This article studies the pricing of options in an extended Black Scholes economy in which the underlying asset is not perfectly liquid. The resulting liquidity risk is modeled as a stochastic supply curve, with the transaction price being a function of the trade size. Consistent with the market microstructure literature, the supply curve is upward sloping with purchases executed at higher prices and sales at lower prices. Optimal discrete time hedging strategies are then derived. Empirical evidence reveals a significant liquidity cost intrinsic to every option.
U. Çetin, R. Jarrow, P. Protter, M. Warachka, Pricing Options in an Extended Black Scholes Economy with Illiquidity: Theory and Empirical Evidence, The Review of Financial Studies, Volume 19, Issue 2, Summer 2006, Pages 493–529, https://doi.org/10.1093/rfs/hhj014
Oxford University Press