■ Jumps and Microstructure Noise in Stock Price Volatility
Hence, there is a need for accurate model free measures of volatility. Note that the volatility of a price process is fairly model free. “Any log-price process subject to a no-arbitrage condition and weak auxiliary assumptions will constitute a semi-martingale that may be decomposed into a locally predictable mean component and a martingale with finite second moment” (Andersen et al., 2005). The predictable quadratic variation of the martingale is the volatility.