A Random Field LIBOR Market Model

A random field LIBOR market model (RFLMM) is proposed by extending the LIBOR market model, with interest rate uncertainties modeled via a random field. First, closed‐form formulas for pricing caplet and swaption are derived. Then the random field LIBOR market model is integrated with the lognormal‐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 can potentially outperform the LIBOR market model in capturing caplet volatility smile and the pricing of swaptions, in addition to possessing other advantages documented in the previous literature (no need of frequent recalibration or to specify the number of factors in advance).