % £ C C + & = 2 : 50 £ % C & £ C && = 0 First ¡nd C + as follows. The hedge ratio is 19 : 00 ¢ 2 : 50 121 : 00 ¢ 104 : 50 = 1 so a portfolio with 1 share purchased and 1 call written is risk free. This has payo&so a portfolio with 1 share purchased and 1 call written is risk free....
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This note was uploaded on 02/10/2010 for the course IEOR 3600 taught by Professor Chudnovsky during the Winter '09 term at Columbia.
 Winter '09
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