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Principles of Financial Engineering, 3rd Edition by Elsevier Science

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image (13.76)

Replacing this in Eq. (13.71) gives

Var(Li|j=u)=EP˜[(ln(Li)12[ln(Liuu)+ln(Liud)])2|j=u] (13.77)

image (13.77)

Simplifying and regrouping, we obtain

Var(Li|j=u)=(12[ln(Liuu)+ln(Liud)])2 (13.78)

image (13.78)

This means that the volatility at time i, in state u, is given by

σiu=12ln[LiuuLiud] (13.79)

image (13.79)

The result for the down state will ...

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