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Hull-White One Factor Model

A quantitative finance repository focused on implementing the Hull-White one-factor short-rate model for interest-rate derivatives.

This project develops the Hull-White model dynamics, calibrates the model to European swaption quotes, and applies it to the pricing of Bermudan swaptions through a PDE-based approach.


Repository Structure

Hull-White-One-Factor-Model/
├── Hull-White One Factor Model.ipynb
└── Hull-White One Factor Model Documentation.pdf

Project Overview

This notebook focuses on the Hull-White one-factor model for interest-rate derivatives.

It starts from the standard short-rate dynamics under the risk-neutral measure and derives the associated zero-coupon bond pricing formula. The model is first applied to the pricing of European swaptions through Jamshidian’s decomposition, before being extended to an analytical calibration framework and a PDE-based pricing method for Bermudan swaptions.

The model calibration is performed on a basket of European swaptions. In this implementation, the mean-reversion parameter is fixed, while the short-rate volatility is modeled as piecewise constant across expiries. The notebook first calibrates the short-rate total variance term structure and then strips the corresponding volatility curve.


Documentation

The repository also includes a dedicated PDF:

  • Hull-White One Factor Model Documentation.pdf

This document provides the theoretical derivation supporting the European swaption pricing formula under the Hull-White model.


Example Output

EURIBOR-6M European diagonal ATM swaptions with an expiry/tenor structure of 2Y/13Y, 3Y/12Y, ..., 14Y/1Y:

image

Best use case

Use this notebook when working with interest-rate derivatives and building a Hull-White pricing framework for calibration and the valuation of European and Bermudan swaptions.


How to Use

Clone the repository:

git clone https://github.com/Idriss-Afra/Hull-White-One-Factor-Model.git
cd Hull-White-One-Factor-Model
jupyter notebook

Then open:

  • Hull-White One Factor Model.ipynb

Author

Idriss Afra