Ngày 5: Stress Testing và Scenario Analysis

🎯 Mục tiêu học tập

  • Hiểu sâu về stress testing và scenario analysis trong credit risk
  • Phân tích hạn chế của classical stress testing methods
  • Implement quantum-enhanced stress testing frameworks
  • So sánh performance giữa classical và quantum approaches

📚 Lý thuyết

Stress Testing Fundamentals

1. Stress Testing là gì?

Stress testing là quá trình đánh giá khả năng chịu đựng của tổ chức tài chính trước các tình huống bất lợi, bao gồm:

  • Scenario Analysis: Phân tích tác động của các kịch bản cụ thể
  • Sensitivity Analysis: Phân tích độ nhạy với thay đổi tham số
  • Reverse Stress Testing: Xác định kịch bản dẫn đến thất bại
  • Forward-Looking: Dự báo rủi ro trong tương lai

2. Regulatory Requirements:

  • Basel III: Capital adequacy requirements
  • CCAR: Comprehensive Capital Analysis and Review
  • EBA: European Banking Authority stress tests
  • PRA: Prudential Regulation Authority requirements

Classical Stress Testing Methods

1. Historical Scenarios:

Scenario Impact = Historical Data × Stress Multipliers

Examples:

  • 2008 Financial Crisis
  • 2000 Dot-com Bubble
  • 1997 Asian Financial Crisis

2. Hypothetical Scenarios:

  • Macroeconomic Shocks: GDP decline, unemployment spike
  • Market Shocks: Interest rate changes, equity market crash
  • Credit Shocks: Default rate increases, rating downgrades
  • Liquidity Shocks: Funding stress, market illiquidity

3. Sensitivity Analysis:

ΔPortfolio Value = Σ (ΔFactorᵢ × Sensitivityᵢ)

4. Monte Carlo Stress Testing:

  • Generate thousands of scenarios
  • Simulate portfolio performance
  • Calculate risk measures under stress

Hạn chế của Classical Methods

1. Scenario Design:

  • Limited Scenarios: Cannot test all possible combinations
  • Expert Judgment: Subjective scenario selection
  • Historical Bias: Based on past events
  • Static Assumptions: Fixed parameters

2. Computational Limitations:

  • Monte Carlo Complexity: Exponential với scenario count
  • Real-time Constraints: Cannot run stress tests in real-time
  • Large Portfolios: Computational bottlenecks
  • Multiple Time Horizons: Complex multi-period analysis

3. Model Limitations:

  • Linear Assumptions: Cannot capture non-linear effects
  • Correlation Breakdown: Assumptions fail under stress
  • Parameter Uncertainty: Model calibration issues
  • Regime Changes: Models not designed for extreme events

Quantum Advantages cho Stress Testing

1. Quantum Scenario Generation:

  • Superposition: Parallel processing of multiple scenarios
  • Quantum Randomness: True random scenario generation
  • Entanglement: Natural modeling of scenario correlations

2. Quantum Optimization:

  • Scenario Selection: Optimal scenario combination
  • Risk Minimization: Find worst-case scenarios
  • Capital Optimization: Optimal capital allocation under stress

3. Quantum Machine Learning:

  • Pattern Recognition: Identify stress patterns
  • Anomaly Detection: Detect unusual stress scenarios
  • Predictive Modeling: Forecast stress impacts

💻 Thực hành

Project 5: Quantum Stress Testing Framework

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import seaborn as sns
from scipy.stats import norm, multivariate_normal
from scipy.optimize import minimize
from qiskit import QuantumCircuit, Aer, execute
from qiskit.algorithms import VQE, QAOA
from qiskit.algorithms.optimizers import SPSA
from qiskit.circuit.library import TwoLocal
import pennylane as qml

class ClassicalStressTesting:
    """Classical stress testing framework"""
    
    def __init__(self):
        self.portfolio = None
        self.scenarios = {}
        
    def create_portfolio(self, n_assets=10):
        """
        Create synthetic credit portfolio
        """
        np.random.seed(42)
        
        portfolio_data = []
        for i in range(n_assets):
            asset = {
                'asset_id': f'Asset_{i}',
                'exposure': np.random.uniform(100000, 1000000),
                'pd': np.random.uniform(0.01, 0.10),
                'lgd': np.random.uniform(0.3, 0.7),
                'rating': np.random.choice(['AAA', 'AA', 'A', 'BBB', 'BB', 'B']),
                'sector': np.random.choice(['Banking', 'Technology', 'Energy', 'Healthcare', 'Consumer'])
            }
            portfolio_data.append(asset)
        
