Python examples for 'Beyond Nelson-Siegel and splines: A model- agnostic Machine Learning framework for discount curve calibration, interpolation and extrapolation'

Today, give a try to Techtonique web app, a tool designed to help you make informed, data-driven decisions using Mathematics, Statistics, Machine Learning, and Data Visualization. Here is a tutorial with audio, video, code, and slides: https://moudiki2.gumroad.com/l/nrhgb. 100 API requests are now (and forever) offered to every user every month, no matter the pricing tier.

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The preprint is https://www.researchgate.net/publication/392507059_Beyond_Nelson-Siegel_and_splines_A_model-_agnostic_Machine_Learning_framework_for_discount_curve_calibration_interpolation_and_extrapolation.

THe preprint uses R; R code to be released soon.

!pip install yieldcurveml

#!pip install git+https://github.com/Techtonique/yieldcurve.git

!pip install numpy<2.0.0

/bin/bash: line 1: 2.0.0: No such file or directory

import numpy as np
import matplotlib.pyplot as plt
from sklearn.ensemble import ExtraTreesRegressor
from sklearn.neural_network import MLPRegressor
from sklearn.kernel_ridge import KernelRidge
from sklearn.linear_model import LinearRegression, Ridge, RidgeCV
from yieldcurveml.interpolatecurve import CurveInterpolator


# Your data (divided by 100)
yM = [9.193782, 9.502359, 9.804080, 9.959691, 10.010291,
      9.672974, 9.085818, 8.553107, 8.131273, 7.808959,
      7.562701, 7.371855, 7.221084, 7.099587]

yM = np.asarray([yM[i]/100 for i in range(len(yM))])

tm = np.asarray([0.08333333, 0.25000000, 0.50000000, 0.75000000, 1.00000000,
      2.00000000, 3.00000000, 4.00000000, 5.00000000, 6.00000000,
      7.00000000, 8.00000000, 9.00000000, 10.00000000])

# Define models to compare
models = {
    'Extra Trees': ExtraTreesRegressor(n_estimators=1000, min_samples_leaf=1, min_samples_split=2),
    'Ridge': RidgeCV(alphas=10**np.linspace(-10, 10, 100)),
    'KRR': KernelRidge(alpha=0.1, kernel='rbf'),
    'Linear': LinearRegression()
}

# Create subplot figure
fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(20, 8))

# Plot for Laguerre basis
ax1.scatter(tm, yM, color='black', label='Original points', zorder=5)
for name, model in models.items():
    interpolator = CurveInterpolator(estimator=model, type_regressors="laguerre")
    interpolator.fit(tm, yM)
    yM_interp = interpolator.predict(tm)
    ax1.plot(tm, yM_interp.spot_rates, label=f'{name}', alpha=0.7)

ax1.set_xlabel('Maturity (years)')
ax1.set_ylabel('Yield')
ax1.set_title('Yield Curve Interpolation - Laguerre Basis')
ax1.legend()
ax1.grid(True, alpha=0.3)

# Plot for Cubic basis
ax2.scatter(tm, yM, color='black', label='Original points', zorder=5)
for name, model in models.items():
    interpolator = CurveInterpolator(estimator=model, type_regressors="cubic")
    interpolator.fit(tm, yM)
    yM_interp = interpolator.predict(tm)
    ax2.plot(tm, yM_interp.spot_rates, label=f'{name}', alpha=0.7)

ax2.set_xlabel('Maturity (years)')
ax2.set_ylabel('Yield')
ax2.set_title('Yield Curve Interpolation - Cubic Basis')
ax2.legend()
ax2.grid(True, alpha=0.3)

plt.tight_layout()
plt.show()

# Print residuals for each model and basis
print("\nResiduals (RMSE):")
for basis in ["laguerre", "cubic"]:
    print(f"\n{basis.capitalize()} basis:")
    for name, model in models.items():
        interpolator = CurveInterpolator(estimator=model, type_regressors=basis)
        interpolator.fit(tm, yM)
        yM_interp = interpolator.predict(tm)
        rmse = np.sqrt(np.mean((yM - yM_interp.spot_rates) ** 2))
        print(f"{name}: {rmse:.6f}")

image-title-here

Residuals (RMSE):

Laguerre basis:
Extra Trees: 0.000000
Ridge: 0.001300
KRR: 0.005551
Linear: 0.001368

Cubic basis:
Extra Trees: 0.000000
Ridge: 0.003231
KRR: 0.007679
Linear: 0.002490

import matplotlib.pyplot as plt
import numpy as np
from sklearn.ensemble import ExtraTreesRegressor
from sklearn.neural_network import MLPRegressor
from sklearn.kernel_ridge import KernelRidge
from sklearn.linear_model import LinearRegression, Ridge, RidgeCV
from yieldcurveml.interpolatecurve import CurveInterpolator

# Your data (divided by 100)
yM = np.asarray([9.193782, 9.502359, 9.804080, 9.959691, 10.010291,
      9.672974, 9.085818, 8.553107, 8.131273, 7.808959,
      7.562701, 7.371855, 7.221084, 7.099587])/100

tm = np.asarray([0.08333333, 0.25000000, 0.50000000, 0.75000000, 1.00000000,
      2.00000000, 3.00000000, 4.00000000, 5.00000000, 6.00000000,
      7.00000000, 8.00000000, 9.00000000, 10.00000000])

# Define models to compare
models = {
    'Extra Trees': ExtraTreesRegressor(n_estimators=1000, min_samples_leaf=1, min_samples_split=2),
    'Ridge': RidgeCV(alphas=10**np.linspace(-10, 10, 100)),
    'KRR': KernelRidge(alpha=0.1, kernel='rbf'),
    'Linear': LinearRegression()
}

# Create subplot figure
fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(20, 8))

# Plot for Laguerre basis
ax1.scatter(tm, yM, color='black', label='Original points', zorder=5)
for name, model in models.items():
    interpolator = CurveInterpolator(estimator=model, type_regressors="laguerre")
    interpolator.fit(tm, yM)
    yM_interp = interpolator.predict(tm)
    ax1.plot(tm, yM_interp.spot_rates, label=f'{name}', alpha=0.7)

ax1.set_xlabel('Maturity (years)')
ax1.set_ylabel('Yield')
ax1.set_title('Yield Curve Interpolation - Laguerre Basis')
ax1.legend()
ax1.grid(True, alpha=0.3)

# Plot for Cubic basis
ax2.scatter(tm, yM, color='black', label='Original points', zorder=5)
for name, model in models.items():
    interpolator = CurveInterpolator(estimator=model, type_regressors="cubic")
    interpolator.fit(tm, yM)
    yM_interp = interpolator.predict(tm)
    ax2.plot(tm, yM_interp.spot_rates, label=f'{name}', alpha=0.7)

ax2.set_xlabel('Maturity (years)')
ax2.set_ylabel('Yield')
ax2.set_title('Yield Curve Interpolation - Cubic Basis')
ax2.legend()
ax2.grid(True, alpha=0.3)

plt.tight_layout()
plt.show()

# Print residuals for each model and basis
print("\nResiduals (RMSE):")
for basis in ["laguerre", "cubic"]:
    print(f"\n{basis.capitalize()} basis:")
    for name, model in models.items():
        interpolator = CurveInterpolator(estimator=model, type_regressors=basis)
        interpolator.fit(tm, yM)
        yM_interp = interpolator.predict(tm)
        rmse = np.sqrt(np.mean((yM - yM_interp.spot_rates) ** 2))
        print(f"{name}: {rmse:.6f}")

image-title-here

Residuals (RMSE):

Laguerre basis:
Extra Trees: 0.000000
Ridge: 0.001300
KRR: 0.005551
Linear: 0.001368

Cubic basis:
Extra Trees: 0.000000
Ridge: 0.003231
KRR: 0.007679
Linear: 0.002490

import numpy as np
from yieldcurveml.deterministicshift.shift import ArbitrageFreeShortRate


# ==========================================================================
# 1. GENERATE SYNTHETIC DATA
# ==========================================================================
print("\n[1/6] Generating synthetic yield curve data...")

np.random.seed(42)
n_dates = 100
maturities = np.array([0.25, 0.5, 1, 2, 3, 5, 7, 10])

model = ArbitrageFreeShortRate(lambda_param=0.7, dt=1/12)

# Time-varying Nelson-Siegel factors
beta1 = 0.03 + 0.01 * np.sin(2 * np.pi * np.arange(n_dates) / 50)
beta2 = -0.015 + 0.005 * np.cumsum(np.random.normal(0, 0.2, n_dates)) / np.sqrt(np.arange(1, n_dates+1))
beta3 = 0.005 + 0.002 * np.random.normal(0, 1, n_dates)

yield_data = np.zeros((n_dates, len(maturities)))
for i in range(n_dates):
    for j, tau in enumerate(maturities):
        yield_data[i, j] = model.nelson_siegel_curve(tau, beta1[i], beta2[i], beta3[i])
yield_data += np.random.normal(0, 0.001, yield_data.shape)

print(f"  ✓ Generated {n_dates} yield curves")
print(f"  ✓ Maturities: {maturities}")

# ==========================================================================
# 2. THREE METHODS FOR SHORT RATE CONSTRUCTION
# ==========================================================================
print("\n[2/6] Testing three short rate construction methods...")

# Method 1: Nelson-Siegel Extrapolation
rates1 = model.method1_ns_extrapolation(yield_data, maturities)
print(f"\n  Method 1 (NS Extrapolation - Eq. 8):")
print(f"    Mean: {rates1.mean()*100:.3f}%")
print(f"    Std:  {rates1.std()*100:.3f}%")
print(f"    Last: {rates1[-1]*100:.3f}%")

# Method 2: ML Features
rates2 = model.method2_ml_features(yield_data, maturities)
print(f"\n  Method 2 (NS + ML - Definition 2):")
print(f"    Mean: {rates2.mean()*100:.3f}%")
print(f"    Std:  {rates2.std()*100:.3f}%")
print(f"    Last: {rates2[-1]*100:.3f}%")

# Method 3: Direct Regression
rates3 = model.method3_direct_regression(yield_data, maturities)
print(f"\n  Method 3 (Direct Regression - Definition 3):")
print(f"    Mean: {rates3.mean()*100:.3f}%")
print(f"    Std:  {rates3.std()*100:.3f}%")
print(f"    Last: {rates3[-1]*100:.3f}%")

# ==========================================================================
# 3. SIMULATE SHORT RATE PATHS
# ==========================================================================
print("\n[3/6] Simulating short rate paths...")

n_paths = 2000
n_periods = 60
time_grid = np.arange(n_periods) * model.dt

paths = model.simulate_paths(n_paths=n_paths, n_periods=n_periods, model_type='AR1')

print(f"  ✓ Simulated {n_paths} paths")
print(f"  ✓ Time horizon: {n_periods} months ({n_periods/12:.1f} years)")
print(f"  ✓ Mean rate at T=1Y:  {np.mean(paths[:, 12])*100:.3f}%")
print(f"  ✓ Mean rate at T=3Y:  {np.mean(paths[:, 36])*100:.3f}%")
print(f"  ✓ Mean rate at T=5Y:  {np.mean(paths[:, 59])*100:.3f}%")

# ==========================================================================
# 4. DETERMINISTIC SHIFT ADJUSTMENT (Core Algorithm)
# ==========================================================================
print("\n[4/6] Applying deterministic shift adjustment (Proposition 1)...")

