Related papers: Full grid solution for multi-asset options pricing…
In this paper, we consider the tensor completion problem representing the solution in the tensor train (TT) format. It is assumed that tensor is high-dimensional, and tensor values are generated by an unknown smooth function. The assumption…
We present a polynomial multigrid method for the nodal interior penalty formulation of the Poisson equation on three-dimensional Cartesian grids. Its key ingredient is a weighted overlapping Schwarz smoother operating on element-centered…
We study an algorithm which has been proposed by Chinesta et al. to solve high-dimensional partial differential equations. The idea is to represent the solution as a sum of tensor products and to compute iteratively the terms of this sum.…
This paper explores advancements in quantum algorithms for derivative pricing of exotics, a computational pipeline of fundamental importance in quantitative finance. For such cases, the classical Monte Carlo integration procedure provides…
We present a simple, fast, and accurate method for pricing a variety of discretely monitored options in the Black-Scholes framework, including autocallable structured products, single and double barrier options, and Bermudan options. The…
In this article we consider the problem of pricing and hedging high-dimensional Asian basket options by Quasi-Monte Carlo simulation. We assume a Black-Scholes market with time-dependent volatilities and show how to compute the deltas by…
A long-standing issue in mathematical finance is the speed-up of option pricing, especially for multi-asset options. A recent study has proposed to use tensor train learning algorithms to speed up Fourier transform (FT)-based option…
The paper focuses on pricing European-style options on several underlying assets under the Black-Scholes model represented by a nonstationary partial differential equation. The proposed method combines the Galerkin method with…
We introduce a fully discrete scheme to solve a class of high-dimensional Mean Field Games systems. Our approach couples semi-Lagrangian (SL) time discretizations with Tensor-Train (TT) decompositions to tame the curse of dimensionality. By…
We consider the problem of pricing discretely monitored Asian options over $T$ monitoring points where the underlying asset is modeled by a geometric Brownian motion. We provide two quantum algorithms with complexity poly-logarithmic in $T$…
We consider the solution of linear systems with tensor product structure using a GMRES algorithm. In order to cope with the computational complexity in large dimension both in terms of floating point operations and memory requirement, our…
In the framework of Black-Scholes-Merton model of financial derivatives, a path integral approach to option pricing is presented. A general formula to price European path dependent options on multidimensional assets is obtained and…
Quasi-Monte Carlo (QMC) method is a useful numerical tool for pricing and hedging of complex financial derivatives. These problems are usually of high dimensionality and discontinuities. The two factors may significantly deteriorate the…
In this paper we solve $m$-parameter eigenvalue problems ($m$EPs), with $m$ any natural number by representing the problem using Tensor-Trains (TT) and designing a method based on this format. $m$EPs typically arise when separation of…
Option pricing is a significant problem for option risk management and trading. In this article, we utilize a framework to present financial data from different sources. The data is processed and represented in a form of 2D tensors in three…
Physics-Informed Neural Networks (PINNs) have emerged as a promising paradigm for solving partial differential equations (PDEs) by embedding physical laws into neural network training objectives. However, their deployment on…
The Black-Scholes model, defined under the assumption of a perfect financial market, theoretically creates a flawless hedging strategy allowing the trader to evade risks in a portfolio of options. However, the concept of a "perfect…
Understanding entanglement remains one of the most intriguing problems in physics. While particle and site entanglement have been studied extensively, the investigation of length or energy scale entanglement, quantifying the information…
Discrete tensor train decomposition is widely employed to mitigate the curse of dimensionality in solving high-dimensional PDEs through traditional methods. However, the direct application of the tensor train method typically requires…
We introduce compositional tensor trains (CTTs) for the approximation of multivariate functions, a class of models obtained by composing low-rank functions in the tensor-train format. This format can encode standard approximation tools,…