We consider a market where traders have asymmetric information regarding the distribution of asset return and study price discovery of derivatives. The informed trader has private information regarding arbitrary higher moments of asset return, such as volatility or skewness, and exploits her private information by trading a complete menu of options. The equilibrium trading strategies of the informed agent in our model reflect those used by traders in the market when trying to exploit higher order moment information, such as the volatility straddle.