Short-Rate Simulation

Simulates the future path of a country’s short-term interest rate with the Hull-White, Vasicek or Cox-Ingersoll-Ross model and summarizes the distribution of the paths per step: the mean and the 5th, 25th, 50th, 75th and 95th percentiles. Simulated rate paths value interest rate derivatives and path-dependent products (such as mortgages with prepayment), and stress the interest income of a balance sheet.

The speed of mean reversion and the volatility are calibrated to the history of the rate, see get_short_rate_model. In the Vasicek and CIR models the rate is pulled to the long-run mean of that history. The Hull-White (1990) model replaces it with a mean that varies over time and follows from today’s zero-coupon curve, so that the model reproduces the discount factors of that curve (its expected short rate lies above the forward rate by the convexity term σ² (1 - e^(-at))² / (2a²)):

dr = [θ(t) - a r] dt + σ dW, θ(t) = ∂f/∂t + a f(t) + σ² (1 - e^(-2at)) / (2a)

with f the instantaneous forward rate. The paths are simulated with an Euler scheme starting at today’s rate (CIR’s are kept at or above zero).

For more information, see the following paper:

• Hull, J. and White, A. (1990). “Pricing Interest-Rate-Derivative Securities.” The Review of Financial Studies, 3(4), 573-592.

Also known as: interest rate simulation, Hull-White model, Monte Carlo short rate, interest rate scenarios.

Short-Rate Simulation in Python or via the MCP

Install the Finance Toolkit with:

pip install financetoolkit -U

Then call get_short_rate_simulation as shown below.

from financetoolkit import FixedIncome

fixedincome = FixedIncome(start_date='2000-01-01', end_date='2026-10-23')

simulation = fixedincome.get_short_rate_simulation(
    short_rate='6M', years=5, steps_per_year=1
)

simulation

Or, after setting up the Finance Toolkit MCP, ask:

Which returns:

Parameters

get_short_rate_simulation accepts the following parameters.

Related Short-Rate Models