Controlling price volatility through financial innovation

In a three-period finite competitive exchange economy with incomplete financial markets and retrading, we study the possibility of controlling asset price volatility through financial innovation. We first give sufficient conditions on preferences and endowments implying that whatever is the innovation which completes markets, it also reduces volatility, typically in this class of economies. We also numerically examine some interesting examples. Then we show the generic existence, even outside this class, of financial innovation which decreases equilibrium price volatility. The existence is obtained under conditions of sufficient market incompleteness. The financial innovation may consist of an asset which is only traded at time zero, or retraded, and with payoffs only at the terminal date. The existence is shown to be robust in the asset payoff space.