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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 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 develop a quantum algorithm to price discretely monitored lookback options in the Black-Scholes framework using imaginary time evolution. By rewriting the pricing PDE as a Schrodinger-type equation, the problem becomes the imaginary time…

Computational Finance · Quantitative Finance 2026-04-02 Florence Paquette , Tania Belabbas , Emmanuel Hamel , Anne MacKay

We study the pricing of derivative securities in financial markets modeled by a sub-mixed fractional Brownian motion with jumps (smfBm-J), a non-Markovian process that captures both long-range dependence and jump discontinuities. Under this…

Pricing of Securities · Quantitative Finance 2025-07-01 Nader Karimi

The accurate valuation of financial derivatives plays a pivotal role in the finance industry. Although closed formulas for pricing are available for certain models and option types, exemplified by the European Call and Put options in the…

Quantum Physics · Physics 2024-04-23 Tom Ewen

Using tools from spectral analysis, singular and regular perturbation theory, we develop a systematic method for analytically computing the approximate price of a derivative-asset. The payoff of the derivative-asset may be path-dependent.…

Computational Finance · Quantitative Finance 2012-04-09 Matthew Lorig

Risk assessment and in particular derivatives pricing is one of the core areas in computational finance and accounts for a sizeable fraction of the global computing resources of the financial industry. We outline a quantum-inspired…

Quantum Physics · Physics 2022-03-08 Michael Kastoryano , Nicola Pancotti

In this paper we provide a quantum Monte Carlo algorithm to solve multidimensional Black-Scholes PDEs with correlation for option pricing. The payoff function of the option is of general form and is only required to be continuous and…

Quantum Physics · Physics 2026-05-05 Jianjun Chen , Yongming Li , Ariel Neufeld

Conventional finite-difference schemes for solving partial differential equations are based on approximating derivatives by finite-differences. In this work, an alternative theory is proposed which view finite-difference schemes as…

Numerical Analysis · Mathematics 2013-09-23 Siu A. Chin

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

Neural networks with sufficiently smooth activation functions can approximate values and derivatives of any smooth function, and they are differentiable themselves. We improve the approximation capability of neural networks by utilizing the…

Computational Engineering, Finance, and Science · Computer Science 2020-07-03 Sang-Mun Chi

Recent progress in the development of efficient computational algorithms to price financial derivatives is summarized. A first algorithm is based on a path integral approach to option pricing, while a second algorithm makes use of a neural…

Statistical Mechanics · Physics 2009-11-07 G. Montagna , M. Morelli , O. Nicrosini , P. Amato , M. Farina

In this article, a numerical scheme is introduced for solving the fractional partial differential equation (FPDE) arising from electromagnetic waves in dielectric media (EMWDM) by using an efficient class of finite difference methods. The…

Numerical Analysis · Mathematics 2022-05-02 Vijay Kumar Patel , Dhirendra Bahuguna

Quantum computing holds significant promise for scientific computing due to its potential for polynomial to even exponential speedups over classical methods, which are often hindered by the curse of dimensionality. While neural networks…

Quantum Physics · Physics 2025-10-10 Junpeng Hu , Shi Jin , Nana Liu , Lei Zhang

We introduce an efficient variational hybrid quantum-classical algorithm designed for solving Caputo time-fractional partial differential equations. Our method employs an iterable cost function incorporating a linear combination of overlap…

Inspired by recent progress in quantum algorithms for ordinary and partial differential equations, we study quantum algorithms for stochastic differential equations (SDEs). Firstly we provide a quantum algorithm that gives a quadratic…

Quantum Physics · Physics 2021-06-30 Dong An , Noah Linden , Jin-Peng Liu , Ashley Montanaro , Changpeng Shao , Jiasu Wang

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 formulate quantum computing solutions to a large class of dynamic nonlinear asset pricing models using algorithms, in theory exponentially more efficient than classical ones, which leverage the quantum properties of superposition and…

Pricing of Securities · Quantitative Finance 2025-08-26 Eric Ghysels , Jack Morgan

The solution of option-pricing problems may turn out to be computationally demanding due to non-linear and path-dependent payoffs, the high dimensionality arising from multiple underlying assets, and sophisticated models of price dynamics.…

Quantum Physics · Physics 2025-11-10 Nikita Guseynov , Mikel Sanz , Ángel Rodríguez-Rozas , Nana Liu , Javier Gonzalez-Conde

Partial differential equations frequently appear in the natural sciences and related disciplines. Solving them is often challenging, particularly in high dimensions, due to the "curse of dimensionality". In this work, we explore the…

Quantum Physics · Physics 2023-05-30 Lukas Mouton , Florentin Reiter , Ying Chen , Patrick Rebentrost