Short Rate Models: Vasiček and CIR

This lecture covers short rate models in interest rate modeling, starting with the Arbitrage Pricing Theorem and the bond pricing formula. It then delves into the Vasiček model, discussing its dynamics, Gaussian nature, and bond price calculations. The lecture also explores the Cox-Ingersoll-Ross (CIR) model, affine bond prices, closed-form expressions for A(t) and B(t), and the proof of the claim for exponential affine bond prices. Additionally, it addresses fitting the initial term structure, time-inhomogeneous models, and calibrating the shift function. Finally, the Hull-White model is introduced as an extension of the Vasiček model.