1. Interest Rate Models

Welcome to the interest rate modeling section! This area explores the mathematical frameworks used to model the term structure of interest rates and price interest rate derivatives.

1.1 Overview

The interest rate models presented here are inspired by the comprehensive works of Damiano Brigo and Fabio Mercurio in their seminal text on interest rate models, as well as Leif Andersen and Vladimir Piterbarg's extensive treatment of interest rate modeling and derivatives pricing. These references provide both the theoretical foundations and practical insights that underpin modern interest rate risk management.

1.2 Topics Covered

• Vasicek Model — The classic mean-reverting Gaussian short rate model: SDE solution, expected value, variance, and distributional properties

• CIR Model — The Cox-Ingersoll-Ross model with square-root diffusion: ensuring non-negative rates, chi-squared distribution, and the Feller condition

• Hull-White Model — Extended Vasicek with time-dependent drift: perfect yield curve calibration and market consistency

• Bond Affine Ansatz Models — Deriving closed-form bond pricing formulas using the affine ansatz approach for Vasicek, CIR, and Hull-White models

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