Ngày 5: Stress Testing và Scenario Analysis
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