In an extension of the Kyle (1985) model of continuous insider trading
, it is shown that asymmetric information can make it impossible to pr
ice options by arbitrage. Even when an option would appear to be redun
dant, its introduction into the market can cause the volatility of the
underlying asset to become stochastic. This eliminates the potential
for dynamically replicating the option. The change in the price proces
s of the asset reflects a change in the information transmitted by vol
ume and prices when the option is traded.