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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…

Numerical Analysis · Mathematics 2023-04-17 Junpeng Hu , Shi Jin , Lei Zhang

In this work we propose a option pricing model based on the Ornstein-Uhlenbeck process. It is a new look at the Black-Scholes formula which is based on the quantum game theory. We show the differences between a classical look which is price…

Quantum Physics · Physics 2009-11-11 Edward W. Piotrowski , Malgorzata Schroeder , Anna Zambrzycka

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 $T$…

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…

Quantum Physics · Physics 2024-06-26 Abhijat Sarma , Thomas W. Watts , Mudassir Moosa , Yilian Liu , Peter L. McMahon

We present a methodology to price options and portfolios of options on a gate-based quantum computer using amplitude estimation, an algorithm which provides a quadratic speedup compared to classical Monte Carlo methods. The options that we…

A derivative is a financial security whose value is a function of underlying traded assets and market outcomes. Pricing a financial derivative involves setting up a market model, finding a martingale (``fair game") probability measure for…

Quantum Physics · Physics 2022-09-20 Patrick Rebentrost , Alessandro Luongo , Samuel Bosch , Seth Lloyd

This study investigates enhancing option pricing by extending the Black-Scholes model to include stochastic volatility and interest rate variability within the Partial Differential Equation (PDE). The PDE is solved using the finite…

Numerical Analysis · Mathematics 2025-04-15 Nikhil Shivakumar Nayak

Quantum computers are not yet up to the task of providing computational advantages for practical stochastic diffusion models commonly used by financial analysts. In this paper we introduce a class of stochastic processes that are both…

Quantum Physics · Physics 2023-11-03 Eric Ghysels , Jack Morgan , Hamed Mohammadbagherpoor

We propose the deep parametric PDE method to solve high-dimensional parametric partial differential equations. A single neural network approximates the solution of a whole family of PDEs after being trained without the need of sample…

Computational Finance · Quantitative Finance 2020-12-14 Kathrin Glau , Linus Wunderlich

We introduce a quantum algorithm to compute the market risk of financial derivatives. Previous work has shown that quantum amplitude estimation can accelerate derivative pricing quadratically in the target error and we extend this to a…

Quantum Physics · Physics 2022-07-27 Nikitas Stamatopoulos , Guglielmo Mazzola , Stefan Woerner , William J. Zeng

We present a quantum algorithm for European option pricing in finance, where the key idea is to work in the unary representation of the asset value. The algorithm needs novel circuitry and is divided in three parts: first, the amplitude…

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.…

Analysis of PDEs · Mathematics 2013-09-18 José Arturo Infante Acevedo , Tony Lelievre

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…

Classical Monte Carlo algorithms can theoretically be sped up on a quantum computer by employing amplitude estimation (AE). To realize this, an efficient implementation of state-dependent functions is crucial. We develop a straightforward…

Quantum Physics · Physics 2024-03-26 Mark-Oliver Wolf , Tom Ewen , Ivica Turkalj

The limitations of the classical Black-Scholes model are examined by comparing calculated and actual historical prices of European call options on stocks from several sectors of the S&P 500. Persistent differences between the two prices…

Pricing of Securities · Quantitative Finance 2022-08-30 Anantya Bhatnagar , Dimitri D. Vvedensky

In this paper we reformulate the problem of pricing options in a quantum setting. Our proposed algorithm involves preparing an initial state, representing the option price, and then evolving it using existing imaginary time simulation…

Quantum Physics · Physics 2021-01-13 Santosh Kumar Radha

We develop quantum algorithms for pricing Asian and barrier options under the Heston model, a popular stochastic volatility model, and estimate their costs, in terms of T-count, T-depth and number of logical qubits, on instances under…

Quantum Physics · Physics 2024-10-23 Guoming Wang , Angus Kan

Option contracts can be valued by using the Black-Scholes equation, a partial differential equation with initial conditions. An exact solution for European style options is known. The computation time and the error need to be minimized…

Computational Engineering, Finance, and Science · Computer Science 2014-02-12 Aishwarya B U , Mohammed Saaqib A , Rajashree H R , Vigasini B

The ongoing progress in quantum technologies has fueled a sustained exploration of their potential applications across various domains. One particularly promising field is quantitative finance, where a central challenge is the pricing of…

Quantum Physics · Physics 2025-10-23 Fernando Alonso , Álvaro Leitao , Carlos Vázquez

Financial derivatives are contracts that can have a complex payoff dependent upon underlying benchmark assets. In this work, we present a quantum algorithm for the Monte Carlo pricing of financial derivatives. We show how the relevant…

Quantum Physics · Physics 2018-08-23 Patrick Rebentrost , Brajesh Gupt , Thomas R. Bromley