volatility models. We discuss several recent developments in the theory of derivative pricing under incompleteness in the context …In this survey we discuss models with level-dependent and stochastic volatility from the viewpoint of derivative asset … start by briefly recalling the standard theory for pricing and hedging derivatives in complete frictionless markets and the …

of the underlying asset. We derive an explicit expression for the transformation of market volatility under the impact of … hedging. It turns out that market volatility increases and becomes price-dependent. The strength of the effects depend not … discuss in what sense hedging strategies calculated under the assumption of constant volatility are still appropriate, even if …

This paper analyzes optimal portfolio choice and consumption with stochastic volatility in incomplete markets. …

We develop a discrete-time stochastic volatility option pricing model, which exploits the informationcontained in high …-frequency data. The Realized Volatility (RV) is used as a proxy of the unobservablelog-returns volatility. We model its dynamics by a … stochastic volatility pricing models. The pricing improvementcan be ascribed to: (i) The direct use of the RV, which provides a …

specicationof (a) the initial density, and (b) the volatility structure of the density. The volatilitystructure is assumed at any …

sufficient condition for market completenessis that the volatility of dividends be invertible and provide higher order …

stochastic skewness component unrelated to volatility shocks. Theseproperties are useful in order (i) to model a term structure … of implied volatility skews moreconsistent with the data and (ii) to capture comovements of short and long term skews … largelyunrelated to the volatility dynamics. We estimate our models using about fourteen years ofS&P 500 index option data and nd that …