Market Illiquidity and the Bid-Ask Spread of Derivatives

This paper analyzes the impact of illiquidity of a stock on the pricing of derivatives. In particular, it is shown how illiquidity generates a bid-ask spread in an option on this stock, even in the absence of other imperfections, such as transaction costs and asymmetry of information. Moreover, the spread is shown to be asymmetric with respect to the option price under perfect liquidity. This fact explains the appearance of a smile e$ect when the implied volatility is estimated from the mid-quote.