Implied Liquidity : Model Sensitivity

The concept of implied liquidity originates from the conic finance theory and more precisely from the law of two prices where market participants buy from the market at the ask price and sell to the market at the lower bid price. The implied liquidity lambda of any financial instrument is determined such that both model prices fit as well as possible the bid and ask market quotes. It reflects the liquidity of the financial instrument: the lower the lambda, the higher the liquidity. The aim of this paper is to study the evolution of the implied liquidity pre- and post crisis under a wide range of models and to study implied liquidity time series which could give insight for future stochastic liquidity modelling. In particular, we perform a maximum likelihood estimation of the CIR and Vasicek mean-reverting processes applied to liquidity and volatility time series. The results show that implied liquidity is far less persistent than implied volatility. Moreover, a comparison of the parameter estimates between the pre- and post credit crisis periods indicates that liquidity tends to decrease and increase for long and short term options, respectively, during troubled periods