{ "cells": [ { "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ "# 信贷风险分析\n", "\n", "*Copyright (c) 2023 Institute for Quantum Computing, Baidu Inc. All Rights Reserved.*" ] }, { "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ "风险分析的任务是评估给定资产在面临金融系统波动时的风险，即在险价值 Value at Risk（VaR）。该价值可以衡量在金融系统下给定资产的潜在损失。决定资产在险价值的因素有很多，包括金融机构对于风险的不同偏好、金融系统的波动特征和资产本身的含风险性质。2014 年 Rutkowski 与 Tarca [1] 给出了一个计算风险资本的数学模型。该模型认为整体金融系统的波动应该遵循高斯布朗运动，从而能够计算出较高可信度下处于该系统中资产损失上界的最小值。" ] }, { "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ "当应用于信贷风险分析问题时，该模型可以用于评估银行的信贷风险监管资本，即银行所持有信贷资产组合在当前金融系统下的在险价值。在该模型中，我们记给定的信贷资产组合为 $\\{ 0, ..., K-1 \\}$, 且决定资产组合总损失的随机变量为\n", "$$\n", "\\mathcal{L} = \\sum_{k=0}^{K - 1} \\lambda_k X_k(Z)\n", "。$$\n", "这里，$\\lambda_k$ 为第 $k$ 个信贷资产的违约损失（loss given default）；$Z$ 为描述金融系统波动过程的潜在随机变量（latent random variable），且其概率分布默认为标准正态分布；$X_k(Z)$ 为描述金融系统下资产违约过程的伯努利随机变量。具体地，当 $Z = z$ 时，随机变量 $X_k(Z)$ 的参数 $p_k(z)$，即第 $k$ 个资产的违约概率，取决于该资产对于系统风险的敏感度（sensitivity）$\\rho_k \\in [0, 1]$ 以及无系统风险下该资产的基础违约概率（base default probability）$p_k^{(0)} \\in [0, 1]$。在标定置信度（confidence level）之后，信贷资产组合的在险价值应定义为『于置信度 $\\alpha$ 下，信贷资产损失上界的最小值』，即\n", "$$\n", "\\textrm{VaR}_\\alpha(\\mathcal{L}) := \\inf \\{ x \\,|\\, \\textrm{Pr}(\\mathcal{L} \\leq x) \\geq \\alpha \\}\n", "。$$\n", "例如，若银行持有的一组信贷资产在置信度 $99\\%$ 下的在险价值正好为 $100$ 万，那么当该资产组合出现违约情况时，由于违约而造成的资产损失超过 $100$ 万的概率不高于 $1\\%$。在经典计算中，信贷风险分析问题中的在险价值可以通过经典蒙特卡罗（classical Monte Carlo）方法和二分搜索（bisection search）方法估算：\n", "1. 根据资产组合性质，选定初始 VaR 猜测值 $\\check{x}$。\n", "2. 使用经典蒙特卡罗算法估算概率值 $p_{\\check{x}} = \\textrm{Pr}(\\mathcal{L} \\leq \\check{x})$。\n", "3. 将概率值 $p_{\\check{x}}$ 与 $\\alpha$ 比较，并根据比较结果和二分搜索方法更新猜测值 $\\check{x}$。\n", "4. 若更新值达到收敛标准，输出 $\\check{x} = \\textrm{VaR}_\\alpha(\\mathcal{L})$；否则返回第 $2$ 步。" ] }, { "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ "## 量子解决方案\n", "\n", "不同于经典算法，量子计算可以使用量子振幅估计（quantum amplitude estimation）算法替换上述第 2 步中使用的经典蒙特卡罗算法，来提高概率值 $p_{\\check{x}}$ 的估算效率。通过量子叠加和纠缠的特性，量子方案与经典方案相比有望在采样次数上获取平方加速的优势 [2]。接下来我们展示如何使用量桨来模拟该量子方案，从而完成信贷风险分析的在险价值计算问题。" ] }, { "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ "### 在线演示" ] }, { "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ "我们已经给出了一个设置好的参数，可以直接用于风险资产组合的在险价值计算。只需要在 `config.toml` 这个配置文件中进行对应的配置，然后输入命令 \n", "`python credit_risk.py --config config.toml`\n", "即可对配置好的资产组合进行在险价值计算。\n", "\n", "这里，我们给出一个在线演示的版本，可以在线进行测试。首先定义配置文件的内容：" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "cra_toml = r\"\"\"\n", "# 用于信贷风险分析模型的整体配置文件。\n", "# 资产数量。\n", "num_assets = 4\n", "# 基础违约概率。\n", "base_default_prob = [0.15, 0.25, 0.39, 0.58]\n", "# 敏感度。\n", "sensitivity = [0.37, 0.21, 0.32, 0.02]\n", "# 违约损失。\n", "lgd = [5, 1, 3, 4]\n", "# 置信度。\n", "confidence_level = 0.99\n", "# 估计精度系数。系数越高，则估计的结果越精确。\n", "degree_of_simulation = 4\n", "\"\"\"" ] }, { "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ "量桨的金融模块实现了量子解决方案的数值模拟。我们可以从 ``paddle_quantum.finance`` 模块里导入 ``CreditRiskAnalyzer`` 来解决配置好的在险价值计算问题。" