Abstract
A random field LIBOR market model is proposed by extending the LIBOR market model with uncertainty modeled via random field. First, closed-form formulas for pricing caplet and swaption are derived. Then the random field LIBOR market model (RFLMM) is integrated with the log-normal-mixture model to capture the implied volatility skew/smile. Finally, the model is calibrated to cap volatility surface and swaption volatilities. Numerical results show that the random field LIBOR market model outperforms LIBOR market model in capturing caplet volatility smile and the pricing of swaptions, in addition to possessing other documented advantages (no need of frequent recalibration or to specify the number of factors in advance).
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