Abstracts

Perfect liquidity of risky assets is a strong assumption in the Black-Scholes model. Several authors proposed alternative models accounting for imperfect liquidity. One such model was proposed and extensively discussed by Schönbucher and Wilmott (2000).
In the present contribution, we argue that the definition of self-financed strategy used in that paper does not take into full account the effects of imperfect liquidity introduced in the model. We propose one alternative formulation and discuss some properties of the resulting price process.
We use the modified model to discuss the effect of collective behaviour by a large number of small hedgers. If a large number of small traders use similar strategies wrongly assuming perfect liquidity, then synchronized trading of large quantities may have a significant impact in the strategy outcome.
We show that in such circumstances, the expected outcome of the classical Black-Scholes hedging strategy for an European put option can diverge significantly from the perfect hedging obtained under perfect liquidity. The effect of illiquidity can be described by a nonlinear Black-Scholes equation having some very unusual features.