Modeling US Stock Market Volatility-Return Dependence Using Conditional Copula and Quantile Regression

Abstract

In this chapter, we examine the return-volatility relationship for some indices reported on exchanges in the United States of America. We utilize both linear quantile regression and copula quantile regression to evaluate the asymmetric volatility-return relationship between changes in the volatility index (VXD, VIX, VXO and VXN) and the corresponding stock index return series (DJIA, S{\&}P 500, the S{\&}P 100 and NASDAQ). The data period is from February 2, 2001 through December 31, 2012. The quantile copula models allow for inference at different quantiles of interest. We find, first, that the relationship between stock return and implied volatility depends on the quartile at which the relationship is being investigated. Second, we obtain results similar to those reported for European exchanges showing the existence of an inverted U-shaped relationship between stock return and implied volatility. This result was obtained even after controlling for changes in volatility of return using a GARCH(1, 1) filter.