# The BasicHullWhite Model¶

## Overview¶

BasicHullWhite is a simple implementation of the Hull-White model. The Hull-White model is a short rate model represented by the stochastic differential equation:

$dr(t) = (\theta(t) - a r(t))dt + \sigma dW$

BasicHullWhite preforms Monte-Carlo simulations and generates paths of the instantaneous short rate based on the Hull-White model. Many properties of the Hull-White model are analytically solvable, and BasicHullWhite also includes formulas analytically solving for the properties.

Formulas for the Monte-Carlo simulation perform computation fast, as they operate on numpy vectors to process all scenarios at once.

All the contents are defined in HullWhite space.

## Model Specifications¶

### The HullWhite Space¶

 HullWhite The main Space in the BasicHullWhite model.