3d Extreme Value Analysis for Stock Return, Interest Rate and Speed of Mean Reversion

B. İzgi and A. Duran, 3D Extreme Value Analysis for Stock Return, Interest Rate and Speed of Mean Reversion, Journal of Computational and Applied Mathematics, 297, 2016, pp. 51-64, DOI: 10.1016/j.cam.2015.10.009

Posted: 23 May 2018

See all articles by Burhaneddin İzgi

Burhaneddin İzgi

Istanbul Technical University - Department of Mathematical Engineering

Ahmet Duran

Istanbul Technical University, Department of Mathematical Engineering; University of Michigan at Ann Arbor

Date Written: March 29, 2015

Abstract

It is important to analyze extreme cases of stock return, interest rate and speed of mean reversion together. While we explore strengths and limitations of Heston stochastic volatility model based on behavior of its numerical solutions using Milstein method simulations, we suggest model improvements in the light of real data applications. First, we perform high peak and fat-tail analysis for the impact of Heston model parameters on the simulations of the extreme situations by using the first four standardized moments and extreme value tools such as quantile–quantile (QQ), mean excess (ME) and Hill plots to examine the fat-tailness of the distributions. Later, we illustrate high peak and fat-tail analysis for BIST-100 index between 02 . 01 . 2004 and 17 . 06 . 2013. Moreover, we investigate 3D dynamics of the average logarithmic stock return, interest rate and speed of mean reversion variables, together. Furthermore, we believe that polarization and the transitions between polarizations and comovements are important part of extreme situation picture. We investigate comovement and polarization of interest rates and daily returns of BIST- 100 index between 2010 and 2013 in order to understand the corresponding behavioral dynamics. Heston stochastic volatility model predicts that the average logarithmic stock return increases as interest rate rises. Actually, we observe that there are also sufficiently large time intervals where interest rates were decreased and stock prices increased gradually in US stock markets and Borsa Istanbul, unlike the Heston stochastic volatility model suggests.

Keywords: 3D extreme value analysis, Fat-tails, High-peaks, Numerical solutions of stochastic differential equations, Heston model, Comovement

Suggested Citation

İzgi, Burhaneddin and Duran, Ahmet, 3d Extreme Value Analysis for Stock Return, Interest Rate and Speed of Mean Reversion (March 29, 2015). B. İzgi and A. Duran, 3D Extreme Value Analysis for Stock Return, Interest Rate and Speed of Mean Reversion, Journal of Computational and Applied Mathematics, 297, 2016, pp. 51-64, DOI: 10.1016/j.cam.2015.10.009. Available at SSRN: https://ssrn.com/abstract=3169307

Burhaneddin İzgi

Istanbul Technical University - Department of Mathematical Engineering ( email )

Ayazaga Kampusu
Fen Edebiyat Fakultesi
İstanbul
Turkey

Ahmet Duran (Contact Author)

Istanbul Technical University, Department of Mathematical Engineering ( email )

Ayazaga Kampusu
Fen Edebiyat Fakultesi
İstanbul
Turkey

HOME PAGE: http://web.itu.edu.tr/aduran

University of Michigan at Ann Arbor ( email )

500 S. State Street
Ann Arbor, MI 48109
United States

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