# Stochastic

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Unformatted text preview: 4 and consider a put option with strike 10, that is gn = (10 sn )+ . The risk neutral probability p⇤ = 0.5 and the recursion is Vn 1 (a) = 0.4[Vn (aH ) + Vn (aT )] On the drawing above, the two numbers above each line are the price of the stock and the value of the option. Below the line are the value of the option if exercised, and the value computed by the recursion if we continue for one more period. A star indicates the large of the two, which is the value of the option at that time. To explain the solution, note that working backwards from the end. V2 (2) = max{8, 0.4(6 + 9) = 6} = 8 V2 (8) = max{2, 0.4(0 + 6) = 2.4} = 2.4 V2 (32) = max{0, 0} = 0 V1 (4) = max{6, 0.4(2.4 + 8) = 4.16} = 6 V1 (16) = max{0, 0.4(0 + 2.4) = 0.96} = 0.96 V0 (8) = max{2, 0.4(0.96 + 6) = 2.784} = 2.784 196 CHAPTER 6. MATHEMATICAL FINANCE This computes the value and the optimal strategy: stop or continue at each node depending on which value is larger. Notice that this is larger than the value 1.728 we computed f...
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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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