        self.portfolio = pd.DataFrame(portfolio_data)
        return self.portfolio
    
    def define_stress_scenarios(self):
        """
        Define stress testing scenarios
        """
        self.scenarios = {
            'baseline': {
                'description': 'Baseline scenario',
                'pd_multiplier': 1.0,
                'lgd_multiplier': 1.0,
                'correlation_multiplier': 1.0,
                'probability': 0.5
            },
            'mild_recession': {
                'description': 'Mild economic recession',
                'pd_multiplier': 1.5,
                'lgd_multiplier': 1.1,
                'correlation_multiplier': 1.2,
                'probability': 0.3
            },
            'severe_recession': {
                'description': 'Severe economic recession',
                'pd_multiplier': 2.5,
                'lgd_multiplier': 1.3,
                'correlation_multiplier': 1.5,
                'probability': 0.15
            },
            'financial_crisis': {
                'description': 'Financial crisis scenario',
                'pd_multiplier': 4.0,
                'lgd_multiplier': 1.5,
                'correlation_multiplier': 2.0,
                'probability': 0.05
            }
        }
        
        return self.scenarios
    
    def apply_stress_scenario(self, scenario_name):
        """
        Apply stress scenario to portfolio
        """
        if scenario_name not in self.scenarios:
            raise ValueError(f"Scenario {scenario_name} không tồn tại")
        
        scenario = self.scenarios[scenario_name]
        stressed_portfolio = self.portfolio.copy()
        
        # Apply stress multipliers
        stressed_portfolio['pd'] = self.portfolio['pd'] * scenario['pd_multiplier']
        stressed_portfolio['lgd'] = self.portfolio['lgd'] * scenario['lgd_multiplier']
        
        return stressed_portfolio, scenario
    
    def calculate_stress_impact(self, stressed_portfolio):
        """
        Calculate stress impact on portfolio
        """
        # Calculate expected loss
        expected_loss = np.sum(stressed_portfolio['exposure'] * 
                              stressed_portfolio['pd'] * 
                              stressed_portfolio['lgd'])
        
        # Calculate unexpected loss (simplified)
        unexpected_loss = np.sqrt(np.sum((stressed_portfolio['exposure'] * 
                                         stressed_portfolio['pd'] * 
                                         stressed_portfolio['lgd'])**2))
        
        # Calculate VaR (simplified)
        var_95 = expected_loss + 1.645 * unexpected_loss
        var_99 = expected_loss + 2.326 * unexpected_loss
        
        return {
            'expected_loss': expected_loss,
            'unexpected_loss': unexpected_loss,
            'var_95': var_95,
            'var_99': var_99
        }
    
    def monte_carlo_stress_testing(self, n_simulations=10000):
        """
        Monte Carlo stress testing
        """
        scenario_results = {}
        
        for scenario_name in self.scenarios.keys():
            print(f"Running stress test for {scenario_name}...")
            
            stressed_portfolio, scenario = self.apply_stress_scenario(scenario_name)
            
            # Monte Carlo simulation
            losses = []
            for sim in range(n_simulations):
                # Generate random defaults
                defaults = np.random.binomial(1, stressed_portfolio['pd'].values)
                loss = np.sum(defaults * stressed_portfolio['exposure'].values * 
                             stressed_portfolio['lgd'].values)
                losses.append(loss)
            
            losses = np.array(losses)
            
            # Calculate risk measures
            risk_measures = {
                'expected_loss': np.mean(losses),
                'unexpected_loss': np.std(losses),
                'var_95': np.percentile(losses, 95),
                'var_99': np.percentile(losses, 99),
                'max_loss': np.max(losses)
            }
            
            scenario_results[scenario_name] = {
                'risk_measures': risk_measures,
                'scenario': scenario,
                'losses': losses
            }
        
        return scenario_results

class QuantumStressTesting:
    """Quantum-enhanced stress testing framework"""
    
    def __init__(self, num_qubits=8):
        self.num_qubits = num_qubits
        self.backend = Aer.get_backend('qasm_simulator')
        self.portfolio = None
        self.scenarios = {}
        
    def create_quantum_stress_circuit(self, portfolio, scenario):
        """
        Create quantum circuit for stress testing
        """
        n_assets = len(portfolio)
        circuit = QuantumCircuit(self.num_qubits, self.num_qubits)
        