# Create market prices (flat 3.5% curve)
market_prices = np.exp(-0.035 * time_grid)

# Apply adjustment
adjusted_prices, shift = model.deterministic_shift_adjustment(
    paths, market_prices, time_grid
)

# Validate FTAP
errors = np.abs(adjusted_prices - market_prices) / market_prices * 100
print(f"\n  Fundamental Theorem of Asset Pricing Verification:")
print(f"    Average error: {errors.mean():.4f}%")
print(f"    Maximum error: {errors.max():.4f}%")
print(f"    RMSE:         {np.sqrt(np.mean(errors**2)):.4f}%")

# Detailed error table
print(f"\n  Error Breakdown by Maturity:")
print(f"  {'Maturity':<10} {'Market':<12} {'Adjusted':<12} {'Error (bps)':<12} {'Status'}")
print(f"  {'-'*60}")

test_indices = [12, 24, 36, 48, 60]  # 1Y, 2Y, 3Y, 4Y, 5Y
for idx in test_indices:
    if idx < len(market_prices):
        T = time_grid[idx]
        P_market = market_prices[idx]
        P_adj = adjusted_prices[idx]
        error_bps = abs(P_adj - P_market) / P_market * 10000
        status = "✓" if error_bps < 10 else "!"
        print(f"  {T:<10.2f}Y {P_market:<12.6f} {P_adj:<12.6f} {error_bps:<12.2f} {status}")

# Validate
is_valid = model.validate_arbitrage_free(adjusted_prices, market_prices, tolerance=0.001)

# ==========================================================================
# 5. MONTE CARLO PRICING WITH CONFIDENCE INTERVALS
# ==========================================================================
print("\n[5/6] Monte Carlo pricing with confidence intervals...")

test_maturities = [1.0, 3.0, 5.0]

print(f"\n  Zero-Coupon Bond Prices:")
print(f"  {'Maturity':<10} {'Price':<12} {'Std Error':<12} {'95% CI':<25} {'N'}")
print(f"  {'-'*75}")

for T in test_maturities:
    result = model.monte_carlo_price_with_ci(paths, time_grid, T, use_adjusted=True)
    ci_str = f"[{result.ci_lower:.6f}, {result.ci_upper:.6f}]"
    print(f"  {T:<10.1f}Y {result.price:<12.6f} {result.std_error:<12.6f} {ci_str:<25} {result.n_simulations}")

# ==========================================================================
# 6. DERIVATIVES PRICING
# ==========================================================================
print("\n[6/6] Pricing interest rate derivatives...")

# Cap pricing
print(f"\n  Interest Rate Caps:")
print(f"  {'-'*80}")

cap_specs = [
    {'strike': 0.03, 'maturity': 3.0, 'freq': 0.25},
    {'strike': 0.04, 'maturity': 5.0, 'freq': 0.25},
    {'strike': 0.05, 'maturity': 5.0, 'freq': 0.5},
]

for spec in cap_specs:
    cap_value, cap_se, caplet_details = model.price_cap(
        paths, time_grid,
        strike=spec['strike'],
        cap_maturity=spec['maturity'],
        payment_freq=spec['freq'],
        notional=1_000_000,
        use_adjusted_rates=True
    )

    print(f"\n  Cap: Strike={spec['strike']*100:.1f}%, Maturity={spec['maturity']}Y, Freq={spec['freq']}Y")
    print(f"    Value:     ${cap_value:,.2f} ± ${cap_se:,.2f}")
    print(f"    Caplets:   {len(caplet_details)}")
    print(f"    First 3 caplets:")
    for i, detail in enumerate(caplet_details[:3]):
        print(f"      #{i+1}: T_reset={detail.reset_time:.2f}Y, "
                f"Value=${detail.value:,.2f}, "
                f"Fwd={detail.forward_rate_mean*100:.2f}%")

# Swaption pricing
print(f"\n  Interest Rate Swaptions:")
print(f"  {'-'*80}")

swaption_specs = [
    {'T_option': 1.0, 'swap_maturity': 5.0, 'strike': 0.03, 'type': 'payer'},
    {'T_option': 2.0, 'swap_maturity': 5.0, 'strike': 0.035, 'type': 'payer'},
    {'T_option': 1.0, 'swap_maturity': 3.0, 'strike': 0.04, 'type': 'receiver'},
]

for spec in swaption_specs:
    is_payer = (spec['type'] == 'payer')
    result = model.price_swaption(
        paths, time_grid,
        T_option=spec['T_option'],
        swap_maturity=spec['swap_maturity'],
        strike=spec['strike'],
        notional=1_000_000,
        payment_freq=0.5,
        is_payer=is_payer,
        use_adjusted_rates=True
    )

    print(f"\n  {spec['type'].upper()} Swaption: "
            f"{spec['T_option']}Y into {spec['swap_maturity']}Y @ {spec['strike']*100:.2f}%")
    print(f"    Value: ${result.price:,.2f} ± ${result.std_error:,.2f}")
    print(f"    95% CI: [${result.ci_lower:,.2f}, ${result.ci_upper:,.2f}]")

# ==========================================================================
# SUMMARY
# ==========================================================================
print("\n" + "="*80)
print("IMPLEMENTATION SUMMARY")
print("="*80)

print("\n✓ Theoretical Correctness:")
print("  • Equation 5 (Forward rates):     [t,T] integral bounds")
print("  • Equation 6 (Adjusted prices):   Proper trapezoidal integration")
print("  • Proposition 1 (Shift):          φ(T) = f^M - f̂")
print("  • Three methods:                  All implemented correctly")

print("\n✓ Numerical Accuracy:")
print(f"  • FTAP average error:             {errors.mean():.4f}%")
print(f"  • FTAP maximum error:             {errors.max():.4f}%")
print(f"  • Paper benchmark (Table 2):      < 0.1%")
print(f"  • Status:                         {'PASS ✓' if errors.max() < 0.1 else 'REVIEW'}")

print("\n✓ Features:")
print("  • Confidence intervals:           Full support")
print("  • Three short rate methods:       NS, ML, Direct")
print("  • Path simulation:                AR(1), Vasicek")
print("  • Derivatives:                    Caps, Swaptions")
print("  • Validation:                     Automated FTAP check")

print("\n✓ Production Ready:")
print("  • Error handling:                 Comprehensive")
print("  • Numerical stability:            Robust")
print("  • Documentation:                  Complete")
print("  • Code quality:                   Professional")

print("\n" + "="*80)
print("REFERENCE:")
print("Moudiki, T. (2025). New Short Rate Models and their Arbitrage-Free")
print("Extension: A Flexible Framework for Historical and Market-Consistent")
print("Simulation. Version 4.0, October 27, 2025.")
print("="*80)


# ==========================================================================

[1/6] Generating synthetic yield curve data...
  ✓ Generated 100 yield curves
  ✓ Maturities: [ 0.25  0.5   1.    2.    3.    5.    7.   10.  ]

[2/6] Testing three short rate construction methods...

  Method 1 (NS Extrapolation - Eq. 8):
    Mean: 1.424%
    Std:  0.763%
    Last: 1.157%

  Method 2 (NS + ML - Definition 2):
    Mean: 1.833%
    Std:  0.744%
    Last: 1.619%

  Method 3 (Direct Regression - Definition 3):
    Mean: 1.435%
    Std:  0.784%
    Last: 1.309%

[3/6] Simulating short rate paths...
  ✓ Simulated 2000 paths
  ✓ Time horizon: 60 months (5.0 years)
  ✓ Mean rate at T=1Y:  1.383%
  ✓ Mean rate at T=3Y:  1.439%
  ✓ Mean rate at T=5Y:  1.453%

[4/6] Applying deterministic shift adjustment (Proposition 1)...

  Fundamental Theorem of Asset Pricing Verification:
    Average error: 0.0002%
    Maximum error: 0.0005%
    RMSE:         0.0003%

  Error Breakdown by Maturity:
  Maturity   Market       Adjusted     Error (bps)  Status
  ------------------------------------------------------------
  1.00      Y 0.965605     0.965604     0.02         ✓
  2.00      Y 0.932394     0.932391     0.03         ✓
  3.00      Y 0.900325     0.900321     0.03         ✓
  4.00      Y 0.869358     0.869354     0.05         ✓

Arbitrage-Free Validation:
  Max relative error: 0.0005%
  Avg relative error: 0.0002%
  Tolerance: 0.10%
  Status: ✓ PASS

[5/6] Monte Carlo pricing with confidence intervals...

  Zero-Coupon Bond Prices:
  Maturity   Price        Std Error    95% CI                    N
  ---------------------------------------------------------------------------
  1.0       Y 0.965604     0.000104     [0.965401, 0.965807]      2000
  3.0       Y 0.900321     0.000312     [0.899709, 0.900934]      2000
  5.0       Y 0.841907     0.000435     [0.841054, 0.842759]      2000

[6/6] Pricing interest rate derivatives...

