We deal with the problem of estimating the volatility of a financial security in a market with frictions. To this end, it is proposed a microstructure model in which the trading price varies only if the value of the information signal is large enough to guarantee a profit in excess of transaction costs. The main statistical properties of such a model are derived and discussed extensively. Using transaction data only, the proposed approach allows to recover: (i) the conditional volatility of the information signal, which is thus cleaned out by market frictions, (ii) an estimate of transaction costs. Our analysis reveals that, after correcting for frictions, the risk of illiquid securities is substantially different from what predicted by traditional volatility models. Furthermore, in periods of high volatility, our estimate of transaction costs remains highly correlated with bid-ask spreads, whereas alternative illiquidity proxies, such as the fraction of zero returns, loose their explanatory power.
 

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