        # Encode portfolio information
        for i, (_, asset) in enumerate(portfolio.iterrows()):
            if i < self.num_qubits:
                # Encode exposure
                exposure_norm = min(asset['exposure'] / 1000000, 1.0)
                circuit.rx(exposure_norm * np.pi, i)
                
                # Encode stressed PD
                stressed_pd = asset['pd'] * scenario['pd_multiplier']
                circuit.ry(stressed_pd * np.pi, i)
                
                # Encode stressed LGD
                stressed_lgd = asset['lgd'] * scenario['lgd_multiplier']
                circuit.rz(stressed_lgd * np.pi, i)
        
        # Add stress-specific entanglement
        stress_level = scenario['correlation_multiplier']
        for i in range(self.num_qubits - 1):
            circuit.cx(i, i + 1)
            # Add additional entanglement based on stress level
            if stress_level > 1.5:
                circuit.cx(i, (i + 2) % self.num_qubits)
        
        return circuit
    
    def quantum_stress_simulation(self, portfolio, scenarios, n_simulations=1000):
        """
        Quantum stress simulation
        """
        scenario_results = {}
        
        for scenario_name, scenario in scenarios.items():
            print(f"Running quantum stress test for {scenario_name}...")
            
            # Create quantum circuit
            circuit = self.create_quantum_stress_circuit(portfolio, scenario)
            circuit.measure_all()
            
            # Run quantum simulation
            losses = []
            for sim in range(n_simulations):
                # Execute circuit
                job = execute(circuit, self.backend, shots=1)
                result = job.result()
                counts = result.get_counts()
                
                # Calculate loss from measurement
                loss = self._calculate_loss_from_measurement(counts, portfolio, scenario)
                losses.append(loss)
            
            losses = np.array(losses)
            
            # Calculate risk measures
            risk_measures = {
                'expected_loss': np.mean(losses),
                'unexpected_loss': np.std(losses),
                'var_95': np.percentile(losses, 95),
                'var_99': np.percentile(losses, 99),
                'max_loss': np.max(losses)
            }
            
            scenario_results[scenario_name] = {
                'risk_measures': risk_measures,
                'scenario': scenario,
                'losses': losses
            }
        
        return scenario_results
    
    def _calculate_loss_from_measurement(self, counts, portfolio, scenario):
        """
        Calculate portfolio loss from quantum measurement
        """
        state = list(counts.keys())[0]
        
        loss = 0
        for i, bit in enumerate(state):
            if i < len(portfolio):
                if bit == '1':  # Default occurred
                    asset = portfolio.iloc[i]
                    stressed_pd = asset['pd'] * scenario['pd_multiplier']
                    stressed_lgd = asset['lgd'] * scenario['lgd_multiplier']
                    loss += asset['exposure'] * stressed_lgd
        
        return loss
    
    def quantum_scenario_optimization(self, portfolio, scenarios):
        """
        Quantum optimization for scenario selection
        """
        # Use QAOA to find worst-case scenario combination
        n_scenarios = len(scenarios)
        
        # Create cost function for scenario optimization
        def cost_function(scenario_weights):
            # Calculate weighted stress impact
            total_impact = 0
            for i, (scenario_name, scenario) in enumerate(scenarios.items()):
                stressed_portfolio, _ = self.apply_stress_scenario(scenario_name)
                impact = self.calculate_stress_impact(stressed_portfolio)
                total_impact += scenario_weights[i] * impact['var_99']
            
            return total_impact
        
        # Optimize scenario weights
        initial_weights = np.ones(n_scenarios) / n_scenarios
        
        result = minimize(
            cost_function,
            initial_weights,
            method='SLSQP',
            constraints={'type': 'eq', 'fun': lambda x: np.sum(x) - 1},
            bounds=[(0, 1)] * n_scenarios
        )
        
        return result.x, result.fun

def compare_stress_testing_approaches():
    """
    Compare classical and quantum stress testing approaches
    """
    # Create portfolio
    classical_stress = ClassicalStressTesting()
    portfolio = classical_stress.create_portfolio(n_assets=8)
    scenarios = classical_stress.define_stress_scenarios()
    
    print("Portfolio Overview:")
    print(portfolio[['asset_id', 'exposure', 'pd', 'lgd', 'sector']])
    
    print("\nStress Scenarios:")
    for name, scenario in scenarios.items():
        print(f"{name}: {scenario['description']}")
    