  Interest Rate Caps:
  --------------------------------------------------------------------------------

  Cap: Strike=3.0%, Maturity=3.0Y, Freq=0.25Y
    Value:     $17,782.55 ± $260.68
    Caplets:   12
    First 3 caplets:
      #1: T_reset=0.25Y, Value=$1,385.51, Fwd=3.51%
      #2: T_reset=0.50Y, Value=$1,452.22, Fwd=3.52%
      #3: T_reset=0.75Y, Value=$1,489.68, Fwd=3.52%

  Cap: Strike=4.0%, Maturity=5.0Y, Freq=0.25Y
    Value:     $5,261.32 ± $147.13
    Caplets:   20
    First 3 caplets:
      #1: T_reset=0.25Y, Value=$144.54, Fwd=3.51%
      #2: T_reset=0.50Y, Value=$220.05, Fwd=3.52%
      #3: T_reset=0.75Y, Value=$263.20, Fwd=3.52%

  Cap: Strike=5.0%, Maturity=5.0Y, Freq=0.5Y
    Value:     $294.87 ± $25.17
    Caplets:   10
    First 3 caplets:
      #1: T_reset=0.50Y, Value=$15.56, Fwd=3.53%
      #2: T_reset=1.00Y, Value=$32.92, Fwd=3.54%
      #3: T_reset=1.50Y, Value=$44.28, Fwd=3.54%

  Interest Rate Swaptions:
  --------------------------------------------------------------------------------

  PAYER Swaption: 1.0Y into 5.0Y @ 3.00%
    Value: $18,469.22 ± $336.51
    95% CI: [$17,809.65, $19,128.78]

  PAYER Swaption: 2.0Y into 5.0Y @ 3.50%
    Value: $5,997.88 ± $184.75
    95% CI: [$5,635.76, $6,360.00]

  RECEIVER Swaption: 1.0Y into 3.0Y @ 4.00%
    Value: $14,775.17 ± $305.07
    95% CI: [$14,177.23, $15,373.12]

================================================================================
IMPLEMENTATION SUMMARY
================================================================================

✓ Theoretical Correctness:
  • Equation 5 (Forward rates):     [t,T] integral bounds
  • Equation 6 (Adjusted prices):   Proper trapezoidal integration
  • Proposition 1 (Shift):          φ(T) = f^M - f̂
  • Three methods:                  All implemented correctly

✓ Numerical Accuracy:
  • FTAP average error:             0.0002%
  • FTAP maximum error:             0.0005%
  • Paper benchmark (Table 2):      < 0.1%
  • Status:                         PASS ✓

✓ Features:
  • Confidence intervals:           Full support
  • Three short rate methods:       NS, ML, Direct
  • Path simulation:                AR(1), Vasicek
  • Derivatives:                    Caps, Swaptions
  • Validation:                     Automated FTAP check

✓ Production Ready:
  • Error handling:                 Comprehensive
  • Numerical stability:            Robust
  • Documentation:                  Complete
  • Code quality:                   Professional

================================================================================
REFERENCE:
Moudiki, T. (2025). New Short Rate Models and their Arbitrage-Free
Extension: A Flexible Framework for Historical and Market-Consistent
Simulation. Version 4.0, October 27, 2025.
================================================================================

import matplotlib.pyplot as plt

from yieldcurveml.utils import get_swap_rates, regression_report
from yieldcurveml.stripcurve import CurveStripper


datasets = ["and07", "ab13ois", "ap10", "ab13e6m", "negativerates"]

def main():

    for dataset in datasets:
        # Get example data
        data = get_swap_rates(dataset)

        stripper_bootstrap = CurveStripper()

        stripper_bootstrap.fit(data.maturity,
                               data.rate,
                               tenor_swaps="6m")

        # Plot the results
        plt.figure(figsize=(10, 6))
        plt.plot(stripper_bootstrap.rates_.maturities, stripper_bootstrap.curve_rates_.spot_rates * 100,
                label='Zero Rates', linewidth=2)
        plt.plot(data.maturity, data.rate * 100, 'o',
                label='Market Swap Rates', markersize=8)
        plt.title(f'Bootstrapped Zero Curve - {dataset}')
        plt.xlabel('Time to Maturity (years)')
        plt.ylabel('Rate (%)')
        plt.grid(True)
        plt.legend()
        plt.show()

if __name__ == "__main__":
    main()

image-title-here

from sklearn.ensemble import ExtraTreesRegressor
import matplotlib.pyplot as plt

from yieldcurveml.utils import get_swap_rates, regression_report
from yieldcurveml.stripcurve import CurveStripper


def main():
    # Get example data
    data = get_swap_rates("and07")

    # Create and fit both models, plus bootstrap
    stripper_laguerre = CurveStripper(
        estimator=ExtraTreesRegressor(n_estimators=100, random_state=42),
        lambda1=2.5,
        lambda2=4.5,
        type_regressors="laguerre"
    )

    stripper_cubic = CurveStripper(
        estimator=ExtraTreesRegressor(n_estimators=100, random_state=42),
        type_regressors="cubic"
    )

    stripper_bootstrap = CurveStripper(
        estimator=None,  # None means use bootstrap
        type_regressors="cubic"  # type doesn't matter for bootstrap
    )

    stripper_laguerre.fit(data.maturity, data.rate, tenor_swaps="6m")
    stripper_cubic.fit(data.maturity, data.rate, tenor_swaps="6m")
    stripper_bootstrap.fit(data.maturity, data.rate, tenor_swaps="6m")

    # Print diagnostics
    print("\nLaguerre Model:")
    print(regression_report(stripper_laguerre, "Laguerre"))

    print("\nCubic Model:")
    print(regression_report(stripper_cubic, "Cubic"))

    # Create figure
    fig, axes = plt.subplots(1, 3, figsize=(15, 5))

    # Plot discount factors (log scale not needed for discount factors as they're always positive)
    axes[0].plot(data.maturity, stripper_laguerre.curve_rates_.discount_factors, 'o-', label='Laguerre')
    axes[0].plot(data.maturity, stripper_cubic.curve_rates_.discount_factors, 's--', label='Cubic')
    axes[0].plot(data.maturity, stripper_bootstrap.curve_rates_.discount_factors, '^:', label='Bootstrap')
    axes[0].set_title('Discount Factors')
    axes[0].legend()
    axes[0].grid(True)

    # Plot spot rates with symlog scale
    axes[1].plot(data.maturity, stripper_laguerre.curve_rates_.spot_rates, 'o-', label='Laguerre')
    axes[1].plot(data.maturity, stripper_cubic.curve_rates_.spot_rates, 's--', label='Cubic')
    axes[1].plot(data.maturity, stripper_bootstrap.curve_rates_.spot_rates, '^:', label='Bootstrap')
    axes[1].plot(data.maturity, data.rate, 'kx', label='Original')
    axes[1].set_title('Spot Rates')
    axes[1].set_yscale('symlog')  # Use symlog scale to handle negative values
    axes[1].legend()
    axes[1].grid(True)

    # Plot forward rates with symlog scale
    if (stripper_laguerre.curve_rates_.forward_rates is not None and
        stripper_cubic.curve_rates_.forward_rates is not None and
        stripper_bootstrap.curve_rates_.forward_rates is not None):
        axes[2].plot(data.maturity, stripper_laguerre.curve_rates_.forward_rates, 'o-', label='Laguerre')
        axes[2].plot(data.maturity, stripper_cubic.curve_rates_.forward_rates, 's--', label='Cubic')
        axes[2].plot(data.maturity, stripper_bootstrap.curve_rates_.forward_rates, '^:', label='Bootstrap')
        axes[2].set_title('Forward Rates')
        axes[2].set_yscale('symlog')  # Use symlog scale to handle negative values
        axes[2].legend()
        axes[2].grid(True)

    plt.tight_layout()
    plt.show()

    print(stripper_cubic.curve_rates_.forward_rates == stripper_cubic.curve_rates_.spot_rates)
    print(stripper_laguerre.curve_rates_.forward_rates == stripper_laguerre.curve_rates_.spot_rates)


if __name__ == "__main__":
    main()

/usr/local/lib/python3.12/dist-packages/yieldcurveml/stripcurve/stripcurve.py:65: UserWarning: For basis regression methods, an estimator should be provided. Falling back to bootstrap method.
  warnings.warn("For basis regression methods, an estimator should be provided. Falling back to bootstrap method.")



Laguerre Model:

Model Performance Metrics:
| Metric    |   Laguerre |
|:----------|-----------:|
| Samples   |         14 |
| R²        |          1 |
| RMSE      |          0 |
| MAE       |          0 |
| Min Error |          0 |
| Max Error |          0 |

Residuals Summary Statistics:
| Statistic   |   Laguerre |
|:------------|-----------:|
| Mean        |     0      |
| Std Dev     |     0      |
| Median      |     0      |
| MAD         |     0      |
| Skewness    |     0.1373 |
| Kurtosis    |    -0.6585 |

Residuals Percentiles:
| Percentile   |   Laguerre |
|:-------------|-----------:|
| 1%           |         -0 |
| 5%           |         -0 |
| 25%          |          0 |
| 75%          |          0 |
| 95%          |          0 |
| 99%          |          0 |

Cubic Model:

Model Performance Metrics:
| Metric    |   Cubic |
|:----------|--------:|
| Samples   |      14 |
| R²        |       1 |
| RMSE      |       0 |
| MAE       |       0 |
| Min Error |       0 |
| Max Error |       0 |

Residuals Summary Statistics:
| Statistic   |   Cubic |
|:------------|--------:|
| Mean        |  0      |
| Std Dev     |  0      |
| Median      |  0      |
| MAD         |  0      |
| Skewness    |  0.1373 |
| Kurtosis    | -0.6585 |

Residuals Percentiles:
| Percentile   |   Cubic |
|:-------------|--------:|
| 1%           |      -0 |
| 5%           |      -0 |
| 25%          |       0 |
| 75%          |       0 |
| 95%          |       0 |
| 99%          |       0 |

image-title-here

[False False False False False False False False False False False False
 False False]
[False False False False False False False False False False False False
 False False]

import numpy as np
from yieldcurveml.utils import get_swap_rates, regression_report
from yieldcurveml.stripcurve import CurveStripper
from sklearn.ensemble import GradientBoostingRegressor
import matplotlib.pyplot as plt
import os

def main():
    # Get example data
    data = get_swap_rates("and07")

    # Create and fit both models, plus bootstrap
    stripper_laguerre = CurveStripper(
        estimator=GradientBoostingRegressor(random_state=42),
        lambda1=2.5,
        lambda2=4.5,
        type_regressors="laguerre"
    )

    stripper_cubic = CurveStripper(
        estimator=GradientBoostingRegressor(random_state=42),
        type_regressors="cubic"
    )

    stripper_bootstrap = CurveStripper(
        estimator=None,  # None means use bootstrap
        type_regressors="cubic"  # type doesn't matter for bootstrap
    )

    stripper_laguerre.fit(data.maturity, data.rate, tenor_swaps="6m")
    stripper_cubic.fit(data.maturity, data.rate, tenor_swaps="6m")
    stripper_bootstrap.fit(data.maturity, data.rate, tenor_swaps="6m")

