Theoretical and empirical analysis of the interest rate spred

在过去的两年中，我们在这个项目中获得了以下结果：在信用风险领域，我们得到了Duffie-Singleton的结果的推广到多因素和离散时间模型。2004年7月在一桥大学举行的研讨会上介绍了部分成果。在参数估计及相关领域，我们得到了如下结果：1.有限总体的渐近分析：得到了U-统计量和Von Mises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。2.障碍型欧式期权的定价：这是2002年与Morimoto共同完成的工作的继续。充分利用Takahashi和Woodroofe的非线性更新理论，得到了离散时间模型下障碍型期权的价格。部分成果已在第八届<th>中日统计研讨会（2004年10月，中国桂林）上发表。3.天气衍生品的定价：与Tobe和Kawanowa共同完成。我们提出了一种新的定价类型的温度衍生物，其中可以考虑未来温度的预测。4.我们在不完全市场中引入了一个嵌入的完全市场，每个交易者可以应用Black-Scholes公式来定价任何基于股票的欧式衍生品。市场上期权的价格可以由这些价格的平均值（OLS）、中位数（平均绝对偏差）或众数（多数决定原则）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).