Impact of Trends on Volatility in Equity Markets

The paper explores the impact of trends on the volatility in equity market, with trends defined as uninterrupted runs of positive or negative returns. The impact of trends is first demonstrated as statistically significant using regression analysis to predict the squared normalised residuals of both (i) "raw" returns, and (ii) two widely-used "asymmetric" volatility models, GJR-GARCH and EGARCH. An extension of the asymmetric GARCH models is then proposed with inclusion of additional explanatory variables in the formula for conditional variance in order to account for presence of trends. The resulting model, subsequently tested using 40 years of daily returns on S&P500 index, has higher explanatory power measured by a number of statistical criteria including AIC, BIC and log-likelihood.