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Asset prices can be stale. We define price staleness as a lack of price adjustments yielding zero returns (i.e., zeros). The term idleness (respectively, near idleness) is, instead, used to define staleness when trading activity is absent (respectively, close to absent). Using statistical and pricing metrics, we show that zeros are a genuine economic phenomenon linked to the dynamics of trading volume and, therefore, liquidity. Zeros are, in general, not the result of institutional features, like price discreteness. In essence, spells of idleness or near idleness are stylized facts suggestive of a key, omitted market friction in the modeling of asset prices. We illustrate how accounting for this friction may generate sizable risk compensations in short-dated option returns. This paper was accepted by Kay Giesecke, finance.

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We show that High Frequency Traders (HFTs) are not beneficial to the stock market during flash crashes. They actually consume liquidity when it is most needed, even when they are rewarded by the exchange to provide immediacy. The behavior of HFTs exacerbate the transient price impact, unrelated to fundamentals, typically observed during a flash crash. Slow traders provide liquidity instead of HFTs, taking advantage of the discounted price. We thus uncover a trade-o↵ between the greater liquidity and e ciency provided by HFTs in normal times, and the disruptive consequences of their trading activity during distressed times.

Asset transaction prices sampled at high frequency are much staler than one might expect in the sense that they frequently lack new updates showing zero returns. In this paper, we propose a theoretical framework for formalizing this phenomenon. It hinges on the existence of a latent continuous-time stochastic process p t valued in the open interval (0, 1), which represents at any point in time the probability of the occurrence of a zero return. Using a standard infill asymptotic design, we develop an inferential theory for nonparametrically testing, the null hypothesis that p t is constant over one day. Under the alternative, which encompasses a semimartingale model for p t , we develop non-parametric inferential theory for the probability of staleness that includes the estimation of various integrated functionals of p t and its quadratic variation. Using a large dataset of stocks, we provide empirical evidence that the null of the constant probability of staleness is fairly rejected. We then show that the variability of p t is mainly driven by transaction volume and is almost unaffected by bid-ask spread and realized volatility.