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "-----------------------------------------------------------------------------------\n", "Begin bisection search for VaR with confidence level >= 99.0%.\n", "-----------------------------------------------------------------------------------\n", "Lower guess: level Middle guess: level Upper guess: level \n", " -1 : 0.000 6 : 0.691 13 : 1.000 \n", " 6 : 0.691 9 : 0.941 13 : 1.000 \n", " 9 : 0.941 11 : 0.962 13 : 1.000 \n", " 11 : 0.962 12 : 0.990 13 : 1.000 \n", "-----------------------------------------------------------------------------------\n", "Estimated VaR is 12 with confidence level 99.0%.\n", "-----------------------------------------------------------------------------------\n", "该资产组合的在险价值大约为 12\n" ] } ], "source": [ "import os\n", "import warnings\n", "warnings.filterwarnings(\"ignore\")\n", "os.environ['PROTOCOL_BUFFERS_PYTHON_IMPLEMENTATION'] = 'python'\n", "\n", "import toml\n", "from paddle_quantum.finance import CreditRiskAnalyzer\n", "\n", "config = toml.loads(cra_toml)\n", "num_assets = config[\"num_assets\"]\n", "base_default_prob = config[\"base_default_prob\"]\n", "sensitivity = config[\"sensitivity\"]\n", "lgd = config[\"lgd\"]\n", "confidence_level = config[\"confidence_level\"]\n", "degree_of_simulation = config[\"degree_of_simulation\"]\n", "\n", "estimator = CreditRiskAnalyzer(num_assets, base_default_prob, sensitivity, lgd, confidence_level, degree_of_simulation)\n", "print(\"该资产组合的在险价值大约为\", estimator.estimate_var())" ] }, { "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ "___\n", "\n", "# 注意事项\n", "\n", "这里提供的模型只用于特定模型的信贷风险分析问题。\n", "\n", "# 引用信息\n", "\n", "```\n", "@article{rutkowski2015regulatory,\n", " title={Regulatory capital modeling for credit risk},\n", " author={Rutkowski, Marek and Tarca, Silvio},\n", " journal={International Journal of Theoretical and Applied Finance},\n", " volume={18},\n", " number={05},\n", " pages={1550034},\n", " year={2015},\n", " publisher={World Scientific}\n", "}\n", "\n", "@article{egger2020credit,\n", " title={Credit risk analysis using quantum computers},\n", " author={Egger, Daniel J and Guti{\\'e}rrez, Ricardo Garc{\\'\\i}a and Mestre, Jordi Cahu{\\'e} and Woerner, Stefan},\n", " journal={IEEE Transactions on Computers},\n", " volume={70},\n", " number={12},\n", " pages={2136--2145},\n", " year={2020},\n", " publisher={IEEE}\n", "}\n", "```\n", "\n", "# 参考文献\n", "\n", "[1] Rutkowski, Marek, and Silvio Tarca. \"Regulatory capital modeling for credit risk.\" International Journal of Theoretical and Applied Finance 18.05 (2015): 1550034.\n", "\n", "[2] Egger, Daniel J., et al. \"Credit risk analysis using quantum computers.\" IEEE Transactions on Computers 70.12 (2020): 2136-2145." ] } ], "metadata": { "kernelspec": { "display_name": "pq", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, 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