RDP 2018-02: Affine Endeavour: Estimating a Joint Model of the Nominal and Real Term Structures of Interest Rates in Australia Equation

\begin{matrix} E (π_{- Δ, i - Δ} \times exp (- y_{i} \times i)) = E (exp (- y_{i} \times i) \times π_{- Δ, 0} \times π_{0, i - Δ}) \\ = π_{- Δ, 0} \times exp (- y_{i} \times i + y_{i - Δ} \times (i - Δ)) E (exp (- y_{i - Δ} \times (i - Δ)) \times π_{0, i - Δ}) \\ = π_{- Δ, 0} \times exp (- y_{i} \times i + y_{i - Δ} \times (i - Δ)) exp (- r_{i - Δ}^{*} \times (i - Δ)) \end{matrix}