We show that there are two distinct ways to make volatility stochastic that are differentiated by their consequences for skewness. Most models in the literature have adopted the relatively tractable methodology of using stochastic time changes to engineer stochastic volatility. Unfortunately,...

In this paper we study an incomplete Brownian motion market and use filtration reduction to obtain a complete market, and hence a unique pricing measure. We then uplift the obtained measure to the original market and study valuation and hedging via the uplifted measure. We show how a general...