Impact of Margin Trading and Short Selling on the Volatility of the Shanghai Composite Index: A GARCH Analysis

China launched a pilot margin trading and securities lending program on 31 March 2010, ending the stock market's single-sided trading regime. The program now has a material effect on stock price volatility, yet the price discovery function of margin trading and short selling has not been fully realized. This paper examines the effect of these activities on the volatility of the Shanghai Composite Index through theoretical and empirical analysis. It first explains the channels through which margin financing and securities lending affect stock market volatility, then fits volatility with a GARCH model and applies Granger causality tests and impulse response analysis. The results indicate that both margin financing and securities lending help stabilize stock market volatility. The paper recommends gradually expanding the range of eligible securities, improving the securities lending and refinancing mechanism, strengthening investor education on market risk, and enhancing risk controls for margin trading and short selling.