Estimating Risk in Illiquid Markets: A Model of Market Friction with Stochastic Volatility

Abstract This article deals with the problem of estimating the volatility of a financial security in a market with frictions. We propose a microstructural model with time-varying fundamental price volatility 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. 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 and (ii) an estimate of transaction costs. Our analysis reveals that, after correcting for frictions, the risk of illiquid securities is substantially different from what is predicted by traditional volatility models. Furthermore, using a big dataset of intraday returns, we show that our transaction cost estimate is highly correlated with the main illiquidity measures and that such correlations are significant under different volatility regimes.