On the information content of implied liquidity measure: Evidence from the S&P 500 index options

Abstract

This paper aims to unfold the information content of the implied liquidity measure, which is introduced through the Conic Finance theory and considered a proxy for the market liquidity level. We propose a partial information setting in which the dynamics of the implied liquidity, representing the noisy information on the unobserved true market liquidity, follow a continuous-time Markov-chain modulated exponential Ornstein-Uhlenbeck process. Model inference requires the filtering of the unobserved states of the true market liquidity, as well as the estimation of the unknown model parameters. We address the inference problem using the EM algorithm methodology, in which we provide novel results on robust filters leading to maximum likelihood estimates. We fit the proposed model to the implied liquidity series obtained from the prices of (closest to) 1-year ATM call options on the S & P 500 covering the period from January 2002 to August 2022. The data application shows that the unobserved true market liquidity follows three regimes. The implied liquidity series contains relevant information as the filtered trajectory of the underlying Markov chain moves according to the economic environment changes due to the Federal Reserve's actions, the global financial crisis of 2007-08, and the COVID-19 pandemic.