Nonliear And Time Varying Correlations For Financial Markets Based On Implied Volatility

Risk management is a key research theme under conditions of economic globalization, uncertainty of international macro environment and multinational investment portfolios. Modern capital management theories focus more on the volatility-return correlations and co-movements between markets. The results of correlations between volatility and return are mixed. It is worthy to study the volatility-return correlations of stock markets and volatility-return correlations between implied volatility and foreign exchange returns for global financial markets and the implied volatility co-movemennts between markets. Understanding the volatility-return correlations and co-movements between markets deeply very helpful for investors and researchers.Implied volatility index, also known as "fear index" is an effective measurement of possible future volatilities including more information than realized volatilities. In this paper, based on implied volatility indexes,we choose U.S., Europe, U.K., Japan and China as sample to investigate the volatility-return correlations and co-movements between regions. As the related researches display the volatility-return correlations and co-movements show nonliear and asymmetric characteristics, we apply time varying copula models to calculate the co-movements and correlations and show the dynamic conditional correlations and tail dependences for the volatility-return correlations and co-movements between markets.In the first place, we review thetheoretical models of copula models and implied volatility indexes.Wegeneralize the definition, commonly used functions and solving method of copula models first. For the implied volatility indexes part, we discuss the constructing processes of historical volatility (realized volatility) and implied volatility and compare the Black-Scholes and model free methods of calculating implied volatility. Then we review the calculation process of implied volatility indexes and indicate the advantages of implied volatility index. This is the theory foundation of empirical studies.We study the volatility-return correlations between the changes of implied volatility indexes and stock, foreign exchange returns of the global major markets. We extend the sample and use U.S., Europe, U.K., Japan and China as sample and test the volatility-return correlations and co-movements between regions. We have new findings. The five sample area show different results. The volatility-return correlations for China and Japan show positive correlations sometimes but the volatility-return correlations for U.S., Europe and U.K. areas are always negative correlated. The stock markets of China and Japan show the existence of risk-lover and risk-chasing. The implied volatility and foreign exchange return are weak correlated and are affected by the extreme cases (U.S. crisis, European debt crisis and the great fall in China).The co-movements between global main financial markets are also studied in this paper. Differently, this empirical study is based on implied volatility indexes and time varying copulas. The co-movements through implied volatility indexes are very strong, especially during extreme events. The tail dependences are asymmetric with stronger co-movements during the risk rising periods. The risk of U.S. and European stock markets can be hedged by that of China's stock market during the bull market of China.Besides, we analyze the co-movement transmission channels between China and other major financial markets. The existing literature indicates the co-movements between China and global markets are reflected in the price channel of stock and foreign exchange rates. We add implied volatility indexes into the co-movement channels and find the co-movements through implied index channel is stronger and performs better.