We consider estimating volatility risk factors using large panels of filtered or realized volatilities. The data structure involves three types of asymptotic expansions. There is the cross-section of volatility estimates at each point in time, namely i = 1,…, N observed at dates t = 1,…, T:...

Minimum price variation rules (tick size rules) in the French stock market prior to 1999 provide a natural experiment on the role of transaction costs for financial price volatility. For stock prices above French francs (FF) 500, the minimal tick size for quotes increases from FF 0.1 to FF 1....