# Stochastic

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

## This document was uploaded on 03/06/2014 for the course MATH 4740 at Cornell University (Engineering School).

Ask a homework question - tutors are online