Vasylchenko I. Modeling price processes at the derivatives financial market.

In the dissertation was conducted an all-inclusive analysis of main research areas regarding derivatives financial markets and was generalized classification of these instruments by both national legislation and international standards. Theoretical and methodological approaches to specifying the models for pricing financial derivatives, which could function real-time, considering macroeconomic background, were analysed. Accuracy of classical and modern economic and mathematical models for pricing financial derivatives, together with structure and limitations of their initial assumptions, was inspected and a comparable analysis of their efficiency was conducted. In particular, models based on Black-Scholes formulae and artificial neural networks with different configurations were built based on the prices of European call and put options with DAX index as an underlying asset. Different datasets were created from available option database, including in the money and out of the money options for model calibrations as well as backtesting. Obtained results from application of above mentioned models to pricing available options' data were analysed and compared. Although both technics can provide precise enough results, it was shown that they can be easily biased with the presence of sporadic jumps in the price data. These jumps can be often detected and their influence successfully diminished using jump test statistics, essential part of whose is integrated quarticity. Efficiency of these test statistics to great extent depends on the preciseness of quarticity estimations. Estimation of integrated quarticity based on high frequency data created additional challenges, which led to development of new measures, robust to jumps and microstructure noise. Among such measures, of particular interest were Multipower Volatility Estimators, Nearest Neighbor Truncation Estimators and Robust Neighborhood Truncation Estimators, thus different combinations of them were analyzed in detail using empirical and simulation approaches. In the empirical part stock prices of several companies from different industries were taken: banking and financial services company, manufacturer and marketer of commodity petrochemicals, research-based global biopharmaceutical company. Collected data covered the timespan from year 2008 to 2010 which also includes market shocks caused by recent economic crisis. Presence of the periods with high and low market volatilities makes it possible to better analyze the efficiency and jump-robustness of considered estimates. Stocks were selected in such a way that different trading volumes and transactions' frequencies are represented. A group of steps and procedures was specified in order to aggregate the available high-frequency data, filter out the possible outliers and obviously distorted data, in particular: median price was used in case several transactions had the same data stamp, transactions were deleted in case the price was greater than sell price plus bid-ask spread and when it was lower than buy price minus bid-ask spread, deleted the transactions with the spread that was greater than 10 times than the median spread on that day. Selected estimators of integrated quarticity were applied to the filtered stock price data and following results were afterwards analyzed.