Studies on Paramaeter Indentification of Factor mode for Bonds

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During the first two years, the new factor model for bond process has been proposed. After checking the various types of the arbitragy free or empirical models, we met with the conclusion that the stochastic Parabolic partial differential equation is the most adequate model. To apply the proposed model to the practical situation, we established the on-line parameter estimation algorithm from the obtained yield curve data. The idea to construct the on-line estimator is to use the particle filter algorithm. Despite the success of particle filter, there are two factors which cause difficulties in its implementation. The first one is the choice of importance functions commonly used in the literature which are far from being optimal. The second one is the combined state and parameter estimation problem. In the final year, we are able to circumvent both these problems. There was an additional difficulty of proper discretization because of the inherently continuous nature of financial model. Numerical results which are presented in the published papers listed below show the effectiveness of the proposed algorithms.