Information asymmetries, volatility, liquidity, and the Tobin Tax

We develop a tractable model in which trade is generated by asymmetry in agents' information sets. We show that, even if news are not generated by a stochastic volatility process, in the presence of information treatment and/or order processing costs, the (unique) equilibrium price process is characterised by stochastic volatility. The intuition behind this result is simple. In the presence of trading costs and dynamic information, agents strategically choose their trading times. Since new (constant volatility) information is released to the market at trading times, the price process sampled at trading times is not characterised by stochastic volatility. But since trading and calendar times differ, the price process at calendar times is the time change of the price process at trading times – i.e. price movements on the calendar time scale are characterised by stochastic volatility. Our closed form solutions show that: i) volatility is autocorrelated and is a non-linear function of both number and volume of trades; ii) the relative informativeness of numbers and volume of trades depends on the sampling frequency of the data; iii) volatility, the limit order book, and liquidity, in terms of tightness, depth, and resilience, are jointly determined by information asymmetries and trading costs. The model is able to rationalise a large set of empirical evidence about stock market volatility, liquidity, limit order books, and market frictions, and provides a natural laboratory for analysing the equilibrium effects of a financial transaction tax.