Market illiquidity and bounds on European option prices

The paper analyses the impact of illiquidity of a stock paying no dividends on the pricing of European options written on that stock. In particular, it is shown how illiquidity generates price bounds on an option on this stock, even in the absence of other imperfections, such as transaction costs and trading constraints, or the assumption of stochastic volatility. Moreover, price bounds are shown to be asymmetric with respect to the option price under perfect liquidity. This fact explains, under some conditions, the appearance of a smile effect when the implied volatility is estimated from the mid-quote.