The use of the Heston model is still challenging because it has a closed formula only when
the parameters are constant [S. Heston, Rev. Financ. Stud., 6 (1993), pp. 327–343] or …

We design a numerical scheme for solving the Multi-step Forward Dynamic Programming
(MDP) equation arising from the time-discretization of backward stochastic differential …

The implied volatility surface (IVS) is a fundamental building block in computational finance.
We provide a survey of methodologies for constructing such surfaces. We also discuss …

By means of classical Itô calculus, we decompose option prices as the sum of the classical
Black–Scholes formula, with volatility parameter equal to the root-mean-square future …

In this paper, we propose two new representation formulas for the conditional marginal
probability density of the multi-factor Heston model. The two formulas express the marginal …

Because of its very general formulation, the local volatility model does not have an analytical
solution for European options. In this article, we present a new methodology to derive closed …

In this paper we propose a closed-form asymptotic expansion approach to pricing discretely
monitored Asian options in general one-dimensional diffusion models. Our expansion is a …

Using the exponential generating function of Hermite polynomials, we expand the prices of
VIX power payoffs (including VIX futures) in various Bergomi models at any order in the …

We propose a novel method for the analytical approximation in local volatility models with
Lévy jumps. The main result is an expansion of the characteristic function in a local Lévy …

In this paper we discuss the basket options valuation for a jump–diffusion model. The
underlying asset prices follow some correlated local volatility diffusion processes with …