Related papers: Pricing multi-asset derivatives by finite differen…
A variational quantum algorithm for numerically solving partial differential equations (PDEs) on a quantum computer was proposed by Lubasch et al. In this paper, we generalize the method introduced by Lubasch et al. to cover a broader class…
In this article, we propose a new numerical approach to high-dimensional partial differential equations (PDEs) arising in the valuation of exotic derivative securities. The proposed method is extended from Reisinger and Wittum (2007) and…
Partial differential equation (PDE) models with multiple temporal/spatial scales are prevalent in several disciplines such as physics, engineering, and many others. These models are of great practical importance but notoriously difficult to…
We give an upper bound on the resources required for valuable quantum advantage in pricing derivatives. To do so, we give the first complete resource estimates for useful quantum derivative pricing, using autocallable and Target Accrual…
This paper addresses the problem of pricing involved financial derivatives by means of advanced of deep learning techniques. More precisely, we smartly combine several sophisticated neural network-based concepts like differential machine…
We present a detailed numerical study of an alternative approach, named Quantum Non-Demolition Measurement (QNDM), to efficiently estimate the gradients or the Hessians of a quantum observable. This is a key step and a resource-demanding…
The quantum algorithms for Monte Carlo integration (QMCI), which are based on quantum amplitude estimation (QAE), speed up expected value calculation compared with classical counterparts, and have been widely investigated along with their…
Accurate and efficient pricing of multi-asset basket options poses a significant challenge, especially when dealing with complex real-world data. In this work, we investigate the role of quantum-enhanced uncertainty modeling in financial…
This study enhances option pricing by presenting unique pricing model fractional order Black-Scholes-Merton (FOBSM) which is based on the Black-Scholes-Merton (BSM) model. The main goal is to improve the precision and authenticity of option…
In this paper, we consider the numerical pricing of financial derivatives using Radial Basis Function generated Finite Differences in space. Such discretization methods have the advantage of not requiring Cartesian grids. Instead, the nodes…
We discuss a Quantum Non-Demolition Measurement (QNDM) protocol to estimate the derivatives of a cost function with a quantum computer. %This is a key step for the implementation of variational quantum circuits. The cost function, which is…
In this paper we focus on the subdiffusive Black Scholes model. The main part of our work consists of the finite difference method as a numerical approach to the option pricing in the considered model. We derive the governing fractional…
Financial derivatives pricing aims to find the fair value of a financial contract on an underlying asset. Here we consider option pricing in the partial differential equations framework. The contemporary models lead to one-dimensional or…
The time-fractional Black-Scholes equation (TFBSE) is intended to price the options for which the underlying price fluctuates within a correlated fractal transmission system. Although the TFBSE is an influential approach for grasping the…
In this paper, we study the benefits of using polyharmonic splines and node layouts with smoothly varying density for developing robust and efficient radial basis function generated finite difference (RBF-FD) methods for pricing of…
Scientific studies often require the precise calculation of derivatives. In many cases an analytical calculation is not feasible and one resorts to evaluating derivatives numerically. These are error-prone, especially for higher-order…
In this article we derive partial differential equations (PDEs) for pricing interest rate derivatives under the generalized Forward Market Model (FMM) recently presented by A. Lyashenko and F. Mercurio in \cite{lyashenkoMercurio:Mar2019} to…
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…
Developing algorithms for solving high-dimensional partial differential equations (PDEs) has been an exceedingly difficult task for a long time, due to the notoriously difficult problem known as the "curse of dimensionality". This paper…
In this paper, we present a quantum version of some portions of Mathematical Finance, including theory of arbitrage, asset pricing, and optional decomposition in financial markets based on finite dimensional quantum probability spaces. As…