Multifractal Volatility Measure And Applications In Financial Market

In modern financial theory, description of financial asset volatility act as one of the core role. The usefulness of volatility measurement and its dynamics has important significance to academic and practice.Measurements and models to describe and predict financial asset volatility abound and many volatility models, such as GARCH models, SV and lnRV-ARFIMA, are presented to be used in financial theory and practice. However, these mainstream models are all defective, hence bring on inconsistency between theory inferrer and empirical results. As an powerful tool to describe complexity of financial volatility, multifractal theory can fetch up limitations of traditional ways. However most of these studies focus on empirical tests of multifractality in different financial data sets. So we wonder whether multifractal analysis can contribute to the measurement and forecasting accuracy of volatility in financial markets. Along with this notion, we propose a so-called multifractal volatility (MFV) measure and its dynamic model based on the multifractal spectrum of high-frequency price movements within one trading day. We further examined MFV's performance in volatility forecasting, risk measuring and financial derivatives pricing. The main research content are as follows:(1) Research on several complex features of volatility, such as inspection to distribution characteristics of financial returns based on different frequency data and descriptive statistics, QQ plot and probability distribution plot; analysis of higher-moments volatility characteristics based on GJRSK-M model; research of long-memory feature of volatility based on R/S analysis.(2) Construction and modeling of multifractal volatility (MFV). Through one group of multifractal language, we empirically studied multifractal feature of financial volatility and further discussed relationship between this important characteristics and volatility measuring. Based on analysis above, we constructed a new volatility measure, named MFV, and comprehensively investigated its statistical property. Consequently, a time series model, lnMFV-ARMA, is used to describe dynamic characteristics of MFV. Finally, distribution of conditional return based on MFV is investigated and compared with those based on GARCH model.(3) Application of MFV in financial volatility forecasting. First, square return, rt2, is selected to be regarded as proxy of potential volatility from several volatility measurements such as rt2,|rt| and RV, et al. Second, rolling time windows is employed to forecast out-of-sample volatility based on some popular volatility models such as GARCH models and SV. Finally, three testing methods, which are median loss function, M-Z regression and SPA test, are employed to empirically test the difference of forecasting accuracy between MFV model and other popular ones.(4) Application of MFV in financial risk measuring. Take S&P500 and SSEC as sample, we compute VaR and ES which are applied extensively in finance theory and practice based on lnMFV-ARMA and other popular models. Furthermore, some backtesting methods, such as LR test, DQR test and bootstrap, are employed to compare VaR and ES accuracy of different volatility models.(5) Application of MFV in financial derivatives pricing. Take 4 call warrants of Chinese stock market as sample, model price based on MFV model is computed under Black-Scholes model framework. Then take market price as benchmark, the pricing accuracy difference between MFV model and other volatility models is compared.