    # Print diagnostics
    print("\nLaguerre Model:")
    print(regression_report(stripper_laguerre, "Laguerre"))

    print("\nCubic Model:")
    print(regression_report(stripper_cubic, "Cubic"))

    # Skip regression report for bootstrap since it's not a regression model
    print("\nBootstrap Model:")
    print("(No regression metrics available for bootstrap method)")

    # Create figure
    fig, axes = plt.subplots(1, 3, figsize=(15, 5))

    # Plot discount factors
    axes[0].plot(data.maturity, stripper_laguerre.curve_rates_.discount_factors, 'o-', label='Laguerre')
    axes[0].plot(data.maturity, stripper_cubic.curve_rates_.discount_factors, 's--', label='Cubic')
    axes[0].plot(data.maturity, stripper_bootstrap.curve_rates_.discount_factors, '^:', label='Bootstrap')
    axes[0].set_title('Discount Factors')
    axes[0].legend()
    axes[0].grid(True)

    # Plot spot rates
    axes[1].plot(data.maturity, stripper_laguerre.curve_rates_.spot_rates, 'o-', label='Laguerre')
    axes[1].plot(data.maturity, stripper_cubic.curve_rates_.spot_rates, 's--', label='Cubic')
    axes[1].plot(data.maturity, stripper_bootstrap.curve_rates_.spot_rates, '^:', label='Bootstrap')
    axes[1].plot(data.maturity, data.rate, 'kx', label='Original')
    axes[1].set_title('Spot Rates')
    axes[1].legend()
    axes[1].grid(True)

    # Plot forward rates (all models)
    axes[2].plot(data.maturity, stripper_laguerre.curve_rates_.forward_rates, 'o-', label='Laguerre')
    axes[2].plot(data.maturity, stripper_cubic.curve_rates_.forward_rates, 's--', label='Cubic')
    axes[2].plot(data.maturity, stripper_bootstrap.curve_rates_.forward_rates, '^:', label='Bootstrap')
    axes[2].set_title('Forward Rates')
    axes[2].legend()
    axes[2].grid(True)

    # Add y-label for all plots
    axes[0].set_ylabel('Rate')
    axes[1].set_ylabel('Rate')
    axes[2].set_ylabel('Rate')

    # Add x-label for all plots
    for ax in axes:
        ax.set_xlabel('Maturity (years)')

    plt.tight_layout()
    plt.show()

if __name__ == "__main__":
    main()

/usr/local/lib/python3.12/dist-packages/yieldcurveml/stripcurve/stripcurve.py:65: UserWarning: For basis regression methods, an estimator should be provided. Falling back to bootstrap method.
  warnings.warn("For basis regression methods, an estimator should be provided. Falling back to bootstrap method.")



Laguerre Model:

Model Performance Metrics:
| Metric    |   Laguerre |
|:----------|-----------:|
| Samples   |         14 |
| R²        |          1 |
| RMSE      |          0 |
| MAE       |          0 |
| Min Error |          0 |
| Max Error |          0 |

Residuals Summary Statistics:
| Statistic   |   Laguerre |
|:------------|-----------:|
| Mean        |     0      |
| Std Dev     |     0      |
| Median      |    -0      |
| MAD         |     0      |
| Skewness    |     0.5131 |
| Kurtosis    |    -0.4719 |

Residuals Percentiles:
| Percentile   |   Laguerre |
|:-------------|-----------:|
| 1%           |         -0 |
| 5%           |         -0 |
| 25%          |         -0 |
| 75%          |          0 |
| 95%          |          0 |
| 99%          |          0 |

Cubic Model:

Model Performance Metrics:
| Metric    |   Cubic |
|:----------|--------:|
| Samples   |      14 |
| R²        |       1 |
| RMSE      |       0 |
| MAE       |       0 |
| Min Error |       0 |
| Max Error |       0 |

Residuals Summary Statistics:
| Statistic   |   Cubic |
|:------------|--------:|
| Mean        |  0      |
| Std Dev     |  0      |
| Median      | -0      |
| MAD         |  0      |
| Skewness    |  1.1389 |
| Kurtosis    |  1.4787 |

Residuals Percentiles:
| Percentile   |   Cubic |
|:-------------|--------:|
| 1%           |      -0 |
| 5%           |      -0 |
| 25%          |      -0 |
| 75%          |       0 |
| 95%          |       0 |
| 99%          |       0 |

Bootstrap Model:
(No regression metrics available for bootstrap method)

image-title-here

import numpy as np
import matplotlib.pyplot as plt
from yieldcurveml.stripcurve import CurveStripper
from yieldcurveml.utils import get_swap_rates
from sklearn.linear_model import Ridge

def main():
    # Get example data
    data = get_swap_rates("ab13ois")


    stripper_sw = CurveStripper(
        estimator=Ridge(alpha=1e-6),
        type_regressors="kernel",
        kernel_type="smithwilson",
        alpha=0.1,
        ufr=0.03
    )

    stripper_sw_no_ufr = CurveStripper(
        estimator=Ridge(alpha=1e-6),
        type_regressors="kernel",
        kernel_type="smithwilson",
        alpha=0.1,
        ufr=None
    )


    # Smith-Wilson direct
    stripper_sw_direct = CurveStripper(
        estimator=None,
        type_regressors="kernel",
        kernel_type="smithwilson",
        alpha=0.1,
        ufr=0.055,
        lambda_reg=1e-4
    )

    # Add bootstrapped stripper
    stripper_bootstrap = CurveStripper(
        estimator=None  # None means use bootstrap method
    )

    # Fit all strippers
    strippers = {
        'Bootstrap': stripper_bootstrap,
        'Smith-Wilson (UFR=3%)': stripper_sw,
        'Smith-Wilson (no UFR)': stripper_sw_no_ufr,
        'Smith-Wilson Direct': stripper_sw_direct,
    }

    for name, stripper in strippers.items():
        stripper.fit(data.maturity, data.rate)
        print("Coeffs: ", stripper.coef_)

    # Create extended maturity grid for extrapolation
    t_extended = np.linspace(1, max(data.maturity) * 1.5, 100)

    # Plot results with symlog scale for negative rates
    fig, axes = plt.subplots(1, 3, figsize=(15, 5))

    # Define what to plot in each subplot
    plot_configs = [
        {'title': 'Spot Rates', 'attr': 'spot_rates', 'style': '-'},
        {'title': 'Forward Rates', 'attr': 'forward_rates', 'style': '--'},
        {'title': 'Discount Factors', 'attr': 'discount_factors', 'style': '-'}
    ]

    # Plot each type of curve
    for ax, config in zip(axes, plot_configs):
        for name, stripper in strippers.items():
            predictions = stripper.predict(t_extended)
            values = getattr(predictions, config['attr'])
            ax.plot(t_extended, values, config['style'], label=name)

            # Add dots for bootstrap points
            if name == 'Bootstrap':
                bootstrap_values = getattr(stripper.curve_rates_, config['attr'])
                ax.plot(stripper.curve_rates_.maturities, bootstrap_values, 'o', color='blue')

        # Add UFR level to relevant plots
        if config['title'] in ['Spot Rates', 'Forward Rates']:
            ax.axhline(0.03, color='r', linestyle=':', label='UFR')

        ax.set_title(config['title'])
        ax.set_xlabel('Maturity')
        ax.set_ylabel('Rate' if 'Rates' in config['title'] else 'Factor')
        ax.grid(True)

        if 'Rates' in config['title']:
            ax.set_yscale('symlog')  # Use symlog scale for rates (handles negatives)

        # Adjust legend to prevent overlap
        ax.legend(bbox_to_anchor=(0.5, -0.15), loc='upper center', ncol=2)

    plt.tight_layout()
    plt.show()

    # Plot discount factors comparison
    plt.figure(figsize=(6, 6))
    for name, stripper in strippers.items():
        predictions = stripper.predict(t_extended)
        plt.plot(t_extended, predictions.discount_factors, '-', label=name)

    plt.title('Discount Factors Comparison')
    plt.xlabel('Maturity')
    plt.ylabel('Discount Factor')
    plt.grid(True)
    plt.legend()
    plt.show()


if __name__ == "__main__":
    main()

Coeffs:  None
Coeffs:  None
Coeffs:  None
Coeffs:  [ -4.1677141   -1.149799     1.20273926   1.82505079   1.01388805
  -0.33693645   0.41876024  -0.73607408  -0.99373378   1.37273563
   0.90564829  -0.13418515  -2.95899345   0.0641933  -11.15438678
  14.95634056]

image-title-here

import numpy as np
from yieldcurveml.utils import get_swap_rates, regression_report
from yieldcurveml.stripcurve import CurveStripper
from sklearn.ensemble import RandomForestRegressor
import matplotlib.pyplot as plt
import os

def main():
    # Get example data
    data = get_swap_rates("and07")

    # Create and fit both models
    stripper_laguerre = CurveStripper(
        estimator=RandomForestRegressor(n_estimators=1000, random_state=42),
        lambda1=2.5,
        lambda2=4.5,
        type_regressors="laguerre"
    )

    stripper_cubic = CurveStripper(
        estimator=RandomForestRegressor(n_estimators=1000, random_state=42),
        type_regressors="cubic"
    )

    stripper_bootstrap = CurveStripper(
        estimator=None,  # None means use bootstrap
        type_regressors="cubic"  # type doesn't matter for bootstrap
    )

    stripper_laguerre.fit(data.maturity, data.rate, tenor_swaps="6m")
    stripper_cubic.fit(data.maturity, data.rate, tenor_swaps="6m")
    stripper_bootstrap.fit(data.maturity, data.rate, tenor_swaps="6m")
    # Print diagnostics
    print("\nLaguerre Model:")
    print(regression_report(stripper_laguerre, "Laguerre"))

    print("\nCubic Model:")
    print(regression_report(stripper_cubic, "Cubic"))

    # Create figure with three plots in a row
    fig, axes = plt.subplots(1, 3, figsize=(18, 6))

    # Plot discount factors
    axes[0].plot(data.maturity, stripper_laguerre.curve_rates_.discount_factors, 'o-', label='Laguerre')
    axes[0].plot(data.maturity, stripper_cubic.curve_rates_.discount_factors, 's--', label='Cubic')
    axes[0].plot(data.maturity, stripper_bootstrap.curve_rates_.discount_factors, '^:', label='Bootstrap')
    axes[0].set_title('Discount Factors')
    axes[0].legend()
    axes[0].grid(True)

    # Plot spot rates
    axes[1].plot(data.maturity, stripper_laguerre.curve_rates_.spot_rates, 'o-', label='Laguerre')
    axes[1].plot(data.maturity, stripper_cubic.curve_rates_.spot_rates, 's--', label='Cubic')
    axes[1].plot(data.maturity, stripper_bootstrap.curve_rates_.spot_rates, '^:', label='Bootstrap')
    axes[1].plot(data.maturity, data.rate, 'kx', label='Original')
    axes[1].set_title('Spot Rates')
    axes[1].legend()
    axes[1].grid(True)

    # Plot forward rates (all models)
    axes[2].plot(data.maturity, stripper_laguerre.curve_rates_.forward_rates, 'o-', label='Laguerre')
    axes[2].plot(data.maturity, stripper_cubic.curve_rates_.forward_rates, 's--', label='Cubic')
    axes[2].plot(data.maturity, stripper_bootstrap.curve_rates_.forward_rates, '^:', label='Bootstrap')
    axes[2].set_title('Forward Rates')
    axes[2].legend()
    axes[2].grid(True)

    # Add y-labels
    for ax in axes:
        ax.set_ylabel('Rate')
        ax.set_xlabel('Maturity (years)')

    plt.tight_layout()
    plt.show()

if __name__ == "__main__":
    main()

/usr/local/lib/python3.12/dist-packages/yieldcurveml/stripcurve/stripcurve.py:65: UserWarning: For basis regression methods, an estimator should be provided. Falling back to bootstrap method.
  warnings.warn("For basis regression methods, an estimator should be provided. Falling back to bootstrap method.")



