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. We show that unlike the case with transaction costs, replication in the presence of price impact is always cheaper than superreplication. This model implies endogenous stochastic volatility. Compared to the Black-Scholes case, a trader generally buys more stock and borrows more (shorts and lends more) to replicate a call (put). The excess replicating cost over the Black-Scholes price is significant. Furthermore, price impact implies that an out-of-money option has lower implied volatility than an in-the-money option. This finding has important implications for empirical analysis on “volatility smile.” Journal of Economic Literature Classification Numbers: D11, D91, G11, C61.