Study On The Methods Of Financial Risk Management Based On Multifractal Theories

Modern financial risk management, e.g. VaR model, and many other classical financial theories and models, such as CAPM and Black-Scheoles option pricing theory, are based on Fama's Efficient Market Hypothesis (EMH). However, many anomalies have been found in world financial markets since 1970s. Therefore, Behavioral Finance, which is risen in the later 1980s, and Econophysics or Phynance, which is risen in the later 1990s, are becoming the front line and hotspot of financial theories. Multifractal analysis of financial markets, which is adopted in this paper, is just one of the most important fields in econophysics. Recently, many empirical studies worldwide have demonstrated that the fluctuations of financial time series, such as exchange rates, stock prices and its returns, show not only chaos and fractal features but also obvious multifractal characteristics. In theories, one may obtain much information about price fluctuations at different times scales with different magnitudes, especially the extreme fluctuations by multifractal analysis of financial markets, which may break a new path in the researches of financial complexity. However, most relative researches by now only focus on the demonstrations of the multifractal characteristics of financial markets, and no further practical decision-supporting information can be obtained from such multifractal analysis. Furthermore, it is well known that information about price fluctuations at different time scales with different magnitudes, especially the extreme fluctuations is imperative in financial risk management. Therefore, based on the hypothesis that financial market is not efficient but fractal and according to the research methods of econophysics, we firstly put forward a new idea that multifractal theories and tools can play important role in the studies of financial risk management. Then we establish a new risk measurement and a risk prediction model based on multifractal theories. The main research contents are as follows:1. The development history of finance, the difficulties and challenges faced by modem finance theories and risk management methods are summarized. The birth, development and the latest fruit of econophysics are also summarized. The prospects of applications of multifractal theories into financial researches are also put forward.2. Many anomalies in Chinese stock markets are empirically studied, such as the autocorrelation, persistence of price fluctuations and fat tailed return distributions, etc. The characteristic time scales of stock indices to recover to normal distribution in Chinese stock market are found. The intraday price volatility and the predictability of high-frequency price fluctuations in Chinese stock market are also studied.3. Fractal and multifractal theories relative to financial markets are summarized. The multifractal phenomenon in economic systems is investigated, and the multifractal characteristic of Chinese stock market is also empirically studied.4. A new idea that the multifractal theories and tools can play important role in the studies of financial risk management are firstly put forward, and its feasibility is also tested.5. Then a new risk measurement and a risk prediction model based on multifractal theories are established, and their validities are also testified.6. Based on the contents studied above, a further research idea that nonlinear, complexity science and behavioral finance theories must be introduced in new financial risk management theories and models.