A time-homogeneous, SABR-consistent extension of the LMM

The SABR and the Libor market model (LMM) have become industry standards for pricing plain-vanilla and complex interest rate products, respectively. (For a description of the SABR model, see, for example, Hagan et al, 2002. The LMM is described, for example, in Brace, Gatarek & Musiela (BGM), 1996, and Jamshidian, 1997.) While similar, the two models do not directly 'talk to each other'. Ultimately, the SABR approach is not a consistent dynamical model for a collection of forward rates: it

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