Delta and vega hedging in the SABR and LMM-SABR models

The SABR model (Hagan et al, 2002) has become a market standard for quoting the prices of plain vanilla options. Its main claim to being better than other models capable of recovering exactly the smile surface (see, for example, the local volatility model of Dupire, 1994, and Derman & Kani, 1996) is its ability to provide better hedging (Hagan et al, 2002, Rebonato, 2004, and Piterbarg, 2005).

The status of market standard for plain vanilla options enjoyed by the SABR model is similar to the sta