Summary
2007 International Symposium on Nonlinear Theory and its Applications
2007
Session Number:19AM2-A
Session:
Number:19AM2-A-4
Genetic Algorithm-based Parameter Optimization of Tsallis Distribution and Its Application to Financial Markets
Kangrong Tan, Shozo Tokinaga,
pp.413-416
Publication Date:2007/9/16
Online ISSN:2188-5079
DOI:10.34385/proc.41.19AM2-A-4
Summary:
This study proposes a heuristic method on how to realize Genetic Algorithm-based parameter optimization of Tsallis dsitribution, and its application to financial markets. Conventionally, returns distribution is tackled as normal, lognormal, or non-Gaussian stable distribution, as it has been shown in previous researches, these methods are not accurate enough to catch the characteristicses of returns distribution, in some cases, serious biases could be introduced, in estimating Value at Risk, for example. On the other hand, to use mixture distribution has been suggested in our previous work, quantitative analyses have shown that it can catch the charateristicses of returns distribution, such as kurtosis, finite moments, and heavy-tailed behavior well, and it also provides an accurate approximation of original distribution. However, it just catches the characteristicses of the distribution at one special tme span, daily, weekly, monthly, and so on. It is well observed that a returns distribution usually evolves over di?erent time spans, especially on kurtosis, and standard deviation. To grasp the whole picture of returns distribution dynamically, we propose to model it as a Tsallis distribution, whose parameters are optimized by Genetic Algorithm. Since Tsallis distribution can provide a dynamic probability density function which evolves over di?erent time spans, as a dynamic trace for returns distribution’s evolution. In our numerical studies, we find that our proposed method works well on tracing the whole evolving picture of returns distribution.