The Hull-White model is a single-factor interest model used to price interest rate derivatives. The Hull-White model assumes that short rates have a normal distribution and that the short rates are subject to mean reversion. In its most generic formulation, it belongs to the class of no-arbitrage models that are able to fit today's term structure of interest rates. I compared Vasicek model and Hull White model, then calibrated Hull White model with Python. You are welcome to provide your comments and subscribe to my YouTube channel.

Using 228 cap prices with different expiry and maturity dates as model input. Then compiled an optimization function in MATLAB to minimize the rooted standard error between market cap prices and the cap prices derived from the model. Finally used Monte-Carlo methods to examine the model, and used 3D visualization tools to output volatility surfaces.

The purpose of this project is to calibrate the HW1F model using the formulas and methods described in the "Calibration Methods of Hull-White Model" document.

Python code used for my master thesis titled "One-Factor Hull-White Model Calibration and Analytical Pricing of Interest Rate Caps and Floors" at Warsaw School of Economics (SGH)

Project for implementation of quantitative stochastic interest models (such as Hull-White) for pricing of interest rates derivatives. Goal is to understand and present calibration and usage of such models step by step together with exploring differences of the models and impact of model choice.

Calibrating Ho and Lee short term interest rate model in C#, ExcelDNA, Alglib, Python and xlwings. In this repository, we use both C# and Python to calibrate Ho Lee model's "theta" on market data. The calibration algo is explained in Veronesi, Fixed Income Securities, Chapter 19, at pages 653-659. The non linear solvers are from https://www.alglib.net/ when working with C#, and scipy.optimize when working with Python. We previously covered the implementation of the Ho Lee model together with three additional interest rate models, Vasicek, CIR and Hull and White, in our Repository "Vasicek_CIR_HoLee_Hull_White_Models_Python". With both C# and Python, we use an excel spreadsheet to enter market data and see calibration results. The communication between C# and excel occurs via "ExcelDNA" whereas when working in Python we used "xlwings". For more on ExcelDNA and C# see also my previous Repository "MortgageLoanCsharpExcelDNA". We also found a similar work in https://mikejuniperhill.blogspot.com/2014/10 by Mikael Katajamäki with a different calibration algo from Veronesi. Mikael's work is in our view an excellent example on how to combine C# and ExcelDNA to solve a financial problem. For the xlwings we refer to https://www.xlwings.org/.

A Python-based framework for modeling negative interest rates via the Hull–White one-factor model, offering Monte Carlo simulation, zero-coupon bond pricing, caplet and floorlet, Swaptions valuation, and Black‑76 implied volatility calibration tools.

Learn C# by HW1F example

FIN551 Final Project

This project implements the calibration of the Hull-White interest rate model using US Treasury market data. The implementation focuses on fitting the model to the current term structure of interest rates and estimating the model's volatility parameters.

Calibration and comparison of short-rate models (CIR, Vasicek, Hull–White) for bond pricing and relative-value arbitrage.

This is a group project trying to use limited Bloomberg data, build Hull–White cap pricing model and calibration engine

Extension of the Hull-White interest rate model with sinusoidal time-varying mean reversion. Includes calibration (Nelder-Mead) and Monte Carlo bond pricing.

Implementation of the Hull–White model from scratch for pricing interest rate derivatives, including CMS, cap swaptions, zero-coupon bond options, and volatility calibration.

Advanced Monte Carlo engine for exotic options pricing with real-time market data calibration. Hybrid Heston-Hull-White-Jump model with 85x speedup and 0.45% accuracy.

Python implementation of the Heston-Hull & White model for modelling price processes under stochastic volatility and interest rates. Includes a sample use case demonstrating calibration to historical interest rate and option data.

A modular quantitative finance library for real-time market data ingestion and stochastic volatility modeling. Quant Atlas implements a high-performance Heston-Hull-White calibration engine, utilizing Neural Networks to estimate model parameters from live market volatility surfaces.

