Intraday and high frequency time series are mostly defined by a non-continuous prices process. This paper introduces an integer based ARMA model found to be a better predictor for absolute intraday price changes than continuous time estimators (such as GARCH or multiplicative error models)....

We study whether prices of traded options contain information about future extreme market events. Our option-implied conditional expectation of market loss due to tail events, or tail loss measure, predicts future market returns, magnitude, and probability of the market crashes, beyond and above...