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Stock price modelling under binomial tree model?

Typically the binomial tree is written as: $$S_{t+\Delta t} = uS_t$$ $$S_{t+\Delta t} = dS_t$$ where $u=e^{\sigma\sqrt{\Delta t}}$ and $d=e^{-\sigma\sqrt{\Delta t}}$. There is $Z$ instead to ...
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