End-to-End PDE-Based Quantum Algorithms for Multi-Asset Option Pricing under Local and Stochastic Volatility

• URL: http://arxiv.org/abs/2605.26610v1
• Date: Tue, 26 May 2026 06:46:40 GMT
• Title: End-to-End PDE-Based Quantum Algorithms for Multi-Asset Option Pricing under Local and Stochastic Volatility
• Abstract summary: We develop an end-to-end quantum PDE framework for European option pricing under local-volatility Black-Scholes and Heston models.<n>The framework takes classical contract and model data as input and returns classical estimates of selected option values.
• Score: 1.8139328267731682
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Multi-asset option pricing under local- and stochastic-volatility models leads naturally to high-dimensional parabolic PDEs. We develop an end-to-end quantum PDE framework for European option pricing under local-volatility Black--Scholes and Heston models. The framework takes classical contract and model data as input and returns classical estimates of selected option values. We solve the pricing PDEs after finite-difference discretization on spatial grids. For $N=2^n$ grid points per spatial direction and $d$ assets, the end-to-end gate complexity for single-point recovery, counted in elementary CNOT gates and one-qubit Pauli-axis rotations, has leading grid-size dependence $\widetilde{O}(d^2 N^{2+d/2})$ for local-volatility Black--Scholes and $\widetilde{O}(d^2 N^{d+2})$ for Heston. Relative to grid-based finite-difference baselines, these scalings correspond to polynomial improvement factors $N^{d/2}$ and $N^d$, respectively. These estimates translate to Clifford+T resources via standard compilation. We complement the complexity analysis with numerical benchmarks against standard classical methods. In the Heston setting, the framework recovers option prices across strikes together with the associated implied-volatility smile/skew. Overall, this work provides a complete end-to-end quantum pricing pipeline with explicit resource accounting and theoretical performance guarantees.

