Quantum Counterparty Credit Risk: A Study of Path-Dependent Derivatives

2026-06-26

AI Summary

This study addresses the high computational complexity of nested Monte Carlo simulations in estimating potential future exposure (PFE) for path-dependent derivatives—such as FX TARFs—under counterparty credit risk. The authors propose a hybrid quantum-classical two-step approach: first computing quantiles classically, then conditioning a quantum circuit on these quantiles to evaluate risk exposure. This work presents the first application of Iterative Quantum Amplitude Estimation (IQAE) to PFE modeling for path-dependent derivatives, incorporating discretization of the FX process and a linear additive approximation of the payoff function to construct a reduced-order model deployable on current quantum hardware. At 97.5% and 99% confidence levels, the method achieves relative errors of 1%–8%. Estimates suggest that only approximately 300 logical qubits are required to compute the full-year PFE across 52 weeks, substantially reducing the sampling complexity associated with tail-risk estimation.

Abstract

Estimating potential future exposure (PFE) for path-dependent derivatives, such as FX Target Redemption Forwards (TARFs), represents a formidable computational challenge due to the demand of nested Monte Carlo simulations. We present a hybrid quantum-classical framework that leverages Iterative Quantum Amplitude Estimation (IQAE) to address this via a reduced-order counterparty credit risk model. Our methodology maps the non-linear TARF payoff -- including cumulative gains and knock-out features -- into a quantum circuit via a two-step formulation, whereby a first-step percentile is computed classically and then used to condition quantum evaluation of subsequent exposure. We employ discretisation of the FX process and a linearised additive approximation of dynamics to enable implementation on current quantum platforms. Developed via the Classiq platform and validated on NVIDIA CUDA-Q and Amazon Braket SV1, our approach achieves relative errors of 1%-8% against classical benchmarks at the 97.5% and 99% confidence levels. While discretisation constraints and approximate monotonicity assumption may introduce bias and limit recovery of the full exposure distribution, our framework offers a tractable testbed for quantum acceleration. Scaling analysis suggests that $\sim$300 logical qubits could enable full 52-week exposure estimation, reducing sample complexity for tail-risk estimation via amplitude estimation at the cost of increased circuit depth.

Problem

• Potential Future Exposure
• Path-Dependent Derivatives
• Counterparty Credit Risk
• Monte Carlo Simulation
• Quantum Computing

Innovation

• Quantum Amplitude Estimation
• Path-Dependent Derivatives
• Counterparty Credit Risk
• Hybrid Quantum-Classical Algorithm
• Potential Future Exposure