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.
Hull-White-One-Factor-Model/
├── Hull-White One Factor Model.ipynb
└── Hull-White One Factor Model Documentation.pdf
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.
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.
EURIBOR-6M European diagonal ATM swaptions with an expiry/tenor structure of 2Y/13Y, 3Y/12Y, ..., 14Y/1Y:
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.
Clone the repository:
git clone https://github.com/Idriss-Afra/Hull-White-One-Factor-Model.git
cd Hull-White-One-Factor-Model
jupyter notebookThen open:
Hull-White One Factor Model.ipynb
Idriss Afra