Quantum Derivative Pricing for SPDEs via BDSDE Representation

• URL: http://arxiv.org/abs/2606.31076v1
• Date: Tue, 30 Jun 2026 03:06:38 GMT
• Title: Quantum Derivative Pricing for SPDEs via BDSDE Representation
• Abstract summary: 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.
• Score: 3.5509633842633335
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study quantum speedups of derivative pricing for stochastic partial differential equation (SPDE) models through their backward doubly stochastic differential equation (BDSDE) representations. We develop conditional and nested quantum-accelerated multilevel Monte Carlo (QA-MLMC) methods for estimating the resulting conditional and nested expectations, improving the sampling complexity of classical Monte Carlo methods from $\widetilde{O}(ε^{-2})$ to $\widetilde{O}(ε^{-1})$ within additive error $ε$. 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 for Greeks, and Heston-type stochastic-volatility models. To enable efficient multilevel coupling, we construct a family of Forward--Backward Taylor discretization schemes for the stochastic integrals arising in the BDSDE representations and establish global strong-error order one convergence for pricing and Greek estimators. Numerical experiments showcase our schemes for first-order and second-order Greeks can reach the required orders for the full quadratic quantum speedups.

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