Using Nonnormal Distributions to Analyze the Relationship Between Stock Returns in Japan and the US

The Pearson distribution system is researched and applied to financial engineering (Nagahara, Financ Eng Jpn Mark 2(2):139–154 in 1995, Financ Eng Jpn Mark 3(2):121–149 in 1996, Stat Prob Lett 43:251–264 in 1999, J Time Ser Anal 24(6):721–738 in 2003, A method of fitting multivariate nonnormal distributions to financial data. Discussion paper of Institute of Social Sciences, F-2006-2, Meiji University in 2006, Asia Pac Financial Markets 15(3–4):175–184 in 2008a). And a method of fitting multivariate nonnormal distributions by using random numbers from the Pearson distribution system was developed (Nagahara, Comput Stat Data Anal 47(1):1–29 in 2004). This method uses the grid search of the parameters for the maximum likelihood. In this paper, we adopt Grid-Computing and its middleware for the parameter sweep in order to reduce the computational time and the workload of this method. In the area of the financial risk management, it is very important to analyze the relationship between stock returns in Japan and the US. We analyze the data based on the same date and the following date because Japanese stock market opens before the US stock market opens in a day. We compare these returns by means of the multivariate nonnormal distributions by using this method. And we test the international transmission of stock markets movement. Furthermore, we obtain the optimal job schedule for our computer system using the middleware in order to reduce the computational time.