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We develop a tractable and flexible stochastic volatility multifactor model of the term structure of interest rates. It features unspanned stochastic volatility factors, correlation between innovations to forward rates and their volatilities, quasi-analytical prices of zero coupon bond options, and dynamics of the forward rate curve, under both the actual and risk-neutral measures, in terms of a finite-dimensional affine state vector. The model has a very good fit to an extensive panel data set of interest rates, swaptions, and caps. In particular, the model matches the implied cap skews and the dynamics of implied volatilities.