ABSTRACT
The London Interbank Offer Rates (LIBOR) market model is a term structure model driven by multiple random factors. For a long time, the nonparametric calibration of the model to fit input correlations and input prices simultaneously had been an unresolved challenge to model users, and it had in fact become a bottleneck for the model's applications. A comprehensive, nonparametric calibration of the market model consists of two parts: fitting the model to input correlations and fitting the model to input prices. Through the calibration of the LIBOR market model, we demonstrate that model calibrations in finance can be very delicate in mathematics as well as in computations. The availability of the Hessian matrix in closed form potentially enables very fast calibration to swaption prices. The numerical tests and other people's tests on swaption calibration have confirmed that Hessian-based algorithms significantly outperform gradient-based algorithms: the former can calibrate the LIB.
