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

The SABR model (Hagan et al, 2002) is now a market standard for quoting prices of plain-vanilla options. Its main claim to being better than other models for 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 SABR model's market-standard status for plain-vanilla options is similar to the status enjoyed by the Black

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