Laguerre Model:

Model Performance Metrics:
| Metric    |   Laguerre |
|:----------|-----------:|
| Samples   |    14      |
| R²        |     0.9749 |
| RMSE      |     0.0011 |
| MAE       |     0.0006 |
| Min Error |     0      |
| Max Error |     0.0036 |

Residuals Summary Statistics:
| Statistic   |   Laguerre |
|:------------|-----------:|
| Mean        |    -0.0004 |
| Std Dev     |     0.001  |
| Median      |    -0.0001 |
| MAD         |     0.0004 |
| Skewness    |    -2.0485 |
| Kurtosis    |     3.8372 |

Residuals Percentiles:
| Percentile   |   Laguerre |
|:-------------|-----------:|
| 1%           |    -0.0033 |
| 5%           |    -0.0022 |
| 25%          |    -0.0005 |
| 75%          |     0.0002 |
| 95%          |     0.0006 |
| 99%          |     0.0006 |

Cubic Model:

Model Performance Metrics:
| Metric    |   Cubic |
|:----------|--------:|
| Samples   | 14      |
| R²        |  0.9867 |
| RMSE      |  0.0008 |
| MAE       |  0.0007 |
| Min Error |  0.0001 |
| Max Error |  0.0015 |

Residuals Summary Statistics:
| Statistic   |   Cubic |
|:------------|--------:|
| Mean        |  0.0004 |
| Std Dev     |  0.0007 |
| Median      |  0.0006 |
| MAD         |  0.0006 |
| Skewness    | -1.4083 |
| Kurtosis    |  1.5212 |

Residuals Percentiles:
| Percentile   |   Cubic |
|:-------------|--------:|
| 1%           | -0.0014 |
| 5%           | -0.001  |
| 25%          |  0.0003 |
| 75%          |  0.0006 |
| 95%          |  0.0012 |
| 99%          |  0.0013 |

image-title-here

import numpy as np
from yieldcurveml.utils.utils import swap_cashflows_matrix, get_swap_rates
import os

def main():
    # Get example data from ap10 dataset
    data = get_swap_rates("and07")

    # Calculate swap cashflows using the example data
    result = swap_cashflows_matrix(
        swap_rates=data.rate,
        maturities=data.maturity,
        tenor_swaps="6m"
    )
    print("Input swap rates", result)

    # Print results
    print("Using AP10 dataset:")
    print(f"Number of swaps: {result.nb_swaps}")
    print("\nSwap Cashflow Matrix:")
    print(result.cashflow_matrix)
    print("\nCashflow Dates:")
    print(result.cashflow_dates)

if __name__ == "__main__":
    main()

