stochastic volatility models with jumps. In this paper we consider a dense subclass of such models and develop analytically … Fourier transforms of vanilla and forward starting option prices as well as a formula for the slope of the implied volatility … volatility swaps and other volatility derivatives are given as a one-dimensional integral of an explicit function. Analytically …

volatility level. Single-factor stochastic volatility models are not flexible enough to account for the stochastic behavior of … the skew. On the other hand, multifactor stochastic volatility models are able to account for the existence of stochastic … that the consideration of additional volatility factors in the context of stochastic volatility models allows us to …

and portfolios. We document that the SDF is dense in characteristics with the impliedrealized volatility spread, option …

, which is defined as the ratio between the realized volatility and trading volume and which refines the popular price impact … measure proposed by Amihud (2002). In our model, both price volatility and market liquidity are assumed to follow stochastic … processes in continuous time. In this setting, characterized by stochastic volatility and liquidity, we prove that the realized …

volatility models. We provide a succinct error analysis to demonstrate that we can achieve an exponential convergence rate in the …