|Title:||Volatility forecasting with fuzzy methods|
|Subject:||Hong Kong Polytechnic University -- Dissertations|
Options (Finance) -- Mathematical models
Securities -- Prices -- Mathematical models
|Department:||Department of Applied Mathematics|
|Pages:||xxii, 131 pages : color illustrations|
|Abstract:||The thesis will present the volatility forecasting using some fuzzy methods. Three topics are considered: 1. The proposed volatility modeling technique based on fuzzy method is used to replace the model averaging technique in multivariate volatility forecasting. 2. Use the Hidden Markov Model (HMM) for the volatility forecasting of the univariate and multivariate time series. 3. Application of this proposed volatility forecasting technique with fuzzy methods. For topic 1, a fuzzy-method-based multivariate volatility model is intended to improve the model averaging technique for multivariate volatility forecasting. Volatility modeling is crucial for risk management and asset allocation. This is an influential area in financial econometrics. The central requirement of volatility modeling is to be able to forecast volatility accurately. The literature review of volatility modeling shows that the approaches of model averaging estimation are commonly used to reduce model uncertainty to achieve a satisfactory forecasting reliability. However, those methods attempt to produce a more reliable forecast by confirming all forecasting outcomes equally from several volatility models. Forecasting patterns generated by each model may be similar. Using all forecasting results may cause redundant computations without improving prediction reliability. The proposed multivariate volatility modeling method which is called the Fuzzy-method-based Multivariate Volatility Model (abbreviated as FMVM) classifies the individual models into smaller scale clusters and selects the most representative model in each group. Hence, repetitive but unnecessary computational burden can be reduced, and forecasting patterns from representative models can be integrated. The proposed FMVM is benchmarked against existing multivariate volatility models on forecasting volatilities of Hong Kong Hang Seng Index (HSI) constituent stocks. Numerical results show that it can obtain relatively smaller forecasting errors with less model complexity.|
For topic 2, HMM-based Multivariate Volatility Model is proposed to present another orientation for multivariate volatility forecasting. The foundation of this method is retrieved from technical analysis, which believes historical data will influence the future performance. Recognition of distinct patterns and search similar pattern is crucial for this approach. The proposed HMM-based volatility forecasting algorithm can obtain a volatility matrix from the past distinct patterns, which is found to generate accurate volatility forecast. We use the K-means clustering algorithm to classify the latest attributes into predetermined clusters and label each attributes vector with the index of its cluster. Then, each attributes vector labeled with a distinct index, and those indexes can form a new pattern with a window of a predetermined size. Subsequently, compute the likelihood values of each pattern using trained HMM and define the similarities by using these likelihood values. The closest value of past likelihood value to the likelihood value of current pattern means the corresponding pattern with this closest value share the same similarity with the current pattern. As the foundation of this method implies, we believe the behavior of the most similar pattern will reoccur. The HMM-based multivariate volatility model is also compared to the FMVM and the volatility averaging model with the same data used in topic 1. Numerical results show that HMM-based multivariate model can obtain a better forecasting accuracy than that of the multivariate volatility model with model averaging technique. For topic 3, A case of portfolio management of a hedge fund is taken as one application of the proposed volatility forecasting algorithms. A framework of a quantitative trading hedge fund is designed, and a changing allocation problem is considered. The application of both our multivariate volatility model and classical portfolio management models is considered at the same time. Regarding the application of these proposed models, a full flow line of product development with quantitative research is shown in this topic.
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