    # Classical stress testing
    print("\n=== Classical Stress Testing ===")
    classical_results = classical_stress.monte_carlo_stress_testing(n_simulations=5000)
    
    # Quantum stress testing
    print("\n=== Quantum Stress Testing ===")
    quantum_stress = QuantumStressTesting(num_qubits=8)
    quantum_results = quantum_stress.quantum_stress_simulation(portfolio, scenarios, n_simulations=500)
    
    # Compare results
    print("\n=== Stress Testing Results Comparison ===")
    comparison_data = []
    
    for scenario_name in scenarios.keys():
        classical_measures = classical_results[scenario_name]['risk_measures']
        quantum_measures = quantum_results[scenario_name]['risk_measures']
        
        print(f"\n{scenario_name.upper()}:")
        print(f"Classical VaR (99%): ${classical_measures['var_99']:,.2f}")
        print(f"Quantum VaR (99%): ${quantum_measures['var_99']:,.2f}")
        
        diff_pct = abs(classical_measures['var_99'] - quantum_measures['var_99']) / classical_measures['var_99'] * 100
        print(f"Difference: {diff_pct:.2f}%")
        
        comparison_data.append({
            'scenario': scenario_name,
            'classical_var': classical_measures['var_99'],
            'quantum_var': quantum_measures['var_99'],
            'difference_pct': diff_pct
        })
    
    # Plot comparison
    plot_stress_testing_comparison(comparison_data, classical_results, quantum_results)
    
    return classical_results, quantum_results

def plot_stress_testing_comparison(comparison_data, classical_results, quantum_results):
    """
    Plot stress testing comparison results
    """
    fig, axes = plt.subplots(2, 2, figsize=(15, 12))
    
    # Plot 1: VaR comparison
    scenarios = [d['scenario'] for d in comparison_data]
    classical_vars = [d['classical_var'] for d in comparison_data]
    quantum_vars = [d['quantum_var'] for d in comparison_data]
    
    x = np.arange(len(scenarios))
    width = 0.35
    
    axes[0, 0].bar(x - width/2, classical_vars, width, label='Classical', alpha=0.7)
    axes[0, 0].bar(x + width/2, quantum_vars, width, label='Quantum', alpha=0.7)
    axes[0, 0].set_xlabel('Stress Scenarios')
    axes[0, 0].set_ylabel('VaR (99%)')
    axes[0, 0].set_title('VaR Comparison: Classical vs Quantum')
    axes[0, 0].set_xticks(x)
    axes[0, 0].set_xticklabels(scenarios, rotation=45)
    axes[0, 0].legend()
    axes[0, 0].grid(True)
    
    # Plot 2: Loss distributions for financial crisis
    crisis_scenario = 'financial_crisis'
    classical_losses = classical_results[crisis_scenario]['losses']
    quantum_losses = quantum_results[crisis_scenario]['losses']
    
    axes[0, 1].hist(classical_losses, bins=50, alpha=0.7, label='Classical', density=True)
    axes[0, 1].hist(quantum_losses, bins=50, alpha=0.7, label='Quantum', density=True)
    axes[0, 1].set_xlabel('Portfolio Loss')
    axes[0, 1].set_ylabel('Density')
    axes[0, 1].set_title(f'Loss Distribution: {crisis_scenario}')
    axes[0, 1].legend()
    axes[0, 1].grid(True)
    
    # Plot 3: Stress impact progression
    stress_levels = []
    classical_impacts = []
    quantum_impacts = []
    
    for scenario_name in ['baseline', 'mild_recession', 'severe_recession', 'financial_crisis']:
        stress_levels.append(scenarios[scenario_name]['pd_multiplier'])
        classical_impacts.append(classical_results[scenario_name]['risk_measures']['var_99'])
        quantum_impacts.append(quantum_results[scenario_name]['risk_measures']['var_99'])
    
    axes[1, 0].plot(stress_levels, classical_impacts, 'o-', label='Classical', linewidth=2)
    axes[1, 0].plot(stress_levels, quantum_impacts, 's-', label='Quantum', linewidth=2)
    axes[1, 0].set_xlabel('Stress Level (PD Multiplier)')
    axes[1, 0].set_ylabel('VaR (99%)')
    axes[1, 0].set_title('Stress Impact Progression')
    axes[1, 0].legend()
    axes[1, 0].grid(True)
    
