a Third workshop on Nonlinear PDEs and Financial Mathematics
BTU
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V. Myrnyy

On the estimation of market liquidity and volatility

Jan-Olof Johansson

Abstract
Market liquidity can be defined as the probability that the next trade of an asset is executed at a price equal to the last one. It can be modeled by the bid-ask spread and the market depth. Different models of these two properties exist and we refer in this talk to a parametric model with a parameter \lambda for the market depth and \gamma for the width of the bid-ask spread. We use intraday data of Microsoft and Intel stock prices and study the parameters over time and relate their appearance to the volatility. The time series of the parameters can conveniently be modeled by the Ornstein-Uhlenbeck process and used for monitoring purpose.