different equities based on their moneyness does offer much guidance in understanding which option offers a better hedging …

market model prices OTC cap exactly and prices OTC swaptions with errors well below two basis points. Tests for the hedging … performance show that the deterministic LIBOR market model is more effective in hedging in- and at-the money OTC caps and …

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 …

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 surfaces. The parameters of this model are directly linked to measurable and observable market risks …