Studies on Paramaeter Indentification of Factor mode for Bonds

在前两年，提出了新的键合过程因子模型。在对各种无套利模型或经验模型进行检验后，我们得出结论：随机抛物型偏微分方程是最合适的模型。为了将所提出的模型应用于实际情况，我们根据获得的收益率曲线数据建立了在线参数估计算法。构造在线估计器的思想是使用粒子滤波算法。尽管粒子滤波取得了成功，但存在两个因素导致其实施困难。首先是文献中常用的重要函数的选择，这些重要函数的选择远非最优。第二个问题是组合状态和参数估计问题。在最后一年，我们能够规避这两个问题。由于财务模型固有的连续性质，适当的离散化还有一个额外的困难。本文所发表的论文的数值结果表明了所提出算法的有效性。

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.