Monte Carlo (MC) simulations are widely used in financial risk management, from estimating value-at-risk (VaR) to pricing over-the-counter derivatives. However, they come at a significant computational cost due to the number of scenarios required for convergence. If a probability distribution is available, Quantum Amplitude Estimation (QAE) algorithms can provide a quadratic speed-up in measuring its properties as compared to their classical counterparts. Recent studies have explored the calculation of common risk measures and the optimisation of QAE algorithms by initialising the input quantum states with pre-computed probability distributions. If such distributions are not available in closed form, however, they need to be generated numerically, and the associated computational cost may limit the quantum advantage. In this paper, we bypass this challenge by incorporating scenario generation – i.e. simulation of the risk factor evolution over time to generate probability distributions – into the quantum computation; we refer to this process as Quantum MC (QMC) simulations. Specifically, we assemble quantum circuits that implement stochastic models for equity (geometric Brownian motion), interest rate (mean-reversion models), and credit (structural, reduced-form, and rating migration credit models) risk factors. We then integrate these models with QAE to provide end-to-end examples for both market and credit risk use cases.

中文翻译：

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用于金融风险分析的量子蒙特卡罗模拟：股权、利率和信用风险因素的场景生成

蒙特卡罗 (MC) 模拟广泛应用于金融风险管理，从估计风险价值 (VaR) 到场外衍生品定价。然而，由于收敛所需的场景数量较多，它们的计算成本很高。如果概率分布可用，则与经典算法相比，量子振幅估计 (QAE) 算法可以在测量其属性时提供二次加速。最近的研究通过使用预先计算的概率分布初始化输入量子态，探索了常见风险度量的计算和 QAE 算法的优化。然而，如果此类分布无法以封闭形式获得，则需要以数字方式生成它们，并且相关的计算成本可能会限制量子优势。在本文中，我们通过将场景生成（即模拟风险因素随时间演变以生成概率分布）纳入量子计算来绕过这一挑战；我们将此过程称为量子 MC (QMC) 模拟。具体来说，我们组装了量子电路，用于实现股权（几何布朗运动）、利率（均值回归模型）和信贷（结构性、简化形式和评级迁移信贷模型）风险因素的随机模型。然后，我们将这些模型与 QAE 集成，为市场和信用风险用例提供端到端示例。