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 …

-of-the-money and long-maturity options. When applied to Heston's stochastic volatility model, our method is shown to be extremely …

's stochastic volatility model, our method is shown to be extremely efficient and fairly accurate …

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 …

volatility models. We provide a succinct error analysis to demonstrate that we can achieve an exponential convergence rate in the …

well as for extracting the implied volatility from quoted options. The latter is of particular importance since it … approximating error of the suggested solution and, by comparing our results in computing the implied volatility with the most common …

.We address the problem of the consistency of the Black-Scholes model with the volatility surface and we show that, under general … conditions, the Black-Scholes formula cannot be generalized to account for the volatility smile …