Volatility skews and extensions of the Libor market model

@article{Andersen1998VolatilitySA,
  title={Volatility skews and extensions of the Libor market model},
  author={Leif Andersen and Jesper Graa Andreasen},
  journal={Applied Mathematical Finance},
  year={1998},
  volume={7},
  pages={1 - 32}
}
The paper considers extensions of the Libor market model to markets with volatility skews in observable option prices. The family of forward rate processes is expanded to include diffusions with non-linear forward rate dependence, and efficient techniques for calibration to quoted prices of caps and swaptions are discussed. Special emphasis is put on generalized CEV processes for which closed-form expressions for cap and swaption prices are derived. Modifications of the CEV process which… 
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