Let (r) be the risk-free continuously compounded rate and (A(0)) today's value of an asset. For a

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Let \(r\) be the risk-free continuously compounded rate and \(A(0)\) today's value of an asset. For a given horizon \(T\), assume the asset can take on two values \(A_{u}, A_{d}\) with risk-neutral probabilities of \((1 / 2,1 / 2)\). Provide an expression for \(A_{u}, A_{d}\) if \(\operatorname{Var}(A(T))=\sigma^{2} T\) for a given volatility parameter \(\sigma\).

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