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 …

general local-stochastic volatility model with zero correlation. We do this using the Freidlin-Wentzell theory of large …-time asymptotic behaviour for call options using Holder's inequality, and the implied volatility. This avoids the use of possibly non …, which is analysed at length in Busca et al. We also derive a series expansion for the implied volatility in the small …

In this paper we prove an approximate formula expressed in terms of elementary functions for the implied volatility in … implied volatility function. The proof is based on saddlepoint methods and classical properties of holomorphic functions …

implied index value and implied volatility whereas the restricted model only solves the implied volatility. Next, this study … for calls. Volatility for calls has no significant effect on the index pricing error. The path-dependent effect on index …

options under low-dimensional stochastic volatility models. We derive multidimensional transforms which allow us to construct … efficient path-independent lattices for virtually all low-dimensional stochastic volatility models given in the literature … including one volatility factor-based stochastic volatility (SV) models, two volatility factors-based SV models, stochastic …

We study a new class of three-factor affine option pricing models with interdependent volatility dynamics and a … stochastic skewness component unrelated to volatility shocks. These properties are useful in order (i) to model a term structure … of implied volatility skews more consistent with the data and (ii) to capture comovements of short and long term skews …

In this paper, we derive a closed-form explicit model-free formula for the (Black-Scholes) implied volatility. The … that the proposed formula converges to the true implied volatility value. In numerical experiments, we verify the … stochastic volatility inspired (SVI) model, and the stochastic alpha beta rho (SABR) model. We also establish an explicit formula …

The stock options implied volatility skew reflects both the structural risk characteristics of the underlying company … default risk. The model can explain as much as 44\% of the cross-sectional variation in implied volatility skew and is …