AnAffine Term Structure Model(ATSM) is said to be solvable if the pricing problem has an explicit solution, i.e., the corresponding Riccati ordinary differential equations have a regular globally integrable flow. We identify the parametric restrictions which are necessary and sufficient for an ATSM with continuous paths, to be solvable in a state space , where , the domain of positive factors, has the geometry of a symmetric cone. This class of state spaces includes as special cases those introduced by Duffie and Kan (1996) , and Wishart term structure processes discussed by Gourieroux and Sufana (2003) . For all solvable models we provide the procedure to find the explicit solution of the Riccati ODE.
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