We consider several market models, where time is subordinated to a stochastic process. These models are based on various time changes in the Lévy processes driving asset returns, or on fractional extensions of the diffusion equation; they were introduced to capture complex phenomena such as...

We consider several market models, where time is subordinated to a stochastic process. These models are based on various time changes in the Lévy processes driving asset returns, or on fractional extensions of the diffusion equation; they were introduced to capture complex phenomena such as...

Considering market-based inflation expectations, we show that investors' forecasts are non-linear. We capture this non-linear behavior with a Markov-switching model that allows us to identify a regime of high uncertainty, and a regime of low uncertainty and low concern about inflation. Using a...

We provide ready-to-use formulas for European options prices, risk sensitivities, and P&L calculations under Lévy-stable models with maximal negative asymmetry. Particular cases, efficiency testing, and some qualitative features of the model are also discussed.

We establish an explicit pricing formula for a class of non-gaussian models (the Lévy-stable, or Log-Lévy model with finite moments) allowing a straightforward evaluation of an European option, without numerical simulations and with as much accuracy as one wishes. The formula can be used by...