Stochastic modeling of stock exchange markets: Three essays

In this study, stochastic modelling is applied to analyze time series of daily closing prices of BIST100 and major stock exchange indices to gain new insight and help develop new applicable tools for investors and market participants alike for their portfolios and investments. The study is comprised of three parts. In the first essay we present the applicability of heavy-tailed distributions with the generalized autoregressive conditional heteroskedasticity (GARCH) model and continuous-time, COGARCH, model with Meixner distribution for BIST100. In the second part, we examine the long memory prop erty of five major stock exchanges by considering different models and show that the autoregressive fractionally integrated moving av erage (ARFIMA) model is a better candidate than the fractionally integrated generalized autoregressive conditional heteroscedastic (FI GARCH) in modelling volatility of the stock indices studied. The fi nal essay focuses on wavelet transformation, which has gained some popularity recently, between DAX and NIKKEI stock indices, and show that there are some level of correlation and coherency between the two. The Hurst exponent also estimated and there exist signs of multifractal process in the time series.