 S_t{\mathbb E^{\widehat \P}\left[\mathcal N\left(d_0(t,S_t,X_{t,T}^\tau) \right)\bigg{|}\widetilde \F_t\right]}-K e^{-\int_t^T r(u) {\mathrm d}u}{\mathbb E^{\widehat \P}\left[\mathcal N\left( d_0(t,S_t,X_{t,T}^\tau) \right) \bigg{|}\widetilde \F_t\right]}