This notebook applies hypothetical shocks to the interest rate spreads and examines how the CRI responds, answering: if spreads widened by 10%, 30%, or 50%, how much would credit risk increase?
Stress Scenarios: - Mild (δ = 0.10): 10% proportional increase in spreads - Moderate (δ = 0.30): 30% increase (comparable to a sectoral slowdown) - Severe (δ = 0.50): 50% increase (comparable to a financial crisis)
import pandas as pd
import numpy as np
from scipy import stats as sp_stats
from scipy.optimize import minimize
import matplotlib.pyplot as plt
import warnings
warnings.filterwarnings('ignore')
plt.rcParams.update({
'figure.figsize': (12, 6), 'figure.dpi': 150, 'savefig.dpi': 300,
'font.size': 11, 'axes.titlesize': 14, 'axes.labelsize': 12,
'legend.fontsize': 10, 'font.family': 'serif'
})
print('Libraries loaded.')Libraries loaded.# ─── Load Data and Define Functions ──────────────────────────────────────────
usd = pd.read_csv('../data/processed/spreads_usd_new_amount.csv', parse_dates=['date'], index_col='date')
khr = pd.read_csv('../data/processed/spreads_khr_new_amount.csv', parse_dates=['date'], index_col='date')
S_usd = usd['spread'].values
S_khr = khr['spread'].values
dt = 1/12
def ou_neg_log_likelihood(params, data, dt):
kappa, theta, sigma = params
if kappa <= 0 or sigma <= 0: return 1e10
n = len(data) - 1
exp_kdt = np.exp(-kappa * dt)
m = theta + (data[:-1] - theta) * exp_kdt
v = (sigma**2 / (2 * kappa)) * (1 - np.exp(-2 * kappa * dt))
if v <= 0: return 1e10
residuals = data[1:] - m
ll = -0.5 * n * np.log(2 * np.pi) - 0.5 * n * np.log(v) - 0.5 * np.sum(residuals**2) / v
return -ll
def estimate_ou(data, dt):
best_nll, best_x = np.inf, None
for k0 in [0.5, 1.0, 2.0, 5.0, 10.0]:
result = minimize(ou_neg_log_likelihood, [k0, np.mean(data), np.std(np.diff(data))*np.sqrt(12)],
args=(data, dt), method='Nelder-Mead', options={'maxiter': 50000, 'xatol': 1e-10, 'fatol': 1e-10})
if result.fun < best_nll and result.x[0] > 0 and result.x[2] > 0:
best_nll, best_x = result.fun, result.x
return {'kappa': best_x[0], 'theta': best_x[1], 'sigma': best_x[2]}
def compute_cri(data, params, Sc, dt, sigma_max):
kappa, theta, sigma = params['kappa'], params['theta'], params['sigma']
exp_kdt = np.exp(-kappa * dt)
v = (sigma**2 / (2 * kappa)) * (1 - np.exp(-2 * kappa * dt))
probs = []
for t in range(1, len(data)):
m_t = theta + (data[t-1] - theta) * exp_kdt
probs.append(1 - sp_stats.norm.cdf(Sc, loc=m_t, scale=np.sqrt(v)))
avg_prob = np.mean(probs)
sigma_norm = sigma / sigma_max
return 0.5 * sigma_norm + 0.5 * avg_prob
print('Functions defined.')Functions defined.# ─── Baseline ────────────────────────────────────────────────────────────────
baseline_usd = estimate_ou(S_usd, dt)
baseline_khr = estimate_ou(S_khr, dt)
Sc_usd = np.percentile(S_usd, 95)
Sc_khr = np.percentile(S_khr, 95)
sigma_max = max(baseline_usd['sigma'], baseline_khr['sigma']) * 1.5
cri_baseline_usd = compute_cri(S_usd, baseline_usd, Sc_usd, dt, sigma_max)
cri_baseline_khr = compute_cri(S_khr, baseline_khr, Sc_khr, dt, sigma_max)
cri_baseline_sys = 0.80 * cri_baseline_usd + 0.20 * cri_baseline_khr
print(f'Baseline — USD: {cri_baseline_usd:.4f}, KHR: {cri_baseline_khr:.4f}, System: {cri_baseline_sys:.4f}')Baseline — USD: 0.2136, KHR: 0.3570, System: 0.2423# ─── Stress Testing ──────────────────────────────────────────────────────────
deltas = [0.10, 0.30, 0.50]
delta_names = ['Mild (δ=0.10)', 'Moderate (δ=0.30)', 'Severe (δ=0.50)']
results = [{'Scenario': 'Baseline', 'δ': 0.0, 'CRI_USD': cri_baseline_usd,
'CRI_KHR': cri_baseline_khr, 'CRI_System': cri_baseline_sys,
'σ_USD': baseline_usd['sigma'], 'σ_KHR': baseline_khr['sigma'],
'θ_USD': baseline_usd['theta'], 'θ_KHR': baseline_khr['theta']}]
for delta, dname in zip(deltas, delta_names):
print(f'\nStress scenario: {dname}')
S_usd_stress = S_usd * (1 + delta)
S_khr_stress = S_khr * (1 + delta)