    # Plot 4: Difference analysis
    differences = [d['difference_pct'] for d in comparison_data]
    axes[1, 1].bar(scenarios, differences, alpha=0.7, color='orange')
    axes[1, 1].set_xlabel('Stress Scenarios')
    axes[1, 1].set_ylabel('Difference (%)')
    axes[1, 1].set_title('Quantum vs Classical Difference')
    axes[1, 1].set_xticklabels(scenarios, rotation=45)
    axes[1, 1].grid(True)
    
    plt.tight_layout()
    plt.show()

# Exercise: Quantum Reverse Stress Testing
def quantum_reverse_stress_testing_exercise():
    """
    Exercise: Implement quantum reverse stress testing
    """
    # Create portfolio
    classical_stress = ClassicalStressTesting()
    portfolio = classical_stress.create_portfolio(n_assets=6)
    
    # Define target loss threshold
    target_loss = 500000  # $500k loss threshold
    
    print("=== Quantum Reverse Stress Testing ===")
    print(f"Target Loss Threshold: ${target_loss:,.2f}")
    
    # Quantum circuit for reverse stress testing
    num_qubits = 6
    circuit = QuantumCircuit(num_qubits, num_qubits)
    
    # Create superposition of stress scenarios
    circuit.h(0)  # Hadamard gate for scenario superposition
    circuit.h(1)  # Additional scenario dimension
    
    # Encode portfolio parameters
    for i in range(num_qubits):
        circuit.rx(np.pi/4, i)  # Base rotation
    
    # Add entanglement for scenario interactions
    circuit.cx(0, 2)
    circuit.cx(1, 3)
    circuit.cx(2, 4)
    circuit.cx(3, 5)
    
    # Measure
    circuit.measure_all()
    
    # Execute circuit
    backend = Aer.get_backend('qasm_simulator')
    job = execute(circuit, backend, shots=1000)
    result = job.result()
    counts = result.get_counts()
    
    # Analyze results for scenarios leading to target loss
    print("\nQuantum Reverse Stress Testing Results:")
    print("Measurement counts:")
    
    scenarios_above_threshold = 0
    total_scenarios = 0
    
    for state, count in counts.items():
        total_scenarios += count
        
        # Calculate loss for this scenario
        loss = calculate_scenario_loss(state, portfolio)
        
        if loss >= target_loss:
            scenarios_above_threshold += count
            print(f"State {state}: Loss ${loss:,.2f} (Count: {count})")
    
    probability_above_threshold = scenarios_above_threshold / total_scenarios
    print(f"\nProbability of loss >= ${target_loss:,.2f}: {probability_above_threshold:.4f}")
    
    return probability_above_threshold

def calculate_scenario_loss(state, portfolio):
    """
    Calculate portfolio loss for a given quantum state
    """
    loss = 0
    for i, bit in enumerate(state):
        if i < len(portfolio) and bit == '1':
            asset = portfolio.iloc[i]
            # Apply stress multiplier based on state
            stress_multiplier = 1 + (i % 3) * 0.5  # Varying stress levels
            loss += asset['exposure'] * asset['lgd'] * stress_multiplier
    
    return loss

# Exercise: Quantum Sensitivity Analysis
def quantum_sensitivity_analysis_exercise():
    """
    Exercise: Implement quantum sensitivity analysis
    """
    # Create portfolio
    classical_stress = ClassicalStressTesting()
    portfolio = classical_stress.create_portfolio(n_assets=6)
    
    print("=== Quantum Sensitivity Analysis ===")
    
    # Define parameter ranges
    pd_multipliers = np.linspace(0.5, 3.0, 10)
    lgd_multipliers = np.linspace(0.8, 1.5, 8)
    
    # Create quantum circuit for sensitivity analysis
    num_qubits = 6
    circuit = QuantumCircuit(num_qubits, num_qubits)
    
    # Encode parameter sensitivity
    for i in range(num_qubits):
        # Encode PD sensitivity
        pd_sensitivity = (i % 3) / 2.0  # Varying sensitivity
        circuit.rx(pd_sensitivity * np.pi, i)
        
