Abstract A model to value Federal Agricultural Mortgage Corporation (Farmer Mac) agricultural mortgage-backed securities (AMBS) is developed and numerically solved. The results suggest prepayment penalties currently being used by Farmer Mac reduce yields on AMBS considerably. Even with prepayment penalties, it can be advantageous for profit maximizing mortgagors to optimally prepay or even default on agricultural mortgages. The model is used to quantify prepayment and default risk by valuing the embedded options in the mortgages. Monte Carlo simulation is also used to determine the probability of optimal prepayment given the term structure assumption used to develop the model.

Unlike most residential mortgage‐backed securities, Farmer Mac agricultural mortgage‐backed securities (AMBS) have prepayment penalties. To quantify the impact of prepayment penalties on the cost of funding loans, prepayment behavior, and AMBS value, an analytic AMBS model is developed and numerically solved using pathwise simulation and dynamic programming. The results suggest prepayment penalties currently being used by Farmer Mac reduce AMBS yields considerably relative to not charging prepayment penalties. Presumably, lower yielding AMBS imply more competitive loan pricing. Even with prepayment penalties in place, however, it can be advantageous for profit‐maximizing mortgagors to optimally prepay or even default on agricultural mortgages. The model is used to quantify prepayment and credit risk by valuing the embedded options in mortgages, namely, the right of the mortgagor to prepay and to default.