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.     

ASYMMETRIC INFORMATION AND EXCHANGE OF INFORMATION ABOUT PRODUCT DIFFERENTIATION

We introduce asymmetric information about consumers’ transportation costs (i.e., the degree of product differentiation) in the model of Hotelling. When transportation costs are high, both firms have lower profits with asymmetric information than with perfect information. Contrarily, if transportation costs are low, both firms may prefer the asymmetric information scenario (the informed firm always prefers the informational advantage, while the uninformed firm may or may not prefer to remain uninformed). Information exchange is ex‐ante advantageous for both firms, but ex‐post damaging if transportation costs turn out to be low. If the information is unverifiable, the informed firm does not represent a reliable source of information, since it always prefers to announce that transportation costs are high and there is no contract that induces truthful revelation.