 = B_t {\mathbb E^{\widehat \P}\left[{\mathbb E^{\widehat \P}\left[\frac{\varphi\left(S_te^{\int_t^T r(u){\mathrm d}u-\frac{\sigma_S^0}{0}X_{t,T}^\tau+ \sigma_S Y_{t,T}}\right)}{B_T}\left\vert\vphantom{\frac{\varphi\left(S_te^{\int_t^T r(u){\mathrm d}u-\frac{\sigma_S^0}{0}X_{t,T}^\tau+ \sigma_S Y_{t,T}}\right)}{B_T}}\right.