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Constructing a Binomial interest rate tree

Hi all,

Why do we need to use forward rate multiplied by e(+1) and e(-1) standard deviation fot Time 1; and by e(+2) and e(-2) standard deviations for Time 2? In my understanding, since Time 1 is accommodating one standard deviation already, would not it be logical to multiply by e(+1)& e(-1) at all consecutive steps?

Thanks

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No, it would not be logical, nor consistent.

If the rate lower rate (rL) at time 1 is the forward rate times e−1×σ and the upper rate (rU) at time 1 is the forward rate times e+1×σ, then the upper rate satisfies:

rU = rL × eσ.

Simplify the complicated side; don't complify the simplicated side.

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