SABR Type Libor (Forward) Market Model (SABR/LMM) with time-dependent skew and smile

Abstract: Volatility Skew and Smile of Interest Rate products (Swaption and Caplet) are represented by SABR (Stochastic Alpha Beta Rho model). So, the Interest Rate derivatives model for pricing the callable exotic swaps should be comparable to the SABR volatility surface. In the interest rate derivatives models, Libor Market Model (LMM) (in a post-Libor world, Forward Market Model (FMM)) is one of the most popular models used in the market. So, there are many attempts to develop LMMs that are comparable to the SABR surface. It is called SABR/LMM. There are many references for SABR/LMM, but most of them only treat SABR/LMM, which is not flexible enough to be used practically in global banks. The purpose of this paper is to provide a comprehensive definition of SABR/LMM and a complete description of how it is to be implemented.