🐍 Dothan One-Factor model 🐍

The Dothan one factor model is a simple model for simulating the evolution of short rates. The model assumes that the short rate process evolves as adriftless geometric Brownian motion.

Problem

When trying to simulate interest rates, there is a variety of models. The choice of the model and its limitations are a key factor in deciding which model to implement. A good practice is to start with simpler models. The Dothan model is one such model.

Solution

One of the simplest models, the Dothan one factor model assumes that the short rate can be described by a simple stochastic process with one source of uncertainty coming from a Brownian motion.

The stochastic differential equation (SDE) of the Dothan model is shown on the Wiki page https://en.wikipedia.org/wiki/Geometric_Brownian_motion but without drift#.

Input

• r0 (float): starting interest rate of the Vasicek process.
• a (float): market price of risk.
• sigma (float): instantaneous volatility measures instant by instant the amplitude of randomness entering the system.
• T (integer): end modelling time. From 0 to T the time series runs.
• dt (float): increment of time that the process runs on. Ex. dt = 0.1 then the time series is 0, 0.1, 0.2,...

Output

• N x 2 Pandas DataFrame with a sample path as values and modelling time as index.

Getting started

import numpy as np
import pandas as pd
from Dothan_one_factor import simulate_Dothan_One_Factor

r0 = 0.1 # The starting interest rate
a = 1.0 # market price of risk
sigma = 0.2 # instantaneous volatility
T = 52 # end modelling time
dt = 0.1 # increments of time

print(simulate_Dothan_One_Factor(r0, a, sigma, T, dt))