Determining bid-ask prices for options with stochastic illiquidity and applications to index options

Abstract

Market makers must quote two prices - bid and ask prices - for options. This article provides a GARCH model with stochastic illiquidity risks and gives analytical approximation solutions for the bid and ask prices for options. A joint calibration method is applied for calibrating the implied parameters. The empirical evidence shows an illiquidity smile for short-term calls and a negatively sloped illiquidity smirk for long-term calls. Similar results are also observed in put option prices. The proposed stochastic illiquidity model significantly outperforms the static illiquidity model in the in-sample and out-of-sample tests, particularly when the stochastic volatility is crucial.