3D extreme value analysis for stock return, interest rate and speed of mean reversion

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.