In this paper, we propose a general framework for the valuation of options in stochas-tic local volatility (SLV) models … as special cases. Standard stochastic volatility models, such as Heston, Hull-White, Scott, Stein-Stein, α …-Hypergeometric, 3/2, 4/2, mean-reverting, and Jacobi stochastic volatility models, also fall within this general framework. We propose a …

This paper addresses several theoretical and practical issues in option pricing and implied volatility calibration in a … volatility term structure when the Hurst exponent is not 0.5, and also that one-year implied volatility is independent of Hurst … exponent and equivalent to fractional volatility. Building on these observations, we introduce a novel 8-parameter fractional …

commodity prices and regime-switching in the commodity returns volatility. After a closed-form solution for the option value in …

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 …

) as limit cases.As an intuitive illustration of the model's power, I choose the phenomenon of volatility surfaces: I show …

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 …

some correlated local volatility diffusion processes with systematic jumps. We derive a forward partial integral …