A tool for pricing interest rate Swaptions (European and Bermudan) using the **Hull-White 1-Factor** and **SABR** models. This project demonstrates advanced quantitative finance concepts, including yield curve bootstrapping (Dual-Curve), model calibration, and trinomial tree pricing based on "Logic in Source, Notebooks as Views" architecture.

Introduction The Hull-White model is financial modeling in Python. It is an ideal of future interest rates in financial mathematics. It is right to the class of no-arbitrage models. Those are capable of appropriate to the latest term structure of interest rates in its best generic development. The Hull-White model is comparatively direct to translate the mathematical description of the progress of future interest rates onto a tree or frame. Therefore, the interest rate derivatives for example Bermudan swaptions may be valued in the model. The first Hull-White model was labeled by John C. Hull and Alan White in 1990. That is quite widespread in the market nowadays. In this article, we will understand the Hull-White model and also do Simulations with QuantLib Python. Description We can define the Hull-White Short Rate Model as: Hull-White Short Rate Model There is a degree of uncertainty among practitioners about exactly that parameters in the model are time-dependent. Similarly, what name to spread over to the model in each case? The most usually known naming convention is the following: Thetta has t (time) dependence that is the Hull-White model. Thetta And Alpha are both time-dependent — the long Vasicek model. We use QuantLib to display how to simulate the Hull-White model and examine some of the properties. We import the libraries and set things up as described below: import QuantLib as ql import matplotlib.pyplot as plt import numpy as np % matplotlib inline We use the constant for this instance is all well-defined as described below. Variables sigma and are the constants that define the Hull-White model. We discretize the time span of length thirty years into 360 intervals. This is defined by the timestep variable in the simulation. We would use a constant forward rate term structure as an input for ease. It is the right way to swap with another term structure here. sigma = 0.1 a = 0.1 timestep = 360 length = 30 # in years forward_rate = 0.05 day_count = ql.Thirty360() todays_date = ql.Date(15, 1, 2015) ql.Settings.instance().evaluationDate = todays_date spot_curve = ql.FlatForward(todays_date, ql.QuoteHandle(ql.SimpleQuote(forward_rate)), day_count) spot_curve_handle = ql.YieldTermStructureHandle(spot_curve) hw_process = ql.HullWhiteProcess(spot_curve_handle, a, sigma) rng = ql.GaussianRandomSequenceGenerator(ql.UniformRandomSequenceGenerator(timestep, ql.UniformRandomGenerator())) seq = ql.GaussianPathGenerator(hw_process, length, timestep, rng, False) The Hull-White process is built bypassing the term structure, a and sigma. One has to make available a random sequence generator along with other simulation inputs for example timestep and `length to create the path generator. A function to make paths may be written as demonstrated below: def generate_paths(num_paths, timestep): arr = np.zeros((num_paths, timestep+1)) for i in range(num_paths): sample_path = seq.next() path = sample_path.value() time = [path.time(j) for j in range(len(path))] value = [path[j] for j in range(len(path))] arr[i, :] = np.array(value) return np.array(time), arr The simulation of the short rates appearance is as follows: num_paths = 10 time, paths = generate_paths(num_paths, timestep) for i in range(num_paths): plt.plot(time, paths[i, :], lw=0.8, alpha=0.6) plt.title("Hull-White Short Rate Simulation") plt.show() The Hull–White model Monte-Carlo simulation On the other hand, valuing vanilla instruments for example caps and swaptions is valuable mainly for calibration. The actual use of the model is to value rather more exotic derivatives for example Bermudan swaptions on a lattice. Also, other derivatives in a multi-currency context for example Quanto Constant Maturity Swaps. These are explained for instance in Brigo and Mercurio (2001). The well-organized and precise Monte-Carlo simulation of the Hull-White model with time-dependent parameters may be easily performed. For more details visit:https://www.technologiesinindustry4.com/2022/01/the-hull-white-model.html