case03 - S<100 100<S<110 S>110 Short call 110...

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Strike Call Put 110 10.25 8.15 Gold price 101.45 Risk-free rate 1.1 1. Gold price Call K=110 Lend 100 Strategy (a) Gold Put K=110 Strategy (b) 85 0 110 110 85 16.45 101.45 90 0 110 110 90 11.45 101.45 95 0 110 110 95 6.45 101.45 100 0 110 110 100 1.45 101.45 105 0 110 110 105 0 105 110 0 110 110 110 0 110 115 5 110 115 115 0 115 120 10 110 120 120 0 120 125 15 110 125 125 0 125 130 20 110 130 130 0 130 135 25 110 135 135 0 135 Cost 10.25 100 110.25 101.45 8.15 109.6 Strategy (b) dominates strategy (a) since it gives exactly the same cash flows but costs $0.65 less 2. In one-year Today S*<110 S*>110 Buy put -8.15 (110-S*) 0 Buy gold -101.45 S* S* Borrow PV(K) 100 -110 -110 Short call 10.25 0 -(S*-110) Net 0.65 0 0 Rocinante should (1) buy N puts (2) short N calls (3) buy N units of gold (4) borrow 100N (5) enjoy 0.65N free dollars N is any number such that the prices do not move against him. 3. Strike Call Put 100 15.32 4.36 In one-year Today
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Unformatted text preview: S*<100 100<S*<110 S*>110 Short call 110 10.25 0 -(S*-110) Buy put 110 (8.15) 110-S* 110-S* Buy call 100 (15.32) 0 S*-100 S*-100 Short put 100 4.36 -(100-S*) Borrow PV(10) 9.09 -10-10-10 Net 0.23 Further intuition is provided by looking at the payoffs of the replicating portfolio Synthetic forwards Long synthetic forward K=100 Gold price Call k=100 Put k=100 K=100 K=110 and short synthetic forward K=110 85 15-15-16.45 1.45 90 10-10-11.45 1.45 95 5-5-6.45 1.45 100-1.45 1.45 105 5 5 5 110 10 10 10 115 15 15 5 10 120 20 20 10 10 125 25 25 15 10 130 30 30 20 10 135 35 35 25 10 Cost 10.96 2.1 8.86...
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This note was uploaded on 11/25/2011 for the course BUSI 588 taught by Professor Staff during the Fall '10 term at UNC.

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