        # Encode LGD sensitivity
        lgd_sensitivity = ((i + 1) % 3) / 2.0
        circuit.ry(lgd_sensitivity * np.pi, i)
    
    # Add parameter interactions
    circuit.cx(0, 1)
    circuit.cx(1, 2)
    circuit.cx(2, 3)
    circuit.cx(3, 4)
    circuit.cx(4, 5)
    
    # Measure
    circuit.measure_all()
    
    # Execute circuit
    backend = Aer.get_backend('qasm_simulator')
    job = execute(circuit, backend, shots=1000)
    result = job.result()
    counts = result.get_counts()
    
    # Analyze sensitivity
    print("Quantum Sensitivity Analysis Results:")
    
    sensitivity_scores = []
    for state, count in counts.items():
        # Calculate sensitivity score
        sensitivity = calculate_sensitivity_score(state, portfolio)
        sensitivity_scores.append(sensitivity)
        
        if count > 50:  # Show significant states
            print(f"State {state}: Sensitivity {sensitivity:.4f} (Count: {count})")
    
    avg_sensitivity = np.mean(sensitivity_scores)
    print(f"\nAverage Sensitivity Score: {avg_sensitivity:.4f}")
    
    return avg_sensitivity

def calculate_sensitivity_score(state, portfolio):
    """
    Calculate sensitivity score for a quantum state
    """
    sensitivity = 0
    for i, bit in enumerate(state):
        if i < len(portfolio):
            asset = portfolio.iloc[i]
            # Calculate sensitivity based on asset characteristics
            base_sensitivity = asset['pd'] * asset['lgd'] * asset['exposure']
            
            if bit == '1':
                sensitivity += base_sensitivity * 2  # Higher sensitivity for '1' states
            else:
                sensitivity += base_sensitivity
    
    return sensitivity

# Run the main comparison
if __name__ == "__main__":
    print("Comparing Classical vs Quantum Stress Testing Approaches...")
    classical_results, quantum_results = compare_stress_testing_approaches()
    
    print("\nQuantum Reverse Stress Testing Exercise:")
    probability = quantum_reverse_stress_testing_exercise()
    
    print("\nQuantum Sensitivity Analysis Exercise:")
    sensitivity = quantum_sensitivity_analysis_exercise()

Exercise 4: Quantum Forward-Looking Stress Testing

def quantum_forward_looking_stress_testing():
    """
    Exercise: Implement quantum forward-looking stress testing
    """
    # Create time series of portfolio data
    np.random.seed(42)
    n_periods = 12  # 12 months
    n_assets = 6
    
    # Generate time series data
    time_series_data = []
    for period in range(n_periods):
        period_data = []
        for asset in range(n_assets):
            # Simulate time-varying parameters
            base_pd = 0.05 + 0.02 * np.sin(2 * np.pi * period / 12)  # Seasonal pattern
            base_lgd = 0.5 + 0.1 * np.random.normal(0, 1)  # Random variation
            
            asset_data = {
                'period': period,
                'asset_id': f'Asset_{asset}',
                'exposure': 500000 + 100000 * np.random.normal(0, 1),
                'pd': max(0.01, base_pd + 0.01 * np.random.normal(0, 1)),
                'lgd': max(0.2, min(0.8, base_lgd)),
                'rating': np.random.choice(['AAA', 'AA', 'A', 'BBB', 'BB', 'B'])
            }
            period_data.append(asset_data)
        
        time_series_data.extend(period_data)
    
    time_series_df = pd.DataFrame(time_series_data)
    
    # Quantum forward-looking analysis
    print("=== Quantum Forward-Looking Stress Testing ===")
    
    # Create quantum circuit for time series analysis
    num_qubits = 8
    circuit = QuantumCircuit(num_qubits, num_qubits)
    
    # Encode time series information
    for period in range(min(4, n_periods)):  # Encode last 4 periods
        period_data = time_series_df[time_series_df['period'] == period]
        
        for i, (_, asset) in enumerate(period_data.iterrows()):
            if i < num_qubits // 4:  # Distribute across qubits
                qubit_idx = period * (num_qubits // 4) + i
                
                # Encode PD trend
                pd_trend = asset['pd'] - 0.05  # Deviation from baseline
                circuit.rx(pd_trend * np.pi, qubit_idx)
                
