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 …

We analyze the implied volatility smile of a lognormal distribution on a 3 – month Lundbeck call option contract using … the Brownian motion. There is significant time variation in the implied volatility smile and the traditional Black … and get better estimates of a risk adjusted measure. Deep in or out of the money contract has higher implied volatility …