-stochastic volatility (LSV) model. Despite their complexity, autocallable structured notes are the most traded equity-linked exotic …, the commonly-used local volatility (LV) model is overly simplified for pricing and risk management. Given its ability to … match the implied volatility smile and reproduce its realistic dynamics, the LSV model is, in contrast, better suited for …

We prove here a general closed-form expansion formula for forward-start options and the forward implied volatility … smile in a large class of models, including the Heston stochastic volatility and time-changed exponential Levy models … particular) many results for the spot implied volatility smile.In passing we (i) show that the forward-start date has to be …

volatility jump diffusion model …

Financial markets exhibit high levels of volatility. Volatile markets are usually associated with high risks and … high volatility using a suitable hedging structure. One particular volatility hedge, involves taking a position in an …

The notion of model-free implied volatility (MFIV), constituting the basis for the highly publicized VIX volatility … more compatible with the related concept of corridor implied volatility (CIV). We provide a comprehensive derivation of the … CIV measure and relate it to MFIV under general assumptions. In addition, we price the various volatility contracts, and …

methodology is based on partitioning the total implied volatility into downside and upside portions. We extract the downside and … upside volatilities for S&P 500 for the years 2007-2011. Not surprisingly, we find that in general the downside volatility is … 2010-2011, the downside volatility accounts for a larger portion of the total volatility when compared with the tumultuous …

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 …