Ouyou toukeigaku
Online ISSN : 1883-8081
Print ISSN : 0285-0370
ISSN-L : 0285-0370
Volume 35, Issue 2
Displaying 1-4 of 4 articles from this issue
  • Kensei Kuroda, Masami Miyakawa, Kentaro Tanaka
    2006 Volume 35 Issue 2 Pages 79-91
    Published: December 30, 2006
    Released on J-STAGE: June 12, 2009
    JOURNAL FREE ACCESS
    Suppose that causal relationships among variables can be described by a causal diagram and the corresponding linear structural equation models. Intervention not to variables but to arrows will be considered, and the intervention effect can be formulated through the conditional intervention proposed by Pearl and Robins(1995). The identifiability criterion for the intervention to arrows is also investigated.The intervention effect on the variance of a response variable can be evaluated under the linear structural equation model.The intervention to arrows method may be useful to reduce variances of intermediate variables or covariates that cannot be controlled directly by an external action. A numerical example illustrates how to utilize the intervention to arrows method to reduce the variability of aresponse variable of interest.
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  • Yasuhisa Hirai, Tadashi Nakamura
    2006 Volume 35 Issue 2 Pages 93-111
    Published: December 30, 2006
    Released on J-STAGE: June 12, 2009
    JOURNAL FREE ACCESS
    To calculate the binomial probability when the sample size is large, many useful approximations without straightforward calculation have been proposed and is often used presently. Faster and more powerful computers are available in the market today that is very cheap. In the present circumstances, question arises that should approximation be used. Among the various kinds of arithmetic which can deal with very large/small number, the most popular one is the multiple-precision arithmetic. In the practical field, for example in order to test hypotheses, we want to get probability quickly without accuracy. In these fields, the multiple-precision arithmetic has demerits such as long calculation time and dependence on the memory size of the personal computer. To avoid these demerits, we propose a new arithmetic on the set of real numbers. Based on the proposed arithmetic, we construct an arithmetic system by C language, which works on the personal computer. This arithmetic system is quite different from the multiple-precision arithmetic. This is applicable to various fields in which numerical calculation is needed. Especially, we try to use this system to calculate the binomial probabilities, because computation of binomial probability by a modern personal computer still includes problems. We propose an algorithm to calculate the binomial probability without approximations and program this algorithm using the proposed arithmetic system. This program enables us to calculate the binomial probability for very large sample size. Numerical experiments show that, from the standpoint of both relative error and calculation time, the proposed algorithm is useful within a very large range of sample size.
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  • A Case of Merton's Jump-Diffusion Model
    Toyofumi Sasaki, Koichi Miyazaki, Satoshi Nomura
    2006 Volume 35 Issue 2 Pages 113-128
    Published: December 30, 2006
    Released on J-STAGE: June 12, 2009
    JOURNAL FREE ACCESS
    This research tackles the following two important problems in the valuation of European option. The first problem is to capture the magnitude of the valuation error due to the Edgeworth expansion of the underlying-asset return distribution generated by Merton's jump diffusion model. The second problem is, from the impact of higher cumulants, to examine the effect of CLT (central limit theorem) that appears in the option price when the maturity of the option becomes longer.
    Regarding the first problem, we derive the approximated option valuation formula based on the Edgeworth expansion of the distribution generated by MJD model up to fourth order. Then, we compare the approximated formula price with the exact one computed by FFT. Our approach toward the second problem is to focus on the fact that the N-days underlying-return distribution is nothing but the N-times convolution of the one-day underlying-return distribution. Thus, through the numerical experiment, we observe the speed that the option value of the MJD model converges to that of the BS model due to the CLT effect. We also examine the impact of the third and fourth cumulants in the convergence.
    The result of our numerical experiment indicates that the precision of our approximated option valuation formula is reasonably well expect the very short maturity option and the impact of the higher cumulants to the option value is not negligible when the maturity of the option is less than 100days even though the CLT effect is actually observed.
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  • [in Japanese]
    2006 Volume 35 Issue 2 Pages 129
    Published: December 30, 2006
    Released on J-STAGE: June 12, 2009
    JOURNAL FREE ACCESS
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