# Bond forward price in terms of dirty price dynamics

Suppose we have a model for the dirty price in terms of repo rate $$q_t$$, coupon process $$\delta_t$$ and volatility $$\sigma_t$$ as: $$\mathrm{d}B_t=q_t B_t \mathrm{d}t+ \sigma_t B_t \mathrm{d}W_t-\mathrm{d}\delta_t$$.

Given this SDE, how do we solve for the T-expiry forward, $$E_t^T[B_T]$$?

• you also need to model either the instantaneous discount rate or the $T$ zero coupon bond – Antoine Conze Dec 3 '20 at 14:49