Related papers

• Potential Matching Optimal Transport: Continuous Normalizing Flows for Exact $p$-Wasserstein Dynamics [7.533486962572339]
  Potential Matching Optimal Transport (PMOT) is a potential-flow framework for general $p$-cost optimal transport.<n>It trains the potential gradient with a self-induced matching loss along straight bridges determined by the model's own endpoints.<n>On synthetic benchmarks, PMOT learns $p$-specific maps that agree with the corresponding $p$-matched OT references.
  arXiv  Detail & Related papers  (2026-08-06T07:04:30Z)
• Quantum Speedups for Stochastic Optimization with Heavy-Tailed Noise [49.730496294398726]
  We develop a novel quantum mean estimator for heavy-tailed random variables.<n>We derive stronger lower bounds for tail index>4/3$, showing that a nontrivial dependence on a dimension is unavoidable.<n>For a convex objective function, we propose a quantum projected gradient descent method.
  arXiv  Detail & Related papers  (2026-07-28T09:29:37Z)
• Exponential Reduction of Mesh Dependence in Quantum Estimation of Parabolic PDE Observables [3.3636842548621275]
  We develop a quantum PDE algorithm that estimates linear and quadratic observables and places fine-coarse cancellation inside the circuit before measurement.<n>We also give a non-Fourier realization based on energyorthogonal dyadic midpoint details in one dimension.
  arXiv  Detail & Related papers  (2026-07-20T16:09:24Z)
• Quantum Derivative Pricing for SPDEs via BDSDE Representation [3.5509633842633335]
  We study quantum speedups of derivative pricing for partial differential equation (SPDE) models through their backward doubly differential equation (BDSDE) representations.<n>We develop conditional and nested quantum-accelerated multilevel Monte Carlo (QA-MLMC) methods for estimating the resulting conditional and nested expectations.<n>We apply the framework to derivative pricing and sensitivity analysis, providing quantum-accelerated estimators for prices as well as first-order and second-order Greeks, likelihood-ratio and Malliavin-weight representations.
  arXiv  Detail & Related papers  (2026-06-30T03:06:38Z)
• How Neural Reward Models Learn Features for Policy Optimization: A Single-Index Analysis [53.063298916923976]
  We study the feedback in a Gaussian single-index model with $r*(x) = *(langle *, xrangle)$ and $x sim N(0, I_d)$.<n>We analyze a two-stage neural reward model that first learns the hidden direction $*$ from reward-weighted samples and then fits the readout layer by weighted ridge regression.
  arXiv  Detail & Related papers  (2026-05-23T22:00:38Z)
• Intrinsic Wasserstein Rates for Score-Based Generative Models on Smooth Manifolds [61.14405512940818]
  We show that Score-based generative models are trained in high-dimensional ambient spaces.<n>We use a ReLU implementation of nearest-projection coordinates via finite intrinsic anchors and Gauss Newton.
  arXiv  Detail & Related papers  (2026-05-15T10:20:05Z)
• Phase Transition for Stochastic Block Model with more than $\sqrt{n}$ Communities (II) [51.320599504997745]
  We show that when the number $K$ of communities remains smaller than $sqrtn$, non-trivial community recovery is possible in time above the Kesten--Stigum threshold.<n>We also show that, in moderately sparse settings, the optimal algorithms appear to be fundamentally different from spectral methods.
  arXiv  Detail & Related papers  (2025-11-26T15:54:17Z)
• A Quantum Algorithm for the Finite Element Method [0.0]
  finite element method (FEM) is a cornerstone numerical technique for solving partial differential equations (PDEs)<n>We present $textbfQu-FEM$, a fault-tolerant era quantum algorithm for the finite element method.
  arXiv  Detail & Related papers  (2025-10-20T23:00:12Z)
• Quantum Framework for Simulating Linear PDEs with Robin Boundary Conditions [0.6144680854063939]
  We propose an explicit, oracle-free quantum framework for numerically simulating general linear partial differential equations (PDEs)<n>Our approach begins with a general finite-difference discretization and applies the Schrodingerisation technique to transform the resulting system into one that admits unitary quantum evolution.
  arXiv  Detail & Related papers  (2025-06-25T14:23:38Z)
• Learning with Norm Constrained, Over-parameterized, Two-layer Neural Networks [54.177130905659155]
  Recent studies show that a reproducing kernel Hilbert space (RKHS) is not a suitable space to model functions by neural networks. In this paper, we study a suitable function space for over- parameterized two-layer neural networks with bounded norms.
  arXiv  Detail & Related papers  (2024-04-29T15:04:07Z)
• Sample-efficient Learning of Infinite-horizon Average-reward MDPs with General Function Approximation [53.17668583030862]
  We study infinite-horizon average-reward Markov decision processes (AMDPs) in the context of general function approximation. We propose a novel algorithmic framework named Local-fitted Optimization with OPtimism (LOOP) We show that LOOP achieves a sublinear $tildemathcalO(mathrmpoly(d, mathrmsp(V*)) sqrtTbeta )$ regret, where $d$ and $beta$ correspond to AGEC and log-covering number of the hypothesis class respectively
  arXiv  Detail & Related papers  (2024-04-19T06:24:22Z)
• Quantum option pricing via the Karhunen-Lo\`{e}ve expansion [11.698830761241107]
  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 $T$ and in $1/epsilon$, where $epsilon$ is the additive approximation error.
  arXiv  Detail & Related papers  (2024-02-15T17:37:23Z)
• Gradient-Free Methods for Deterministic and Stochastic Nonsmooth Nonconvex Optimization [94.19177623349947]
  Non-smooth non optimization problems emerge in machine learning and business making. Two core challenges impede the development of efficient methods with finitetime convergence guarantee. Two-phase versions of GFM and SGFM are also proposed and proven to achieve improved large-deviation results.
  arXiv  Detail & Related papers  (2022-09-12T06:53:24Z)
• Fermionic partial tomography via classical shadows [0.0]
  We propose a tomographic protocol for estimating any $ k $-body reduced density matrix ($ k $-RDM) of an $ n $-mode fermionic state. Our approach extends the framework of classical shadows, a randomized approach to learning a collection of quantum-state properties, to the fermionic setting.
  arXiv  Detail & Related papers  (2020-10-30T06:28:26Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.