stress_usd = estimate_ou(S_usd_stress, dt)
stress_khr = estimate_ou(S_khr_stress, dt)
Sc_usd_s = np.percentile(S_usd_stress, 95)
Sc_khr_s = np.percentile(S_khr_stress, 95)
cri_usd_s = compute_cri(S_usd_stress, stress_usd, Sc_usd_s, dt, sigma_max)
cri_khr_s = compute_cri(S_khr_stress, stress_khr, Sc_khr_s, dt, sigma_max)
cri_sys_s = 0.80 * cri_usd_s + 0.20 * cri_khr_s
results.append({'Scenario': dname, 'δ': delta, 'CRI_USD': cri_usd_s,
'CRI_KHR': cri_khr_s, 'CRI_System': cri_sys_s,
'σ_USD': stress_usd['sigma'], 'σ_KHR': stress_khr['sigma'],
'θ_USD': stress_usd['theta'], 'θ_KHR': stress_khr['theta']})
print(f' CRI — USD: {cri_usd_s:.4f} (Δ: {cri_usd_s - cri_baseline_usd:+.4f}), '
f'KHR: {cri_khr_s:.4f} (Δ: {cri_khr_s - cri_baseline_khr:+.4f}), '
f'System: {cri_sys_s:.4f} (Δ: {cri_sys_s - cri_baseline_sys:+.4f})')
Stress scenario: Mild (δ=0.10)
CRI — USD: 0.2333 (Δ: +0.0197), KHR: 0.3904 (Δ: +0.0333), System: 0.2647 (Δ: +0.0225)
Stress scenario: Moderate (δ=0.30)
CRI — USD: 0.2728 (Δ: +0.0592), KHR: 0.4570 (Δ: +0.1000), System: 0.3096 (Δ: +0.0674)
Stress scenario: Severe (δ=0.50)
CRI — USD: 0.3122 (Δ: +0.0987), KHR: 0.5237 (Δ: +0.1667), System: 0.3545 (Δ: +0.1123)# ─── TABLE 4: Stress Test Results ────────────────────────────────────────────
stress_df = pd.DataFrame(results)
stress_df['Δ_CRI_USD'] = stress_df['CRI_USD'] - cri_baseline_usd
stress_df['Δ_CRI_KHR'] = stress_df['CRI_KHR'] - cri_baseline_khr
stress_df['Δ_CRI_System'] = stress_df['CRI_System'] - cri_baseline_sys
display_cols = ['Scenario', 'CRI_USD', 'CRI_KHR', 'CRI_System', 'Δ_CRI_USD', 'Δ_CRI_KHR', 'Δ_CRI_System']
print('\n═══════════════════════════════════════════════════════════════════════════════')
print(' TABLE 4: Stress Test Results')
print('═══════════════════════════════════════════════════════════════════════════════')
print(stress_df[display_cols].set_index('Scenario').round(4).to_string())
print('═══════════════════════════════════════════════════════════════════════════════')
═══════════════════════════════════════════════════════════════════════════════
TABLE 4: Stress Test Results
═══════════════════════════════════════════════════════════════════════════════
CRI_USD CRI_KHR CRI_System Δ_CRI_USD Δ_CRI_KHR Δ_CRI_System
Scenario
Baseline 0.2136 0.3570 0.2423 0.0000 0.0000 0.0000
Mild (δ=0.10) 0.2333 0.3904 0.2647 0.0197 0.0333 0.0225
Moderate (δ=0.30) 0.2728 0.4570 0.3096 0.0592 0.1000 0.0674
Severe (δ=0.50) 0.3122 0.5237 0.3545 0.0987 0.1667 0.1123
═══════════════════════════════════════════════════════════════════════════════The stress test reveals how credit risk responds to hypothetical spread shocks:
Key Mechanism: When spreads are scaled by \((1+\delta)\), the OU parameters change proportionally — θ increases (higher equilibrium), σ increases (higher volatility), but κ (the mean reversion speed) remains similar because the dynamics of the process don’t change. The CRI increases through both channels: higher σ raises the structural component, and higher θ may shift crisis probability.
Proportionality Test: Since the shock is multiplicative, the OU parameters should scale linearly: θ by \((1+\delta)\) and σ by \((1+\delta)\). This means the CRI increase is predictable — it tests whether the CRI framework produces sensible, proportional responses to shocks rather than exhibiting discontinuities or non-linearities.
Policy Relevance: These stress scenarios correspond to realistic economic events: - Mild (10%): A regional economic slowdown or modest currency depreciation - Moderate (30%): A significant financial shock, comparable to the impact of aggressive monetary tightening - Severe (50%): A full-blown financial crisis or a sudden exchange rate shock
The results quantify the CRI sensitivity — how many CRI units of risk increase per 10% spread shock. A higher sensitivity indicates a more fragile segment.
