用于金融风险分析的量子蒙特卡洛模拟：股票、利率和信用风险因子的情景生成
Quantum Monte Carlo simulations for financial risk analytics: scenario generation for equity, rate, and credit risk factors
AI总结：
本文将风险因子情景生成直接纳入量子计算，构建股票、利率和信用风险的量子电路随机模型，并与QAE集成，为市场和信用风险提供端到端的量子蒙特卡洛模拟方案。
摘要：
蒙特卡洛（MC）模拟在金融风险管理中被广泛使用，从估计在险价值（VaR）到为场外衍生品定价。然而，由于收敛所需的场景数量巨大，它们带来了显著的计算成本。如果可以获得概率分布，量子振幅估计（QAE）算法与经典对应方法相比，在测量其性质方面可以提供二次加速。最近的研究探索了常见风险度量的计算以及通过用预先计算好的概率分布初始化输入量子态来优化QAE算法。然而，如果此类分布无法以闭合形式获得，则需要通过数值方法生成，而相关的计算成本可能会限制量子优势。在本文中，我们通过将情景生成——即模拟风险因子随时间的演化以生成概率分布——纳入量子计算来绕过这一挑战；我们将这一过程称为量子MC（QMC）模拟。具体而言，我们组装了实现股票（几何布朗运动）、利率（均值回归模型）和信用（结构化模型、简化模型和评级迁移信用模型）风险因子随机模型的量子电路。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的示例。
英文摘要：
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.
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