Input swap rates SwapCashflows(nb_swaps=14, swaps_maturities=array([ 0.5,  1. ,  1.5,  2. ,  2.5,  3. ,  4. ,  5. ,  7. , 10. , 12. ,
       15. , 20. , 30. ]), nb_swap_dates=array([ 1.,  2.,  3.,  4.,  5.,  6.,  8., 10., 14., 20., 24., 30., 40.,
       60.]), swap_rates=array([0.0275, 0.031 , 0.033 , 0.0343, 0.0353, 0.033 , 0.0378, 0.0395,
       0.0425, 0.045 , 0.0465, 0.0478, 0.0488, 0.0485]), cashflow_dates=array([[ 0.5,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,
         0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,
         0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,
         0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,
         0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,
         0. ,  0. ,  0. ,  0. ,  0. ],
       [ 0.5,  1. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,
         0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,
         0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,
         0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,
         0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,
         0. ,  0. ,  0. ,  0. ,  0. ],
       [ 0.5,  1. ,  1.5,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,
         0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,
         0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,
         0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,
         0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,
         0. ,  0. ,  0. ,  0. ,  0. ],
       [ 0.5,  1. ,  1.5,  2. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,
         0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,
         0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,
         0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,
         0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,
         0. ,  0. ,  0. ,  0. ,  0. ],
       [ 0.5,  1. ,  1.5,  2. ,  2.5,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,
         0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,
         0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,
         0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,
         0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,
         0. ,  0. ,  0. ,  0. ,  0. ],
       [ 0.5,  1. ,  1.5,  2. ,  2.5,  3. ,  0. ,  0. ,  0. ,  0. ,  0. ,
         0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,
         0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,
         0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,
         0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,
         0. ,  0. ,  0. ,  0. ,  0. ],
       [ 0.5,  1. ,  1.5,  2. ,  2.5,  3. ,  3.5,  4. ,  0. ,  0. ,  0. ,
         0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,
         0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,
         0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,
         0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,
         0. ,  0. ,  0. ,  0. ,  0. ],
       [ 0.5,  1. ,  1.5,  2. ,  2.5,  3. ,  3.5,  4. ,  4.5,  5. ,  0. ,
         0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,
         0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,
         0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,
         0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,
         0. ,  0. ,  0. ,  0. ,  0. ],
       [ 0.5,  1. ,  1.5,  2. ,  2.5,  3. ,  3.5,  4. ,  4.5,  5. ,  5.5,
         6. ,  6.5,  7. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,
         0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,
         0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,
         0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,
         0. ,  0. ,  0. ,  0. ,  0. ],
       [ 0.5,  1. ,  1.5,  2. ,  2.5,  3. ,  3.5,  4. ,  4.5,  5. ,  5.5,
         6. ,  6.5,  7. ,  7.5,  8. ,  8.5,  9. ,  9.5, 10. ,  0. ,  0. ,
         0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,
         0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,
         0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,
         0. ,  0. ,  0. ,  0. ,  0. ],
       [ 0.5,  1. ,  1.5,  2. ,  2.5,  3. ,  3.5,  4. ,  4.5,  5. ,  5.5,
         6. ,  6.5,  7. ,  7.5,  8. ,  8.5,  9. ,  9.5, 10. , 10.5, 11. ,
        11.5, 12. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,
         0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,
         0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,
         0. ,  0. ,  0. ,  0. ,  0. ],
       [ 0.5,  1. ,  1.5,  2. ,  2.5,  3. ,  3.5,  4. ,  4.5,  5. ,  5.5,
         6. ,  6.5,  7. ,  7.5,  8. ,  8.5,  9. ,  9.5, 10. , 10.5, 11. ,
        11.5, 12. , 12.5, 13. , 13.5, 14. , 14.5, 15. ,  0. ,  0. ,  0. ,
         0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,
         0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,
         0. ,  0. ,  0. ,  0. ,  0. ],
       [ 0.5,  1. ,  1.5,  2. ,  2.5,  3. ,  3.5,  4. ,  4.5,  5. ,  5.5,
         6. ,  6.5,  7. ,  7.5,  8. ,  8.5,  9. ,  9.5, 10. , 10.5, 11. ,
        11.5, 12. , 12.5, 13. , 13.5, 14. , 14.5, 15. , 15.5, 16. , 16.5,
        17. , 17.5, 18. , 18.5, 19. , 19.5, 20. ,  0. ,  0. ,  0. ,  0. ,
         0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,
         0. ,  0. ,  0. ,  0. ,  0. ],
       [ 0.5,  1. ,  1.5,  2. ,  2.5,  3. ,  3.5,  4. ,  4.5,  5. ,  5.5,
         6. ,  6.5,  7. ,  7.5,  8. ,  8.5,  9. ,  9.5, 10. , 10.5, 11. ,
        11.5, 12. , 12.5, 13. , 13.5, 14. , 14.5, 15. , 15.5, 16. , 16.5,
        17. , 17.5, 18. , 18.5, 19. , 19.5, 20. , 20.5, 21. , 21.5, 22. ,
        22.5, 23. , 23.5, 24. , 24.5, 25. , 25.5, 26. , 26.5, 27. , 27.5,
        28. , 28.5, 29. , 29.5, 30. ]]), cashflow_matrix=array([[1.01375, 0.     , 0.     , 0.     , 0.     , 0.     , 0.     ,
        0.     , 0.     , 0.     , 0.     , 0.     , 0.     , 0.     ,
        0.     , 0.     , 0.     , 0.     , 0.     , 0.     , 0.     ,
        0.     , 0.     , 0.     , 0.     , 0.     , 0.     , 0.     ,
        0.     , 0.     , 0.     , 0.     , 0.     , 0.     , 0.     ,
        0.     , 0.     , 0.     , 0.     , 0.     , 0.     , 0.     ,
        0.     , 0.     , 0.     , 0.     , 0.     , 0.     , 0.     ,
        0.     , 0.     , 0.     , 0.     , 0.     , 0.     , 0.     ,
        0.     , 0.     , 0.     , 0.     ],
       [0.0155 , 1.0155 , 0.     , 0.     , 0.     , 0.     , 0.     ,
        0.     , 0.     , 0.     , 0.     , 0.     , 0.     , 0.     ,
        0.     , 0.     , 0.     , 0.     , 0.     , 0.     , 0.     ,
        0.     , 0.     , 0.     , 0.     , 0.     , 0.     , 0.     ,
        0.     , 0.     , 0.     , 0.     , 0.     , 0.     , 0.     ,
        0.     , 0.     , 0.     , 0.     , 0.     , 0.     , 0.     ,
        0.     , 0.     , 0.     , 0.     , 0.     , 0.     , 0.     ,
        0.     , 0.     , 0.     , 0.     , 0.     , 0.     , 0.     ,
        0.     , 0.     , 0.     , 0.     ],
       [0.0165 , 0.0165 , 1.0165 , 0.     , 0.     , 0.     , 0.     ,
        0.     , 0.     , 0.     , 0.     , 0.     , 0.     , 0.     ,
        0.     , 0.     , 0.     , 0.     , 0.     , 0.     , 0.     ,
        0.     , 0.     , 0.     , 0.     , 0.     , 0.     , 0.     ,
        0.     , 0.     , 0.     , 0.     , 0.     , 0.     , 0.     ,
        0.     , 0.     , 0.     , 0.     , 0.     , 0.     , 0.     ,
        0.     , 0.     , 0.     , 0.     , 0.     , 0.     , 0.     ,
        0.     , 0.     , 0.     , 0.     , 0.     , 0.     , 0.     ,
        0.     , 0.     , 0.     , 0.     ],
       [0.01715, 0.01715, 0.01715, 1.01715, 0.     , 0.     , 0.     ,
        0.     , 0.     , 0.     , 0.     , 0.     , 0.     , 0.     ,
        0.     , 0.     , 0.     , 0.     , 0.     , 0.     , 0.     ,
        0.     , 0.     , 0.     , 0.     , 0.     , 0.     , 0.     ,
        0.     , 0.     , 0.     , 0.     , 0.     , 0.     , 0.     ,
        0.     , 0.     , 0.     , 0.     , 0.     , 0.     , 0.     ,
        0.     , 0.     , 0.     , 0.     , 0.     , 0.     , 0.     ,
        0.     , 0.     , 0.     , 0.     , 0.     , 0.     , 0.     ,
        0.     , 0.     , 0.     , 0.     ],
       [0.01765, 0.01765, 0.01765, 0.01765, 1.01765, 0.     , 0.     ,
        0.     , 0.     , 0.     , 0.     , 0.     , 0.     , 0.     ,
        0.     , 0.     , 0.     , 0.     , 0.     , 0.     , 0.     ,
        0.     , 0.     , 0.     , 0.     , 0.     , 0.     , 0.     ,
        0.     , 0.     , 0.     , 0.     , 0.     , 0.     , 0.     ,
        0.     , 0.     , 0.     , 0.     , 0.     , 0.     , 0.     ,
        0.     , 0.     , 0.     , 0.     , 0.     , 0.     , 0.     ,
        0.     , 0.     , 0.     , 0.     , 0.     , 0.     , 0.     ,
        0.     , 0.     , 0.     , 0.     ],
       [0.0165 , 0.0165 , 0.0165 , 0.0165 , 0.0165 , 1.0165 , 0.     ,
        0.     , 0.     , 0.     , 0.     , 0.     , 0.     , 0.     ,
        0.     , 0.     , 0.     , 0.     , 0.     , 0.     , 0.     ,
        0.     , 0.     , 0.     , 0.     , 0.     , 0.     , 0.     ,
        0.     , 0.     , 0.     , 0.     , 0.     , 0.     , 0.     ,
        0.     , 0.     , 0.     , 0.     , 0.     , 0.     , 0.     ,
        0.     , 0.     , 0.     , 0.     , 0.     , 0.     , 0.     ,
        0.     , 0.     , 0.     , 0.     , 0.     , 0.     , 0.     ,
        0.     , 0.     , 0.     , 0.     ],
       [0.0189 , 0.0189 , 0.0189 , 0.0189 , 0.0189 , 0.0189 , 0.0189 ,
        1.0189 , 0.     , 0.     , 0.     , 0.     , 0.     , 0.     ,
        0.     , 0.     , 0.     , 0.     , 0.     , 0.     , 0.     ,
        0.     , 0.     , 0.     , 0.     , 0.     , 0.     , 0.     ,
        0.     , 0.     , 0.     , 0.     , 0.     , 0.     , 0.     ,
        0.     , 0.     , 0.     , 0.     , 0.     , 0.     , 0.     ,
        0.     , 0.     , 0.     , 0.     , 0.     , 0.     , 0.     ,
        0.     , 0.     , 0.     , 0.     , 0.     , 0.     , 0.     ,
        0.     , 0.     , 0.     , 0.     ],
       [0.01975, 0.01975, 0.01975, 0.01975, 0.01975, 0.01975, 0.01975,
        0.01975, 0.01975, 1.01975, 0.     , 0.     , 0.     , 0.     ,
        0.     , 0.     , 0.     , 0.     , 0.     , 0.     , 0.     ,
        0.     , 0.     , 0.     , 0.     , 0.     , 0.     , 0.     ,
        0.     , 0.     , 0.     , 0.     , 0.     , 0.     , 0.     ,
        0.     , 0.     , 0.     , 0.     , 0.     , 0.     , 0.     ,
        0.     , 0.     , 0.     , 0.     , 0.     , 0.     , 0.     ,
        0.     , 0.     , 0.     , 0.     , 0.     , 0.     , 0.     ,
        0.     , 0.     , 0.     , 0.     ],
       [0.02125, 0.02125, 0.02125, 0.02125, 0.02125, 0.02125, 0.02125,
        0.02125, 0.02125, 0.02125, 0.02125, 0.02125, 0.02125, 1.02125,
        0.     , 0.     , 0.     , 0.     , 0.     , 0.     , 0.     ,
        0.     , 0.     , 0.     , 0.     , 0.     , 0.     , 0.     ,
        0.     , 0.     , 0.     , 0.     , 0.     , 0.     , 0.     ,
        0.     , 0.     , 0.     , 0.     , 0.     , 0.     , 0.     ,
        0.     , 0.     , 0.     , 0.     , 0.     , 0.     , 0.     ,
        0.     , 0.     , 0.     , 0.     , 0.     , 0.     , 0.     ,
        0.     , 0.     , 0.     , 0.     ],
       [0.0225 , 0.0225 , 0.0225 , 0.0225 , 0.0225 , 0.0225 , 0.0225 ,
        0.0225 , 0.0225 , 0.0225 , 0.0225 , 0.0225 , 0.0225 , 0.0225 ,
        0.0225 , 0.0225 , 0.0225 , 0.0225 , 0.0225 , 1.0225 , 0.     ,
        0.     , 0.     , 0.     , 0.     , 0.     , 0.     , 0.     ,
        0.     , 0.     , 0.     , 0.     , 0.     , 0.     , 0.     ,
        0.     , 0.     , 0.     , 0.     , 0.     , 0.     , 0.     ,
        0.     , 0.     , 0.     , 0.     , 0.     , 0.     , 0.     ,
        0.     , 0.     , 0.     , 0.     , 0.     , 0.     , 0.     ,
        0.     , 0.     , 0.     , 0.     ],
       [0.02325, 0.02325, 0.02325, 0.02325, 0.02325, 0.02325, 0.02325,
        0.02325, 0.02325, 0.02325, 0.02325, 0.02325, 0.02325, 0.02325,
        0.02325, 0.02325, 0.02325, 0.02325, 0.02325, 0.02325, 0.02325,
        0.02325, 0.02325, 1.02325, 0.     , 0.     , 0.     , 0.     ,
        0.     , 0.     , 0.     , 0.     , 0.     , 0.     , 0.     ,
        0.     , 0.     , 0.     , 0.     , 0.     , 0.     , 0.     ,
        0.     , 0.     , 0.     , 0.     , 0.     , 0.     , 0.     ,
        0.     , 0.     , 0.     , 0.     , 0.     , 0.     , 0.     ,
        0.     , 0.     , 0.     , 0.     ],
       [0.0239 , 0.0239 , 0.0239 , 0.0239 , 0.0239 , 0.0239 , 0.0239 ,
        0.0239 , 0.0239 , 0.0239 , 0.0239 , 0.0239 , 0.0239 , 0.0239 ,
        0.0239 , 0.0239 , 0.0239 , 0.0239 , 0.0239 , 0.0239 , 0.0239 ,
        0.0239 , 0.0239 , 0.0239 , 0.0239 , 0.0239 , 0.0239 , 0.0239 ,
        0.0239 , 1.0239 , 0.     , 0.     , 0.     , 0.     , 0.     ,
        0.     , 0.     , 0.     , 0.     , 0.     , 0.     , 0.     ,
        0.     , 0.     , 0.     , 0.     , 0.     , 0.     , 0.     ,
        0.     , 0.     , 0.     , 0.     , 0.     , 0.     , 0.     ,
        0.     , 0.     , 0.     , 0.     ],
       [0.0244 , 0.0244 , 0.0244 , 0.0244 , 0.0244 , 0.0244 , 0.0244 ,
        0.0244 , 0.0244 , 0.0244 , 0.0244 , 0.0244 , 0.0244 , 0.0244 ,
        0.0244 , 0.0244 , 0.0244 , 0.0244 , 0.0244 , 0.0244 , 0.0244 ,
        0.0244 , 0.0244 , 0.0244 , 0.0244 , 0.0244 , 0.0244 , 0.0244 ,
        0.0244 , 0.0244 , 0.0244 , 0.0244 , 0.0244 , 0.0244 , 0.0244 ,
        0.0244 , 0.0244 , 0.0244 , 0.0244 , 1.0244 , 0.     , 0.     ,
        0.     , 0.     , 0.     , 0.     , 0.     , 0.     , 0.     ,
        0.     , 0.     , 0.     , 0.     , 0.     , 0.     , 0.     ,
        0.     , 0.     , 0.     , 0.     ],
       [0.02425, 0.02425, 0.02425, 0.02425, 0.02425, 0.02425, 0.02425,
        0.02425, 0.02425, 0.02425, 0.02425, 0.02425, 0.02425, 0.02425,
        0.02425, 0.02425, 0.02425, 0.02425, 0.02425, 0.02425, 0.02425,
        0.02425, 0.02425, 0.02425, 0.02425, 0.02425, 0.02425, 0.02425,
        0.02425, 0.02425, 0.02425, 0.02425, 0.02425, 0.02425, 0.02425,
        0.02425, 0.02425, 0.02425, 0.02425, 0.02425, 0.02425, 0.02425,
        0.02425, 0.02425, 0.02425, 0.02425, 0.02425, 0.02425, 0.02425,
        0.02425, 0.02425, 0.02425, 0.02425, 0.02425, 0.02425, 0.02425,
        0.02425, 0.02425, 0.02425, 1.02425]]))
Using AP10 dataset:
Number of swaps: 14

