Chapter12 - Investment Science Chapter 12 Solutions to...

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Investment Science Chapter 12 Solutions to Suggested Problems Dr. James A. Tzitzouris < [email protected] > 12.1 The initial cost of the spread is nonnegative since C(K 1 ) ≥ C(K 2 ) for K 1 < K 2 (see 12.4). 12.2 Use the same portfolio as in the text: 1. buy one call 2. sell one put 3. lend an amount d K This will reproduce the payment of the stock, except that it will be short by an amount with present value D . Hence: C – P + dK = S – D . 12.3 Q = max { 0, S K }− max { 0, K S } K , = { S K 0 K , if S K 0 K S K , if S K } = S. 12.4 1. Assume K 2 > K 1 , and suppose to the contrary that C(K 2 ) > C(K 1 ) . Buy option 1 and sell option 2. Use option 1 to cover the obligations of option 2, since we have that max{0, S- K 1 } ≥ max{0, S- K 2 } for all S . Keep profit of C(K 2 ) – C(K 1 ) . 2. Assume K 2 > K 1 , and suppose to the contrary that K 2 K 1 < C(K 1 ) – C(K 2 ) . Buy option 2 and short option 1 to obtain K 2 K
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Chapter12 - Investment Science Chapter 12 Solutions to...

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