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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, $E_t^T[B_T]$?

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

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