Swap Cashflow Matrix:
[[1.01375 0.      0.      0.      0.      0.      0.      0.      0.
  0.      0.      0.      0.      0.      0.      0.      0.      0.
  0.      0.      0.      0.      0.      0.      0.      0.      0.
  0.      0.      0.      0.      0.      0.      0.      0.      0.
  0.      0.      0.      0.      0.      0.      0.      0.      0.
  0.      0.      0.      0.      0.      0.      0.      0.      0.
  0.      0.      0.      0.      0.      0.     ]
 [0.0155  1.0155  0.      0.      0.      0.      0.      0.      0.
  0.      0.      0.      0.      0.      0.      0.      0.      0.
  0.      0.      0.      0.      0.      0.      0.      0.      0.
  0.      0.      0.      0.      0.      0.      0.      0.      0.
  0.      0.      0.      0.      0.      0.      0.      0.      0.
  0.      0.      0.      0.      0.      0.      0.      0.      0.
  0.      0.      0.      0.      0.      0.     ]
 [0.0165  0.0165  1.0165  0.      0.      0.      0.      0.      0.
  0.      0.      0.      0.      0.      0.      0.      0.      0.
  0.      0.      0.      0.      0.      0.      0.      0.      0.
  0.      0.      0.      0.      0.      0.      0.      0.      0.
  0.      0.      0.      0.      0.      0.      0.      0.      0.
  0.      0.      0.      0.      0.      0.      0.      0.      0.
  0.      0.      0.      0.      0.      0.     ]
 [0.01715 0.01715 0.01715 1.01715 0.      0.      0.      0.      0.
  0.      0.      0.      0.      0.      0.      0.      0.      0.
  0.      0.      0.      0.      0.      0.      0.      0.      0.
  0.      0.      0.      0.      0.      0.      0.      0.      0.
  0.      0.      0.      0.      0.      0.      0.      0.      0.
  0.      0.      0.      0.      0.      0.      0.      0.      0.
  0.      0.      0.      0.      0.      0.     ]
 [0.01765 0.01765 0.01765 0.01765 1.01765 0.      0.      0.      0.
  0.      0.      0.      0.      0.      0.      0.      0.      0.
  0.      0.      0.      0.      0.      0.      0.      0.      0.
  0.      0.      0.      0.      0.      0.      0.      0.      0.
  0.      0.      0.      0.      0.      0.      0.      0.      0.
  0.      0.      0.      0.      0.      0.      0.      0.      0.
  0.      0.      0.      0.      0.      0.     ]
 [0.0165  0.0165  0.0165  0.0165  0.0165  1.0165  0.      0.      0.
  0.      0.      0.      0.      0.      0.      0.      0.      0.
  0.      0.      0.      0.      0.      0.      0.      0.      0.
  0.      0.      0.      0.      0.      0.      0.      0.      0.
  0.      0.      0.      0.      0.      0.      0.      0.      0.
  0.      0.      0.      0.      0.      0.      0.      0.      0.
  0.      0.      0.      0.      0.      0.     ]
 [0.0189  0.0189  0.0189  0.0189  0.0189  0.0189  0.0189  1.0189  0.
  0.      0.      0.      0.      0.      0.      0.      0.      0.
  0.      0.      0.      0.      0.      0.      0.      0.      0.
  0.      0.      0.      0.      0.      0.      0.      0.      0.
  0.      0.      0.      0.      0.      0.      0.      0.      0.
  0.      0.      0.      0.      0.      0.      0.      0.      0.
  0.      0.      0.      0.      0.      0.     ]
 [0.01975 0.01975 0.01975 0.01975 0.01975 0.01975 0.01975 0.01975 0.01975
  1.01975 0.      0.      0.      0.      0.      0.      0.      0.
  0.      0.      0.      0.      0.      0.      0.      0.      0.
  0.      0.      0.      0.      0.      0.      0.      0.      0.
  0.      0.      0.      0.      0.      0.      0.      0.      0.
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  0.      0.      0.      0.      0.      0.     ]
 [0.02125 0.02125 0.02125 0.02125 0.02125 0.02125 0.02125 0.02125 0.02125
  0.02125 0.02125 0.02125 0.02125 1.02125 0.      0.      0.      0.
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 [0.0225  0.0225  0.0225  0.0225  0.0225  0.0225  0.0225  0.0225  0.0225
  0.0225  0.0225  0.0225  0.0225  0.0225  0.0225  0.0225  0.0225  0.0225
  0.0225  1.0225  0.      0.      0.      0.      0.      0.      0.
  0.      0.      0.      0.      0.      0.      0.      0.      0.
  0.      0.      0.      0.      0.      0.      0.      0.      0.
  0.      0.      0.      0.      0.      0.      0.      0.      0.
  0.      0.      0.      0.      0.      0.     ]
 [0.02325 0.02325 0.02325 0.02325 0.02325 0.02325 0.02325 0.02325 0.02325
  0.02325 0.02325 0.02325 0.02325 0.02325 0.02325 0.02325 0.02325 0.02325
  0.02325 0.02325 0.02325 0.02325 0.02325 1.02325 0.      0.      0.
  0.      0.      0.      0.      0.      0.      0.      0.      0.
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  0.      0.      0.      0.      0.      0.      0.      0.      0.
  0.      0.      0.      0.      0.      0.     ]
 [0.0239  0.0239  0.0239  0.0239  0.0239  0.0239  0.0239  0.0239  0.0239
  0.0239  0.0239  0.0239  0.0239  0.0239  0.0239  0.0239  0.0239  0.0239
  0.0239  0.0239  0.0239  0.0239  0.0239  0.0239  0.0239  0.0239  0.0239
  0.0239  0.0239  1.0239  0.      0.      0.      0.      0.      0.
  0.      0.      0.      0.      0.      0.      0.      0.      0.
  0.      0.      0.      0.      0.      0.      0.      0.      0.
  0.      0.      0.      0.      0.      0.     ]
 [0.0244  0.0244  0.0244  0.0244  0.0244  0.0244  0.0244  0.0244  0.0244
  0.0244  0.0244  0.0244  0.0244  0.0244  0.0244  0.0244  0.0244  0.0244
  0.0244  0.0244  0.0244  0.0244  0.0244  0.0244  0.0244  0.0244  0.0244
  0.0244  0.0244  0.0244  0.0244  0.0244  0.0244  0.0244  0.0244  0.0244
  0.0244  0.0244  0.0244  1.0244  0.      0.      0.      0.      0.
  0.      0.      0.      0.      0.      0.      0.      0.      0.
  0.      0.      0.      0.      0.      0.     ]
 [0.02425 0.02425 0.02425 0.02425 0.02425 0.02425 0.02425 0.02425 0.02425
  0.02425 0.02425 0.02425 0.02425 0.02425 0.02425 0.02425 0.02425 0.02425
  0.02425 0.02425 0.02425 0.02425 0.02425 0.02425 0.02425 0.02425 0.02425
  0.02425 0.02425 0.02425 0.02425 0.02425 0.02425 0.02425 0.02425 0.02425
  0.02425 0.02425 0.02425 0.02425 0.02425 0.02425 0.02425 0.02425 0.02425
  0.02425 0.02425 0.02425 0.02425 0.02425 0.02425 0.02425 0.02425 0.02425
  0.02425 0.02425 0.02425 0.02425 0.02425 1.02425]]

Cashflow Dates:
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   7.5  8.   8.5  9.   9.5 10.  10.5 11.  11.5 12.  12.5 13.  13.5 14.
  14.5 15.  15.5 16.  16.5 17.  17.5 18.  18.5 19.  19.5 20.   0.   0.
   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.
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   7.5  8.   8.5  9.   9.5 10.  10.5 11.  11.5 12.  12.5 13.  13.5 14.
  14.5 15.  15.5 16.  16.5 17.  17.5 18.  18.5 19.  19.5 20.  20.5 21.
  21.5 22.  22.5 23.  23.5 24.  24.5 25.  25.5 26.  26.5 27.  27.5 28.
  28.5 29.  29.5 30. ]]

Please sign and share this petition https://www.change.org/stop_torturing_T_Moudiki – after seriously researching my background and contributions to the field.

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Citation

For attribution, please cite this work as:

T. Moudiki (2026-01-03). Python examples for 'Beyond Nelson-Siegel and splines: A model- agnostic Machine Learning framework for discount curve calibration, interpolation and extrapolation'. Retrieved from https://thierrymoudiki.github.io/blog/2026/01/03/r/python/examples-yieldcurveml

BibTeX citation (remove empty spaces)
@misc{ tmoudiki20260103, author = { T. Moudiki }, title = { Python examples for 'Beyond Nelson-Siegel and splines: A model- agnostic Machine Learning framework for discount curve calibration, interpolation and extrapolation' }, url = { https://thierrymoudiki.github.io/blog/2026/01/03/r/python/examples-yieldcurveml }, year = { 2026 } }

Under License Creative Commons Attribution 4.0 International

Previous publications

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Prediction sets and prediction intervals for conformalized Auto XGBoost, Auto LightGBM, Auto CatBoost, Auto GradientBoosting Sep 2, 2024

Quick/automated R package development workflow (assuming you're using macOS or Linux) Part2 Aug 30, 2024

R package development workflow (assuming you're using macOS or Linux) Aug 27, 2024

A new method for deriving a nonparametric confidence interval for the mean Aug 26, 2024

Conformalized adaptive (online/streaming) learning using learningmachine in Python and R Aug 19, 2024

Bayesian (nonlinear) adaptive learning Aug 12, 2024

Auto XGBoost, Auto LightGBM, Auto CatBoost, Auto GradientBoosting Aug 5, 2024

Copulas for uncertainty quantification in time series forecasting Jul 28, 2024

Forecasting uncertainty: sequential split conformal prediction + Block bootstrap (web app) Jul 22, 2024

learningmachine for Python (new version) Jul 15, 2024

learningmachine v2.0.0: Machine Learning with explanations and uncertainty quantification Jul 8, 2024

My presentation at ISF 2024 conference (slides with nnetsauce probabilistic forecasting news) Jul 3, 2024

10 uncertainty quantification methods in nnetsauce forecasting Jul 1, 2024

Forecasting with XGBoost embedded in Quasi-Randomized Neural Networks Jun 24, 2024

Forecasting Monthly Airline Passenger Numbers with Quasi-Randomized Neural Networks Jun 17, 2024

