Wat is Forward-variance model?

A forward-variance model specifies the dynamics of the whole curve $\bigl(\xi_t(u)\bigr)_{u\ge t}$, starting from the market’s $\xi_0$, with each $\xi_t(u)$ a martingale in $t$ under the pricing measure. The instantaneous variance is the curve’s short end, $v_t=\xi_t(t)$.