Measuring Financial Risks

本课题的主要目的是重新审视计量经济学和金融工程文献中常用的计量金融风险的统计方法。首先，我们研究了金融风险分析和未定权益价格评估的主要概率方法。它们是基于随机过程理论，特别是连续扩散过程和半鞅过程，我们已经研究了它们的应用，包括未定权益估值方法。特别地，我们发展了一种新的渐近展开方法来评估复杂的未定权益，当利率是随机的，这是一个很有前途的新方法，以未定权益评估的数学金融。此外，我们还研究了金融问题的半鞅方法，并审查了现有的信用风险定价方法。当金融市场存在违约风险时， ...更多信息 其次，研究了金融风险度量的统计方法，包括统计时间序列分析和统计生存分析（统计可靠性理论）。特别是我们研究了统计分析中相关系数的推广Copula和研究金融风险包括利率风险的状态空间模型。第三，在本项目的研究工作中，我们在金融风险度量方面取得了许多新的成果。本课题的研究成果已在国内外学术会议上发表，并已（或将）在本报告所列的学术论文中发表。总之，我们完成了本课题的主要目标。正式参与本项目的六名成员撰写了许多论文，并激发了大量相关领域的研究人员和一些具有国际学术视野的统计学家，我们感谢文部科学省和日本科学促进协会对我们研究项目的慷慨支持。少

The main purpose of this project was to re-examine the existing statistical methods often used in measuring financial risks in econometric analysis and financial engineering literatures.First we have inverstigated the major probabilistic methods for analyzing financial risks and evaluation of contingent claim prices. They are based on the theory of stochastic processes, the continuous diffusion processes and the semi-martingale processes in particular, and we have investigated their applications including contingent claim valuation methods. In particular we have developed the new asymptotic expansion approach for evaluating complicated contingent claims when the interest rates are stochastic, which is a promising new approach to the contingent claims evaluations in mathematical finance. Also we have investigated the semi-martingale approach to financial problems and examined the existing pricing methods of credit risks. When there are some default risks in the financial market, it coul … More d be incomplete and we have examined the mathematical finance theories of related problems in the incomplete financial market.Second, we have investigated the statistical methods for measuring financial risks including the statistical time series analysis and statistical survival analysis (statistical reliability theory). In particular we have investigated the copulas which is an extension of the correlation coefficient in stattistical analysis and the state space modeling for investigating the financial risks including the interest rates risks.Third, there have been many new results we have obtained under the research efforts of this project on the financial risk measurements. The details of the results under our research project have been reported in domestic as well as international academic meetings and have been (or will be) reported in academic papers listed in this report.In conclusion, we have acomplished the most important objectives of this project. Six members participated in this projectofficially have written many papers and also stimulated a large number of researchers in the related fields and some statisticians in the academic international perspectives We thank The Ministry of Education, Science, Sports and Culture and Japan Society for the Promotion of Science for giving the generous support to our research project. Less