@MISC{Rainer_calibrationof, author = {Martin Rainer}, title = {Calibration of stochastic models for interest rate derivatives ∗}, year = {} }

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Abstract

For the pricing of interest rate derivatives, various stochastic interest rate models are used. The shape of such a model can take very different forms, such as direct modeling of the probability distribution (e.g. a generalized beta function of second kind), a short rate model (e.g. a Hull-White model), or a forward rate model (e.g. a LIBOR market model). This paper describes the general structure of optimization in the context of interest rate derivatives. Optimization in finance finds its particular application within the context of calibration problems. In this case, calibration of the (vector-valued) state of a given stochastic model to some target state, which is determined by available relevant market data, implies a continuous optimization of the model parameters such that, a global minimum of the distance between the target state and the model state is achieved. In this paper, a novel numerical algorithm for the optimization of parameters of stochastic interest rate models is presented. The optimization algorithm operates within the model parameter space on an adaptive lattice with a number of lattice points per dimension which