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 …

This thesis presents our study on using the hybrid stochastic-local volatility model for option pricing. Many … researchers have demonstrated that stochastic volatility models cannot capture the whole volatility surface accurately, although … the model parameters have been calibrated to replicate the market implied volatility data for near at-the-money strikes …

along with the specification of (a) the initial density, and (b) the volatility structure of the density. The volatility …

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 …

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 …

volatility level. Single-factor stochastic volatility models are not flexible enough to account for the stochastic behavior of … the skew. On the other hand, multifactor stochastic volatility models are able to account for the existence of stochastic … that the consideration of additional volatility factors in the context of stochastic volatility models allows us to …

Volatility products have become popular in the past 15 years as a hedge against market uncertainty. In particular …, there is growing interest in options on the VIX volatility index. A number of recent empirical studies examine whether there … proposing and analyzing a stochastic volatility model with regime switching. The basic Heston model cannot capture VIX implied …

volatility model, by developing efficient transform based pricing methods. This non-affine model gives prices of options on … realized variance which allow upward sloping implied volatility of variance smiles. Heston's (1993) model, the benchmark affine … stochastic volatility model, leads to downward sloping volatility of variance smiles - in disagreement with variance markets in …