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5882数理金融困难数值题medium

Completing A Trinomial Probability Set

题目

A one-step trinomial tree has multipliers u=1.2, m=1, d=0.8. The middle probability is fixed at p_m=0.6, r=0.04, Δt=1. Find the up-move probability p_u that makes the discounted underlying a martingale (so p_u+p_m+p_d=1 and E[S_1]=S_0 e^{rΔt}).

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