Interest Rate Forecasting

Work with historical Euribor data and forecast interest rates utilizing stochastic models and Monte Carlo simulations.

Features

• Fetch historical Euribor data from 1999 onwards by maturity in standardized format
• Initialize discrete Vasicek and Cox-Ingersoll-Ross models
• Simulate and visualize interest rate paths with Monte Carlo simulations

Requirements

NumPy, pandas, Matplotlib and seaborn are required:

pip install numpy
pip install pandas
pip install matplotlib
pip install seaborn

The Anaconda distribution for Python is recommended, which includes all the requirements:

https://www.anaconda.com/download

Usage

Copy the following files from src to your working directory:

• interest_rates.py for fetching historical data
• ir_models.py for initializing interest rate models
• monte_carlo.py for simulating and visualizing the models

Example

This example shows how to fetch historical Euribor data, initialize the interest rate models and simulate them with Monte Carlo.

from interest_rates import Euribor
from ir_models import VasicekModel, CIRModel
from monte_carlo import MonteCarlo

Fetching Euribor Data

Historical Euribor data is available for the following maturities:

• 1 week
• 1 month
• 3 months
• 6 months
• 12 months

There are four methods for fetching the data:

• get_current()
• get_daily(start: str, end: str)
• get_monthly(start: str, end: str)
• get_yearly(start: str, end: str)

The get_current() method returns the most recent rate of the previous business day as a float, whereas the others return date indexed DataFrames for the user specified date ranges:

# Monthly Euribor rates from January 2024 to July 2025
r = Euribor(maturity="3 months")
monthly = r.get_monthly(start="2024/01", end="2025/07")
print(monthly)

Date	Euribor (3 months)
2024-01-01	0.03905
2024-02-01	0.03884
2024-03-01	0.03938
2024-04-01	0.03883
2024-05-01	0.03853
2024-06-03	0.03782
2024-07-01	0.03709
2024-08-01	0.03638
2024-09-02	0.03469
2024-10-01	0.03252
2024-11-01	0.03085
2024-12-02	0.02924
2025-01-01	0.02736
2025-02-03	0.02562
2025-03-03	0.02464
2025-04-01	0.02324
2025-05-01	0.02142
2025-06-02	0.01979
2025-07-01	0.01961

Initializing Interest Rate Models

The package contains two stochastic models for forecasting interest rates:

• Vasicek Model
• Cox-Ingersoll-Ross Model

For theoretical background on the models, see:
https://en.wikipedia.org/wiki/Vasicek_model
https://en.wikipedia.org/wiki/Cox%E2%80%93Ingersoll%E2%80%93Ross_model

Both models are initialized with the following parameters:

• theta: the mean reversion speed
• mu: the long-term mean interest rate
• sigma: interest rate volatility
• r0: the initial/current interest rate
• T: time horizon in years (default 1)
• N: the number of time steps to simulate (default 252, the amount of business days in a year)

Example: Current interest rate is 0.03, long-term mean is 0.05, volatility is 0.02 and mean reversion speed is 1.5:

# Using the same parameters for both Vasicek and CIR models
mean_reversion_speed = 1.5
long_term_mean = 0.05
volatility = 0.02
initial_rate = 0.03

# Use default T = 1 and N = 252 for both models
vasicek = VasicekModel(theta=mean_reversion_speed,
                       mu=long_term_mean,
                       sigma=volatility,
                       r0=initial_rate)

cir = CIRModel(theta=mean_reversion_speed,
               mu=long_term_mean,
               sigma=volatility,
               r0=initial_rate)

Simulating Interest Rate Paths with Monte Carlo

Important

The example below is a result of a random process.

Simulate the Vasicek Model with 100 Monte Carlo simulation runs:

# Monte Carlo simulation with 100 simulation runs
vasicek_mc = MonteCarlo(model=vasicek,
                        number_of_simulations=100)

cir_mc = MonteCarlo(model=cir,
                    number_of_simulations=100)

The results() method returns a DataFrame with each column representing a single simulation run. The visualize() method shows the results alongside with 0.9 and 0.1 confidence bounds and the median:

vasicek_mc.visualize()
cir_mc.visualize()

The stats() method shows summary statistic of the simulations:

print(vasicek_mc.stats())

	Results for 100 simulations
Model	Vasicek
Initial Interest Rate (r0)	0.03
Long-Term Mean (mu)	0.05
90% quantile at T = 252	0.06308053381856575
Median at T = 252	0.04662813286319578
10% quantile at T = 252	0.029547065622756635

print(cir_mc.stats())

	Results for 100 simulations
Model	CIR
Initial Interest Rate (r0)	0.03
Long-Term Mean (mu)	0.05
90% quantile at T = 252	0.04893487926964539
Median at T = 252	0.045827135163105465
10% quantile at T = 252	0.04260202605388624