Option pricing with an illiquid underlying asset market

We examine how price impact in the underlying asset market affects the replication of a European contingent claim. We obtain a generalized Black-Scholes pricing PDE and establish the existence and uniqueness of a classical solution to this PDE. Unlike the case with transaction costs, we prove that replication with price impact is always cheaper than superreplication. Compared to the Black-Scholes case, it trader generally buys more Stock and borrows more (shorts and ends more) to replicate a call (put). furthermore, price impact implies endogenous stochastic volatility and all out-of-money option has lower implied volatility than in in-the-money option. This finding has important implications for empirical analysis on volatility smile. (c) 2005 Elsevier B.V. All rights reserved.