Related papers: Sparse grid high-order ADI scheme for option prici…

Based on empirical market data, a stochastic volatility model is proposed with volatility driven by fractional noise. The model is used to obtain a risk-neutrality option pricing formula and an option pricing equation.

Pricing and hedging exotic options using local stochastic volatility models drew a serious attention within the last decade, and nowadays became almost a standard approach to this problem. In this paper we show how this framework could be…

In this paper, we propose a novel family of high-order numerical schemes for the gradient flow models based on the scalar auxiliary variable (SAV) approach, which is named the high-order scalar auxiliary variable (HSAV) method. The newly…

In this paper, we propose an RADI-type method for large-scale stochastic continuous-time algebraic Riccati equations with sparse and low-rank matrices. This new variant of RADI-type methods is developed by integrating the core concept of…

First-order fully implicit as well as implicit--explicit schemes for coupled elliptic-parabolic systems are discussed in [Ern and Meunier, ESAIM: M2AN, 2009] and [Altmann et al., Math.\ Comp., 2021], respectively. The extension of the…

In this paper, we price European Call three different option pricing models, where the volatility is dynamically changing i.e. non constant. In stochastic volatility (SV) models for option pricing a closed form approximation technique is…

In this paper, we introduce a Lagrange multiplier approach to construct linearly implicit energy-preserving schemes of arbitrary order for general Hamiltonian PDEs. Unlike the widely used auxiliary variable methods, this novel approach does…

Many model selection algorithms rely on sparse dictionary learning to provide interpretable and physics-based governing equations. The optimization algorithms typically use a hard thresholding process to enforce sparse activations in the…

The multidimensional Uncertain Volatility Model leads to robust option pricing problems under joint volatility and correlation uncertainty. Their numerical resolution quickly becomes challenging because the associated stochastic control…

The Fokker-Planck (FP) model is one of the commonly used methods for studies of the dynamical evolution of dense spherical stellar systems such as globular clusters and galactic nuclei. The FP model is numerically stable in most cases, but…

We introduce some sparse grids interpolations used in Semi-Lagrangian schemes for linear and fully non-linear diffusion Hamilton Jacobi Bellman equations arising in stochastic control. We prove that the method introduced converges toward…

We introduce an efficient and accurate staggered-grid finite-difference (SGFD) method to solve the two-dimensional elastic wave equation. We use a coupled first-order stress-velocity formulation. In the standard implementation of SGFD…

We propose a new paradigm for designing efficient p-adaptive arbitrary high order methods. We consider arbitrary high order iterative schemes that gain one order of accuracy at each iteration and we modify them in order to match the…

In this study, we present a novel stabilized finite element analysis for transient Stokes model. The algebraic subgrid multiscale approach has been employed to arrive at the stabilized coupled variational formulation. Derivation of the…

We propose a WENO finite difference scheme to approximate anelastic flows, and scalars advected by them, on staggered grids. In contrast to existing WENO schemes on staggered grids, the proposed scheme is designed to be arbitrarily…

This paper presents a novel adaptive-sparse polynomial dimensional decomposition (PDD) method for stochastic design optimization of complex systems. The method entails an adaptive-sparse PDD approximation of a high-dimensional stochastic…

Stochastic differential equation (SDE) models are the foundation for pricing and hedging financial derivatives. The drift and volatility functions in SDE models are typically chosen to be algebraic functions with a small number (less than…

In this article, we propose an implicit finite difference scheme for a two-dimensional parabolic stochastic partial differential equation (SPDE) of Zakai type. The scheme is based on a Milstein approximation to the stochastic integral and…

American options are studied in a general discrete market in the presence of proportional transaction costs, modelled as bid-ask spreads. Pricing algorithms and constructions of hedging strategies, stopping times and martingale…

The two-dimensional unsteady coupled Burgers' equations with moderate to severe gradients, are solved numerically using higher-order accurate finite difference schemes; namely the fourth-order accurate compact ADI scheme, and the…