equations for approximate option prices in models that combine stochastic and local. This new model, FB-SABR-LMM, can be used to price interest rate instruments with negative strikes as well as to recover implied volatility surface. where r is the (assumed constant) risk-free interest rate and the. We focus on introducing FB-SABR into LMM to handle volatility smile under negative rates. Summary note 'The three volumes of Interest rate modeling are aimed primarily at practitioners working in the area of interest rate derivatives, but much of the material is quite general and, we believe, will also hold significant appeal to researchers working in other asset classes. The key idea of FB-SABR is to apply absolute value of forward rate )] in the rate dynamic d = )].sup.].sub.t]d, which naturally allows interest rates to across zero boundary.
In this paper, we adopt the approach of Free-Boundary SABR (FB-SABR), which is an extension based on standard SABR. Nevertheless, the limitation of applying CEV-/SABR-LMM to model negative interest rates still exists. (1992) can be found in Andersen & Piterbarg (2010). Piterbarg: Interest Rate Modeling Atlantic Financial Press, approx. Abstract : Variations of Libor Market Model (LMM), including Constant Elasticity of VarianceLMM (CEV-LMM) and Stochastic Alpha-Beta-Rho LMM (SABR-LMM), have become popular for modeling interest rate term structure. calibrating the model to interest rate and commodity volatility smiles is constructed.
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