                # Encode LGD trend
                lgd_trend = asset['lgd'] - 0.5
                circuit.ry(lgd_trend * np.pi, qubit_idx)
    
    # Add time series entanglement
    for i in range(num_qubits - 1):
        circuit.cx(i, i + 1)
    
    # Add temporal correlations
    circuit.cx(0, 4)  # Connect periods
    circuit.cx(1, 5)
    circuit.cx(2, 6)
    circuit.cx(3, 7)
    
    # Measure
    circuit.measure_all()
    
    # Execute circuit
    backend = Aer.get_backend('qasm_simulator')
    job = execute(circuit, backend, shots=1000)
    result = job.result()
    counts = result.get_counts()
    
    # Analyze forward-looking predictions
    print("Quantum Forward-Looking Analysis Results:")
    
    future_predictions = []
    for state, count in counts.items():
        if count > 20:  # Significant states
            prediction = analyze_future_prediction(state, time_series_df)
            future_predictions.append(prediction)
            print(f"State {state}: Future Risk Level {prediction:.4f} (Count: {count})")
    
    if future_predictions:
        avg_future_risk = np.mean(future_predictions)
        print(f"\nAverage Predicted Future Risk Level: {avg_future_risk:.4f}")
        
        if avg_future_risk > 0.7:
            print("⚠️  HIGH FUTURE RISK DETECTED")
        elif avg_future_risk > 0.4:
            print("⚠️  MODERATE FUTURE RISK DETECTED")
        else:
            print("✅ LOW FUTURE RISK DETECTED")
    
    return future_predictions

def analyze_future_prediction(state, time_series_df):
    """
    Analyze future risk prediction from quantum state
    """
    # Extract trend information from quantum state
    trend_indicators = []
    
    for i, bit in enumerate(state):
        if bit == '1':
            trend_indicators.append(1)
        else:
            trend_indicators.append(0)
    
    # Calculate trend strength
    trend_strength = np.mean(trend_indicators)
    
    # Get recent portfolio performance
    recent_data = time_series_df[time_series_df['period'] >= 8]  # Last 4 periods
    recent_pd_avg = recent_data['pd'].mean()
    recent_lgd_avg = recent_data['lgd'].mean()
    
    # Combine trend and current performance
    future_risk = (trend_strength * 0.6 + recent_pd_avg * 0.3 + recent_lgd_avg * 0.1)
    
    return future_risk

# Run forward-looking exercise
if __name__ == "__main__":
    future_predictions = quantum_forward_looking_stress_testing()

📊 Kết quả và Phân tích

Performance Comparison:

Classical Stress Testing:

  • Historical Scenarios: Based on past events
  • Monte Carlo: Computationally intensive
  • Sensitivity Analysis: Linear approximations
  • Reverse Stress Testing: Limited scenario space

Quantum Stress Testing:

  • Quantum Scenarios: Parallel scenario processing
  • Quantum Monte Carlo: Potential speedup
  • Quantum Sensitivity: Non-linear analysis
  • Quantum Reverse Testing: Expanded scenario space

Key Insights:

1. Quantum Advantages:

  • Scenario Generation: Superposition enables parallel scenario analysis
  • Correlation Modeling: Entanglement captures complex dependencies
  • Non-linear Effects: Quantum transformations handle non-linear stress impacts
  • Forward-looking: Quantum circuits can model temporal patterns

2. Classical Advantages:

  • Interpretability: Clear scenario definitions
  • Regulatory Acceptance: Well-established methods
  • Computational Efficiency: Fast for simple scenarios
  • Historical Validation: Based on observed events

3. Hybrid Approach:

  • Use quantum cho complex scenario generation
  • Use classical cho scenario interpretation
  • Combine both cho comprehensive stress testing

🎯 Bài tập về nhà

Exercise 1: Quantum Regulatory Stress Testing

Implement quantum models cho regulatory stress testing requirements.

Exercise 2: Quantum Multi-Period Stress Testing

Build quantum multi-period stress testing framework.

Exercise 3: Quantum Stress Testing Dashboard

Create interactive dashboard cho quantum stress testing results.

Exercise 4: Quantum Stress Testing Validation

Implement validation framework cho quantum stress testing models.


“Quantum stress testing enables more comprehensive scenario analysis by naturally capturing complex, non-linear relationships and temporal patterns.” - Quantum Finance Research

Ngày tiếp theo: Quantum Probability và Finance