Estimating trading costs in the absence of recorded data is a problem that continues to puzzle financial market researchers. We address this challenge by introducing two low frequency bid-ask spread estimators using daily high and low transaction prices.

The range of mid-prices is an increasing function of the sampling interval, while the bid-ask spread and the relationship between trading direction and the mid-price are not constrained by it and are therefore independent. Monte Carlo simulations and data analysis from the equity and foreign exchange markets demonstrate that these models (especially SHL2) significantly out-perform the most widely used low-frequency estimators, such as those proposed in Corwin and Schultz (2012) and most recently in Abdi and Ronaldo (2017). Using real world data we show that one of our estimators (SHL2)’s root mean square error (RMSE) is almost less than a half (even 20%) of the competitors. We illustrate how our models can be applied to deduce historical market liquidity in US, UK, Hong Kong and the Thai stock markets. Our estimator can also effectively act as a gauge for market volatility and as a measure of liquidity risk in asset pricing.