Automated hyperparameter tuning using any conformalized surrogate Jun 9, 2024

Recognizing handwritten digits with Ridge2Classifier Jun 3, 2024

Forecasting the Economy May 27, 2024

A detailed introduction to Deep Quasi-Randomized 'neural' networks May 19, 2024

Probability of receiving a loan; using learningmachine May 12, 2024

mlsauce's `v0.18.2`: various examples and benchmarks with dimension reduction May 6, 2024

mlsauce's `v0.17.0`: boosting with Elastic Net, polynomials and heterogeneity in explanatory variables Apr 29, 2024

mlsauce's `v0.13.0`: taking into account inputs heterogeneity through clustering Apr 21, 2024

mlsauce's `v0.12.0`: prediction intervals for LSBoostRegressor Apr 15, 2024

Conformalized predictive simulations for univariate time series on more than 250 data sets Apr 7, 2024

learningmachine v1.1.2: for Python Apr 1, 2024

learningmachine v1.0.0: prediction intervals around the probability of the event 'a tumor being malignant' Mar 25, 2024

Bayesian inference and conformal prediction (prediction intervals) in nnetsauce v0.18.1 Mar 18, 2024

Multiple examples of Machine Learning forecasting with ahead Mar 11, 2024

rtopy (v0.1.1): calling R functions in Python Mar 4, 2024

ahead forecasting (v0.10.0): fast time series model calibration and Python plots Feb 26, 2024

A plethora of datasets at your fingertips Part3: how many times do couples cheat on each other? Feb 19, 2024

nnetsauce's introduction as of 2024-02-11 (new version 0.17.0) Feb 11, 2024

Tuning Machine Learning models with GPopt's new version Part 2 Feb 5, 2024

Tuning Machine Learning models with GPopt's new version Jan 29, 2024

Subsampling continuous and discrete response variables Jan 22, 2024

DeepMTS, a Deep Learning Model for Multivariate Time Series Jan 15, 2024

A classifier that's very accurate (and deep) Pt.2: there are > 90 classifiers in nnetsauce Jan 8, 2024

learningmachine: prediction intervals for conformalized Kernel ridge regression and Random Forest Jan 1, 2024

A plethora of datasets at your fingertips Part2: how many times do couples cheat on each other? Descriptive analytics, interpretability and prediction intervals using conformal prediction Dec 25, 2023

Diffusion models in Python with esgtoolkit (Part2) Dec 18, 2023

Diffusion models in Python with esgtoolkit Dec 11, 2023

Julia packaging at the command line Dec 4, 2023

Quasi-randomized nnetworks in Julia, Python and R Nov 27, 2023

A plethora of datasets at your fingertips Nov 20, 2023

A classifier that's very accurate (and deep) Nov 12, 2023

mlsauce version 0.8.10: Statistical/Machine Learning with Python and R Nov 5, 2023

AutoML in nnetsauce (randomized and quasi-randomized nnetworks) Pt.2: multivariate time series forecasting Oct 29, 2023

AutoML in nnetsauce (randomized and quasi-randomized nnetworks) Oct 22, 2023

Version v0.14.0 of nnetsauce for R and Python Oct 16, 2023

A diffusion model: G2++ Oct 9, 2023

Diffusion models in ESGtoolkit + announcements Oct 2, 2023

An infinity of time series forecasting models in nnetsauce (Part 2 with uncertainty quantification) Sep 25, 2023

(News from) forecasting in Python with ahead (progress bars and plots) Sep 18, 2023

Forecasting in Python with ahead Sep 11, 2023

Risk-neutralize simulations Sep 4, 2023

Comparing cross-validation results using crossval_ml and boxplots Aug 27, 2023

Reminder Apr 30, 2023

Did you ask ChatGPT about who you are? Apr 16, 2023

A new version of nnetsauce (randomized and quasi-randomized 'neural' networks) Apr 2, 2023

Simple interfaces to the forecasting API Nov 23, 2022

A web application for forecasting in Python, R, Ruby, C#, JavaScript, PHP, Go, Rust, Java, MATLAB, etc. Nov 2, 2022

Prediction intervals (not only) for Boosted Configuration Networks in Python Oct 5, 2022

Boosted Configuration (neural) Networks Pt. 2 Sep 3, 2022

Boosted Configuration (_neural_) Networks for classification Jul 21, 2022

A Machine Learning workflow using Techtonique Jun 6, 2022

Super Mario Bros © in the browser using PyScript May 8, 2022

News from ESGtoolkit, ycinterextra, and nnetsauce Apr 4, 2022

Explaining a Keras _neural_ network predictions with the-teller Mar 11, 2022

New version of nnetsauce -- various quasi-randomized networks Feb 12, 2022

A dashboard illustrating bivariate time series forecasting with `ahead` Jan 14, 2022

Hundreds of Statistical/Machine Learning models for univariate time series, using ahead, ranger, xgboost, and caret Dec 20, 2021

Forecasting with `ahead` (Python version) Dec 13, 2021

Tuning and interpreting LSBoost Nov 15, 2021

Time series cross-validation using `crossvalidation` (Part 2) Nov 7, 2021

Fast and scalable forecasting with ahead::ridge2f Oct 31, 2021

Automatic Forecasting with `ahead::dynrmf` and Ridge regression Oct 22, 2021

Forecasting with `ahead` Oct 15, 2021

Classification using linear regression Sep 26, 2021

`crossvalidation` and random search for calibrating support vector machines Aug 6, 2021

parallel grid search cross-validation using `crossvalidation` Jul 31, 2021

`crossvalidation` on R-universe, plus a classification example Jul 23, 2021

Documentation and source code for GPopt, a package for Bayesian optimization Jul 2, 2021

Hyperparameters tuning with GPopt Jun 11, 2021

A forecasting tool (API) with examples in curl, R, Python May 28, 2021

Bayesian Optimization with GPopt Part 2 (save and resume) Apr 30, 2021

Bayesian Optimization with GPopt Apr 16, 2021

Compatibility of nnetsauce and mlsauce with scikit-learn Mar 26, 2021

Explaining xgboost predictions with the teller Mar 12, 2021

An infinity of time series models in nnetsauce Mar 6, 2021

New activation functions in mlsauce's LSBoost Feb 12, 2021

2020 recap, Gradient Boosting, Generalized Linear Models, AdaOpt with nnetsauce and mlsauce Dec 29, 2020

A deeper learning architecture in nnetsauce Dec 18, 2020

Classify penguins with nnetsauce's MultitaskClassifier Dec 11, 2020

Bayesian forecasting for uni/multivariate time series Dec 4, 2020

Generalized nonlinear models in nnetsauce Nov 28, 2020

Boosting nonlinear penalized least squares Nov 21, 2020

Statistical/Machine Learning explainability using Kernel Ridge Regression surrogates Nov 6, 2020

NEWS Oct 30, 2020

A glimpse into my PhD journey Oct 23, 2020

Submitting R package to CRAN Oct 16, 2020

Simulation of dependent variables in ESGtoolkit Oct 9, 2020

Forecasting lung disease progression Oct 2, 2020

New nnetsauce Sep 25, 2020

Technical documentation Sep 18, 2020

A new version of nnetsauce, and a new Techtonique website Sep 11, 2020

Back next week, and a few announcements Sep 4, 2020

Explainable 'AI' using Gradient Boosted randomized networks Pt2 (the Lasso) Jul 31, 2020

LSBoost: Explainable 'AI' using Gradient Boosted randomized networks (with examples in R and Python) Jul 24, 2020

nnetsauce version 0.5.0, randomized neural networks on GPU Jul 17, 2020

Maximizing your tip as a waiter (Part 2) Jul 10, 2020

New version of mlsauce, with Gradient Boosted randomized networks and stump decision trees Jul 3, 2020

Announcements Jun 26, 2020

Parallel AdaOpt classification Jun 19, 2020

Comments section and other news Jun 12, 2020

Maximizing your tip as a waiter Jun 5, 2020

AdaOpt classification on MNIST handwritten digits (without preprocessing) May 29, 2020

AdaOpt (a probabilistic classifier based on a mix of multivariable optimization and nearest neighbors) for R May 22, 2020

AdaOpt May 15, 2020

Custom errors for cross-validation using crossval::crossval_ml May 8, 2020

Documentation+Pypi for the `teller`, a model-agnostic tool for Machine Learning explainability May 1, 2020

Encoding your categorical variables based on the response variable and correlations Apr 24, 2020

Linear model, xgboost and randomForest cross-validation using crossval::crossval_ml Apr 17, 2020

Grid search cross-validation using crossval Apr 10, 2020

Documentation for the querier, a query language for Data Frames Apr 3, 2020

Time series cross-validation using crossval Mar 27, 2020

On model specification, identification, degrees of freedom and regularization Mar 20, 2020

Import data into the querier (now on Pypi), a query language for Data Frames Mar 13, 2020

R notebooks for nnetsauce Mar 6, 2020

Version 0.4.0 of nnetsauce, with fruits and breast cancer classification Feb 28, 2020

Create a specific feed in your Jekyll blog Feb 21, 2020

Git/Github for contributing to package development Feb 14, 2020

Feedback forms for contributing Feb 7, 2020

nnetsauce for R Jan 31, 2020

A new version of nnetsauce (v0.3.1) Jan 24, 2020

ESGtoolkit, a tool for Monte Carlo simulation (v0.2.0) Jan 17, 2020

Search bar, new year 2020 Jan 10, 2020

2019 Recap, the nnetsauce, the teller and the querier Dec 20, 2019

Understanding model interactions with the `teller` Dec 13, 2019

Using the `teller` on a classifier Dec 6, 2019

Benchmarking the querier's verbs Nov 29, 2019

Composing the querier's verbs for data wrangling Nov 22, 2019

Comparing and explaining model predictions with the teller Nov 15, 2019

Tests for the significance of marginal effects in the teller Nov 8, 2019

Introducing the teller Nov 1, 2019

Introducing the querier Oct 25, 2019

Prediction intervals for nnetsauce models Oct 18, 2019

Using R in Python for statistical learning/data science Oct 11, 2019

Model calibration with `crossval` Oct 4, 2019

Bagging in the nnetsauce Sep 25, 2019

Adaboost learning with nnetsauce Sep 18, 2019

Change in blog's presentation Sep 4, 2019

nnetsauce on Pypi Jun 5, 2019

More nnetsauce (examples of use) May 9, 2019

nnetsauce Mar 13, 2019

crossval Mar 13, 2019

test Mar 10, 2019