A fresh engineering approach for the forecast of financial index volatility and hedging strategies

This thesis attempts a new light on a problem of importance in Financial Engineering. Volatility is a commonly accepted measure of risk in the investment field. The daily volatility is the determining factor in evaluating option prices and in conducting different hedging strategies. The volatility estimation and forecast are still far from successfully complete for industry acceptance, judged by their generally lower than 50% forecasting accuracy.; By judiciously coordinating the current engineering theory and analytical techniques such as wavelet transform, evolutionary algorithms in a Time Series Data Mining framework, and the Markov chain based discrete stochastic optimization methods, this work formulates a systematic strategy to characterize and forecast crucial as well as critical financial time series. Typical forecast features have been extracted from different index volatility data sets which exhibit abrupt drops, jumps and other embedded nonlinear characteristics so that accuracy of forecasting can be markedly improved in comparison with those of the currently prevalent methods adopted in the industry.; The key aspect of the presented approach is "transformation and sequential deployment": (i) transform the data from being non-observable to observable i.e., from variance into integrated volatility; (ii) conduct the wavelet transform to determine the optimal forecasting horizon; (iii) transform the wavelet coefficients into 4-lag recursive data sets or viewed differently as a Markov chain; (iv) apply certain genetic algorithms to extract a group of rules that characterize different patterns embedded or hidden in the data and attempt to forecast the directions/ranges of the one-step ahead events; and (v) apply genetic programming to forecast the values of the one-step ahead events. By following such a step by step approach, complicated problems of time series forecasting become less complex and readily resolvable for industry application.; To implement such an approach, the one year, two year and five year S&P100 historical data are used as training sets to derive a group of 100 rules that best describe their respective signal characteristics. These rules are then used to forecast the subsequent out-of-sample time series data. This set of tests produces an average of over 75% of correct forecasting rate that surpasses any other publicly available forecast results on any type of financial indices. Genetic programming was then applied on the out of sample data set to forecast the actual value of the one step-ahead event.; The forecasting accuracy reaches an average of 70%, which is a marked improvement over other current forecasts. To validate the proposed approach, indices of S&P500 as well as S&P100 data are tested with the discrete stochastic optimization method, which is based on Markov chain theory and involves genetic algorithms. Results are further validated by the bootstrapping operation. All these trials showed a good reliability of the proposed methodology in this research work. Finally, the thus established methodology has been shown to have broad applications in option pricing, hedging, risk management, VaR determination, etc.