Theoretical and empirical analysis of the interest rate spred

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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).