Volatility Skews and Extensions of the Libor Market Model

Abstract

This paper considers extensions of the Libor market model (Brace et al (1997), Jamshidian (1997), Miltersen et al (1997)) to markets with volatility skews in observable option prices. We expand the family of forward rate processes to include diffusions with non-linear forward rate dependence and discuss efficient techniques for calibration to quoted prices of caps and swaptions. Special emphasis is put on generalized CEV processes for which exact closed-form expressions for cap prices are derived. We also discuss modifications of the CEV process which exhibit appealing growth and boundary characteristics. The proposed models are investigated numerically through Crank-Nicholson finite difference schemes and Monte Carlo simulations.

JEL Classification: G12, G13, E43