Financial Applications of Stable Distributions: Implications on Turkish Stock Market

Abstract

Purpose- The aim of this study is modelled by examining the trading volumes of the tourism companies located in the high-risk tourism sector and traded in BIST. This modelling will gain point of view for the tourism firms as well as make an important contribution to the decision making of investors who want to invest in this sector. Methodology- The study is conducted for a sample of 2803 daily trading volumes over the period 01.01.2007-28.09.2017. Then, it is used daily returns rather than daily trading volume data because it provides the ability to measure investment performance independently of the scale used. Daily return data is modelled with stable distributions used with increasing interest in many application areas and that are well-suited to financial asset returns. Parameter estimates is made by using quantiles method which is one of the most known estimation methods. Findings- By means of the Chi-square test and graphs, it is seen that normal distribution was not suitable for trading volume data. Stable distribution parameters for the log-returns data are estimated according to the quantiles method and obtained the stable parameters 𝛼, 𝛽, 𝛾 and 𝛿 . Stable density function is obtained using the MATLAB STBL command according to estimated parameters. Conclusion- Estimated parameter values indicate that stable distributions can be used as a suitable model for modelling the transaction volume data of analysed index. It has been concluded that it is more appropriate to use the scale parameter of the stable distribution instead of the standard deviation as the risk measure.