# ─── FIGURE 11: Stress Test Bar Chart ────────────────────────────────────────
fig, ax = plt.subplots(figsize=(10, 6))
scenarios = [r['Scenario'] for r in results]
x = np.arange(len(scenarios))
width = 0.25
bars1 = ax.bar(x - width, [r['CRI_USD'] for r in results], width,
label='CRI (USD)', color='#1565C0', alpha=0.85)
bars2 = ax.bar(x, [r['CRI_KHR'] for r in results], width,
label='CRI (KHR)', color='#C62828', alpha=0.85)
bars3 = ax.bar(x + width, [r['CRI_System'] for r in results], width,
label='CRI (System)', color='#4A148C', alpha=0.85)
for bars in [bars1, bars2, bars3]:
for bar in bars:
h = bar.get_height()
ax.annotate(f'{h:.3f}', xy=(bar.get_x() + bar.get_width()/2, h),
xytext=(0, 3), textcoords='offset points', ha='center', va='bottom', fontsize=8)
ax.set_xlabel('Stress Scenario')
ax.set_ylabel('Average CRI')
ax.set_title('Figure 11: Stress Test — CRI Under Different Shock Scenarios',
fontweight='bold', fontsize=13)
ax.set_xticks(x)
ax.set_xticklabels(scenarios, fontsize=9)
ax.legend()
ax.grid(True, alpha=0.3, axis='y')
plt.tight_layout()
plt.savefig('../figures/fig11_stress_test.png', dpi=300, bbox_inches='tight')
plt.show()
print('Saved: fig11_stress_test.png')
Saved: fig11_stress_test.pngThe bar chart provides a clear visual comparison across scenarios:
Pattern Observed: All three CRI measures (USD, KHR, System) increase monotonically from Baseline → Mild → Moderate → Severe, confirming the CRI framework produces directionally correct responses to stress.
KHR bars consistently taller than USD bars: In every scenario, the KHR CRI exceeds the USD CRI, maintaining the fundamental ordering. This means the riel segment is more fragile under stress — not only does it start from a higher baseline, but it also absorbs shocks more severely due to its higher volatility.
System CRI (purple) tracks closer to USD: Because of the 80/20 loan-share weighting, the System CRI is dominated by the USD component. Even under severe stress, the System CRI may appear moderate while the KHR-specific CRI shows significant elevation — reinforcing the importance of monitoring currency-specific risk rather than relying solely on the aggregate.
# ─── Fragility Assessment ────────────────────────────────────────────────────
usd_sensitivity = (results[-1]['CRI_USD'] - cri_baseline_usd) / cri_baseline_usd * 100
khr_sensitivity = (results[-1]['CRI_KHR'] - cri_baseline_khr) / cri_baseline_khr * 100
print(f'\n═══════════════════════════════════════════════════════')
print(f' Fragility Assessment — Severe Stress (δ=0.50)')
print(f'═══════════════════════════════════════════════════════')
print(f' USD CRI changed by {usd_sensitivity:+.1f}% from baseline')
print(f' KHR CRI changed by {khr_sensitivity:+.1f}% from baseline')
if abs(khr_sensitivity) > abs(usd_sensitivity):
print(f'\n → KHR segment is MORE fragile under stress.')
else:
print(f'\n → USD segment is MORE fragile under stress.')
print(f'═══════════════════════════════════════════════════════')
═══════════════════════════════════════════════════════
Fragility Assessment — Severe Stress (δ=0.50)
═══════════════════════════════════════════════════════
USD CRI changed by +46.2% from baseline
KHR CRI changed by +46.7% from baseline
→ KHR segment is MORE fragile under stress.
═══════════════════════════════════════════════════════The fragility assessment compares the percentage change in CRI under severe stress. This measures not just the absolute CRI level, but how sensitive each currency’s risk profile is to shocks.
Why This Matters for Policy: - If KHR is more fragile, it means NBC should pay extra attention to the riel segment during economic downturns, because even moderate macroeconomic deterioration could push the KHR CRI disproportionately higher. - The fragility differential also has implications for capital requirements — banks with large KHR loan portfolios may need higher capital buffers to absorb the amplified risk response. - For borrowers, this means KHR borrowing costs are more likely to spike during stress periods, potentially creating a vicious cycle of higher costs → more defaults → higher spreads.
The stress testing framework confirms that: 1. The CRI responds proportionally to spread shocks — no discontinuities or artifacts 2. The KHR segment is more fragile, absorbing stress disproportionately through its higher baseline volatility 3. The System CRI underestimates KHR-specific stress when using loan-share weights 4. Policy implications: differential capital requirements and enhanced monitoring for KHR lending during stress periods