The Research Of Nonlinear Hedging Model Based On Wavelets

Wavelets analysis, as a new mathematical tool, has been widely used in electronic engineering, physics and other disciplines, and a lot of valuable research results have been facilitated. It is known as the "mathematical microscope", because of its wonderful performance to localize details of the signal in the time domain and frequency domain.Since the mid-1980s, the research in economy and finance using wavelet analysis began to develop, involved business cycle, stock market, foreign exchange market, futures market, and multi-scale decomposition of economic relationship. With the wavelets analysis theory getting more and more sophisticated, the demand of its practical application and interdisciplinary research methods become urgent.This paper consists of five parts. The research background and significance, framework and research methods used, and the innovation of this paper as well as limitations and inadequacies are contained in the first part. The second chapter has introduced the concept of wavelets and the basic theory of wavelets analysis, including wavelets transformation, multi-resolution analysis, wavelets decomposition algorithm and reconstruction algorithm, wavelet variance, principle of detecting singularity in signal and denoising by threshold. In order to maintain the continuity of describing the basic theory, specific proofs of the theorem are simplified, if interested, you can refer to the relevant literature. The third chapter contains the application of wavelets in detecting singularity and denoising of the signal. The data are composed of daily closing prices for each index obtained from Shanghai Stock Exchange for the period December19,1990, to March15,2013and for CSI300stock index futures obtained from China Financial Futures Exchange for the period January17,2012, to March15,2013. By contrast to the original signal, it is found that the singularity in data can be effectively detected by wavelets analysis. The singularities detected are conducive researchers to quickly lock the scope of the study to identify the cause of the singularities. The process of denoising can remove the high-frequency portion of the signal to smooth the original signal, which is benefit to observe the trends of the useful signal in a noisy signal, especially the long-term trends. The main innovations of this paper are included in the fourth part. Given the current lack of multi-scale study of relationship between the optimal hedge ratio and hedge term in hedging model, I do an attempt to introduce wavelet variance to hedging model for using the excellent time-frequency localization of wavelets analysis. After reviewing the studies of different hedging model, I found the shortcomings and merits of previous studies, then determined the idea of deriving the optimal hedge ratio based on wavelets analysis. By contrast to optimal hedge ratio derived by traditional linear mean-variance hedging model, it was not difficult to find that the traditional result which the optimal hedge ratio only depends on the covariance between the stock and futures prices and the variance of the change in futures prices requests implicit assumptions, such as the zero trading margin of futures contracts, the zero yield of risk-free asset, the zero hedging period. But these assumptions are clearly inconsistent with the actual. To improve hedging model, I proposed the hedging model based on wavelets analysis. The result produced by the improve model indicated the optimal hedge ratio not only depends on the covariance between the stock and futures prices and the variance of the change in futures prices, also on the trading margin ratio of futures contracts, the risk-free rate, and the length of the term of hedging, which sets entry point for time-resolved function of wavelets analysis. That will be conducive to the multi-scale study of relationship between the optimal hedging ratio and hedging term.Considering the failure of hedging probably caused by funding constraint, the model must meet the condition, money held greater than the required each period. Then a conclusion come in line with common sense, which the gain of portfolio was influenced by the funding.Wavelets analysis theory, as a starting point, combines programming based on MATLAB wavelets toolbox to cope with financial time series data by using the time-frequency localized function of wavelets. In the process of introducing wavelet analysis, displaying the combination of the abstract and the concrete. After comparative analyzing the hedging model research literatures, I summarized the similarities and differences of the research and found the shortcomings and the merits of the previous studies, then learned from other author’s point of view and research methods to identify the direction of improving hedging model.