Theoretical and empirical analysis of the interest rate spred

在信用风险领域，我们将Duffie-Singleton的结果推广到多因素离散时间模型。其结果在2004年7月在一桥大学举行的研讨会上作了部分介绍。关于参数估计以及相关领域，我们得到了以下结果：1.有限总体的渐近分析：我们得到了U-统计量和Von Mise统计泛函的渐近展开式。其结果可用于验证Bootstrap方法的准确性。这项研究是由H.Motoyam.先生共同完成的。2.障碍型欧式期权定价：这是2002年与森本先生共同完成的工作的继续。在充分利用Takahashi和Woodroofe的非线性更新理论的离散时间模型中，我们得到了障碍型期权的价格。部分结果发表在第8届日本-中国统计学研讨会(2004年10月，中国)上。3.天气导数定价：这是与Tobe和Kawanowa共同完成的。我们提出了一种新的温度导数定价方法，其中可以考虑对未来温度的预测。我们用实际数据检验了模型的准确性。4.我们引入了一个嵌入完全市场的不完全市场，在这个市场中，每个交易者都可以应用Black-Scholes公式来为任何基于股票的欧式衍生品定价。市场上的期权价格可以由这些价格的平均值(OLS)、中位数(平均绝对偏差)或模式(多数规则)决定。

We have obtained the following results in this project in the last two years : In the field of credit risk, we have obtained an extension of the results of Duffie-Singleton to the multi-factor and discrete time model. The result of which was partially presented at the seminar held in Hitotsubashi University July 2004. Related to the parameter estimation as well as the related field, we have the following results.1.Asymptotic analysis in finite population : We have obtained the asymptotic expansions in U-statistic and Von Mises statistical functional. The results of which may be used to justify the accuracy of bootstrap method. The research is jointly done by Mr.H.Motoyama.2.Pricing of barrier type European option : This is a continuation of the work done jointly with Morimoto in 2002. We have obtained the price of barrier type option in discrete time model where the non-linear renewal theory of Takahashi and Woodroofe was fully utilized. The part of the result was presented at the 8^<th> Japan-China Symposium on Statistics (Oct.2004,Guillin China).3.Pricing on weather derivative : This is jointly done with Tobe and Kawanowa. We have proposed a new type of pricing a temperature derivatives where the prediction of future temperature may be taken into account. We have investigated the accuracy of our model using the real data.4.We have introduced an embedded complete market inside incomplete market with which each trader may apply the Black-Scholes formula is used to pricing any stock based European type derivatives. The price of option in the market may be determined by the mean of these prices (OLS), median (Mean absolute deviation), or mode (majority rule).