Stochastic

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Unformatted text preview: l use the binomial model in (6.16) but now suppose S0 = 8 and consider the put option with value V3 = (10 S3 )+ . The value of this option depends only on the price so we can reduce the tree considered above to: 189 6.3. CONCRETE EXAMPLES 64 0 32 H 0 HH H 0 HH 16 16 H H 0 0.96 HH 8 H8 0.1 H H H H 1.728 2.4 HH H HH 4 HH 4 0.1866 1/2 HH H 6 3.2 HH H H2 0.6 H H 6 HH HH 1 1 H 9 On the tree itself stock prices are above the nodes and option prices below. To explain the computation of the option price note that by (6.17). V2 (2) = 0.4[V3 (4) + V3 (1)] = 0.4 · [8 + 9] = 6.8 V2 (8) = 0.4[V3 (16) + V3 (2)] = 0.4 · [0 + 6] = 2.4 V2 (32) = 0 V1 (4) = 0.4[V2 (8) + V2 (2)] = 0.4 · [2.4 + 6] = 3.36 V1 (16) = 0.4[V2 (32) + V2 (8)] = 0.4 · [0 + 2.4] = 0.96 V0 (8) = 0.4[V1 (16) + V1 (40] = 0.4 · [0.96 + 3.36] = 1.728 Again if one only wants the option price then Theorem 6.5 is much quicker: 1 3 3 = 1.728 V0 = (4/5) · 6 · + 9 · 8 8 However if we want to compute the replicating strategy n (a) = Vn+1 (a...
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This document was uploaded on 03/06/2014 for the course MATH 4740 at Cornell University (Engineering School).

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